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No. 2 (2012)

ESMSJ ISSN: 2247 – 2479 ISSSN – L: 2247 – 2479 Vol II, Issue 2 / 2012

About

Econophysics, Sociophysics & Other Multidisciplinary Sciences Journal (ESMSJ) provides a resource of the most important developments in the rapidly evolving area of Econophysics, Sociophysics & other new multidisciplinary sciences. The journal contains articles from Physics, Econophysics, Sociophysics, Demographysics, Socioeconomics, Quantum Economics, Econooperations Research, or many other transdisciplinary, multidisciplinary and modern sciences and related fundamental methods and concepts.

Econophysics, Sociophysics & Other Multidisciplinary Sciences Journal (ESOMSJ) Staff

University of Pitesti

Address: Str. Targul din Vale, Nr.1, Pitesti 110040, Arges, Phone: 0248218804; Fax: 0248216448 Editors in chief Gheorghe Săvoiu Ion Iorga-Simăn Editorial Board Mladen Čudanov Cătălin Ducu Ivana Mijatovic Jelena Minović Sant Sharan Mishra Viorel Malinovschi Benedict Oprescu Sebastian Pârlac Turturean Ciprian – Ionel Scientific Board Muhittin Acar Marius Enăchescu Vasile Dinu Marius Peculea Laurenţiu Tăchiciu Ioan Ştefănescu Editorial secretary Gheorghe Săvoiu On – line edition http://www.esmsj.upit.ro/Dragos Popescu

Editors 2

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English version and harmonization of the scientific language Constantin Manea Assistant Editors Maria – Daniela Bondoc Daniela Giosanu Camelia Manea Sorin Moga Marian Ţaicu Cristina Zarioiu

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CONTENTS

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Gheorghe SĂVOIU and Ion IORGA SIMĂN Science and Religion in the Contemporary Reality: Dialogue, Convergence and Multidisciplinary Results..........................................................................................................5 Mircea GLIGOR Nonlinear Models for the Fractal Evolution of Cities and Towns..........................................11 Jelena MINOVIĆ and Božo DRAŠKOVIĆ Gross Domestic Product and External Costs: The Case of Sustainable Management in Serbia……………………………………………………………………………………..17

Sant Sharan MISHRA, Prem Prakash MISHRA and S.K.SHARMA Trait Analysis of Investment Packages as Eoq by Using Computational Technique: A Case Study of Insurance Companies……………………………………………………..22

Gheorghe SĂVOIU and Ion IORGA SIMĂN Variables in the Specific Thought of Multidisciplinary Research..........................................29 Gheorghe SĂVOIU Mladen ČUDANOV and Mariana VLADU Profile Method – An Example of Multidisciplinary Applied Method..................................36

SCIENCE AND RELIGION IN THE CONTEMPORARY REALITY: DIALOGUE, CONVERGENCE AND MULTIDISCIPLINARY RESULTS

Gheorghe Săvoiu1 and Ion Iorga Simăn2

1,2University of Piteşti e-mail: 1gsavoiu@yahoo.com and 2ioniorgasiman@yahoo.com

Abstract. This paper is the result of a dialogue converging towards multidisciplinarity, whose starting points are science and religion, scientific and religious inquiry. The first section of the paper analyzes the existence of a deep conflict between modern science and religion in the 21st century, while the second section emphasizes the historical complementarity holding between the two forms of knowledge, the scientific and and the religious one. An interesting example of science-religion complementarity, or a manifestation of interference of religion with economics, ecology and sociology in the newly appeared human ecology, is the content of the fourth section. A final remark describes the coexistence of science and religion in the contemporary world, appealing to an approach at once scientific and religious.

Keywords: science, religion, multidisciplinarity, knowledge, scientific and religious truth, complementarity.

1. INTRODUCTION

There are dialogues hard to unimagine in other time periods

or interrogative interstices of spirituality, very much as there can exist questions and queries generating dialogue, which are related to the development of scientific research, as well as the volution of the apparently divergent relations between certain forms of knowledge of reality.

Two such questions were felicitously stated as: "Does sin reach to the core of the atom? Are black holes and antimatter [in themselves] demonic?"(Dulgheru, 2012).

These questions were launched during the symposium hosted by a physical engineering university in Moscow, before the Russian Patriarch Kiril, and were followed by similar ones, as natural and challenging as the former, describing a rapprochement between science and religion, which has lately become increasingly stringent; placing under the microscope lens the spiritual significance of the material world, including the laws of physics and interconnection between the two worlds, represents the content, sublimated through dialogue, of the present paper. It all started with the religious foundation of scientific ethics, which rediscovers "the beauty of science", which is more and more acutely referred to in various papers, like the scientists inspired by Biblical thinking, and religious thinking in general.

Yet, to reach a relatively stable harmony, and especially a harmony of great historical perspective, a conflicting start was necessary, a debut that was temporarily pointless. The state of general harmony of the gradual emergence of the world was offset by an initial imbalance in knowledge, but the two together will lead to a generalized harmony of knowledge, which will accompany a process of extinction of

the world, in the end, according to the physical mechanism of resurrection of the universe. (Tipler, 2008). 2. RELIGION VS. SCIENCE OR SCIENCE VS. RELIGION

Constantly, science and religion have been virtually seen as

the two great, lasting examples of man’s desire to know the truth; however, there is a significant difference between the manner of investigating scientific truth and religious truth. If the truths provided by science can be demonstrated and explained, with an almost universally accepted relativity, afforded by the development of human knowledge, religious truths are accessible only through revelation or spiritualisation. Over the millennia, the two have been in conflict, mainly due to the different nature of the assumptions of knowledge that they promoted. We can state without the shadow of a doubt that there was a conflict between the truths provided by science and those provided by religion, an obvious conflict, which unfortunately amounted to sacrifices, whose historical impact seemed to lead to a cleavage with no hope for convergence in knowledge, a sine die conflict. A number of early prejudices of scientific knowledge specific to remote, seemingly forgotten ages, based on various religious theories, generated a kind of "intellectual barrier", or else represented limitations, evn significant restrictions on the scientific approach.

Two well-known examples, which were extensively discussed, have constantly been invoked in this respect: the first is the case of Galileo Galilei, whom the leaders of the Catholic Church forced to retract all his ideas concerning the scientific theory regarding the position of planet Earth in the Universe, and the second is the far more dramatic case of Giordano Bruno, who was burned at the stake by the Inquisition because his ideas were deemed incompatible with the doctrine-ruled manner of knowing the outside world, and not the interior world, specific to religion itself.

In essence, however, things are much simpler today. In-depth analysis of the laws of physics shows that they actually obey the laws of the spirit. They are a projection, on the material plane, of the spiritual laws, in other words the order of scientific knowledge is subordinated to a higher spiritual order, just like the shaping presence of the observer’s thinking in quantum physics.

The flimsiness of Inquisition-like approaches does not represent the subject of the present paper, nor does it need even to be demonstrated to highlight the nonexistence of a deep conflict between scientific knowledge and religious belief, though the sacrifices caused by the excesses of religious or scientific pride must not be forgotten.

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Another example of cleavage is provided by a certain element of conflict between science and religion, none other than miracles, which "by definition, violate the principles of science" (Dawkins, 2006). However, miracles do coexist in the researcher’s own tenacity, in the team spirit of modern scientific inquiry, which does not make it less true, while the existence of matter is still considered a miracle by a majority of scientists. Miracles do not jeopardize the survival of science, on the contrary, they demand more and more scientific research to know the simultaneously religious and scientific truth. The first object of knowledge in science was especially human outside world, while in theology it was, and still is, God and the inside of the human world. The feverishness of scientific search seems to be counterpoised by religious prayer and meditation, the scientific investigation outer to human being seems to be paralleled by the introspective approach specific to religious man, etc. The scientific method allows the articulation of an intellectual construction meant to represent and understand the world through intense intellectual involvement, apparently solely based on brain activity, on reason, considered scientific.

Following a scientific, rational path, man tries to understand phenomena that can be observed in nature, and their understanding allows him to gradually build conceptual or material tools, made by entirely copying things or in a creative manner, thus exercising, in his turn, an influence, which is not always beneficial, on nature. To do that, science makes use especially of scientific experiment, of modelling and simulation of reality.

Scientific methodology seems to be unique and invariant in relation to the time factor. Since Galileo’s astronomy works or the outline of Descartes’ method, as well as the multitude of founders of particular sciences in modern times, scientific methodology does not seem to have changed, although nothing excludes the hypothesis of its transformation, perhaps under the influence of religion… But this change can only occur under the pressure of an absolute necessity from experimental facts, rather than by the subjective and irrelevant will of any particular scientist or philosopher. Nevertheless, both the methodological interrogative cycle, however elaborate it may be, and the methodical investigative cycle lack an essential element, without which there could be no scientific discovery, that is revelation, intuition or a specific attitude, defined a priori by a certain faith in a particular aspect of the experiment, a certain objective and a certain impact it will have in improving human life through knowledge.

Is there a real conflict, or major, consistent adversity between scientific knowledge and religious knowledge or belief, or rather an overlapping of the two, aiming at a higher purpose?

Science and religion do not assume the same questions, the same methods, the same human impact areas, they do not dispute their fields of knowledge, and so they have been and

remain essentially distinct experiences of the universe, elements that cannot enter into a state of conflict or adversity (Gould,2002). 3. CONTRARIA SUNT COMPLEMENTA

It can be noted that, today, there is an approach to

integrating scientific knowledge with religious knowledge, based on the principle "contraria sunt complementa", which stands a fair chance of being the future relation between science and religion, an approach that seems difficult to understand completely within the span of a single generation.

The original intention of this paper was to provide a relatively objective statistic survey, or one as close to the truth as possible, of the number of scientists who had major contributions in the history of religion, or declared with admiration their faith in God, and also another survey, at once opposite and complementary to the former, concerning the servants of faith in God whose scientific work represented an epoch-making step in the formation and development of science in general.

Such an idea, which is itself quite generous, was due to statistical thinking, which is hard to conceive without the cotribution of the English minister Thomas Bayes (1702-1761), who became famous posthumously through his memoirs, two of which are sources of scientific knowledge even today, generating Bayesian inference and the analysis of the Stirling or de Moivre series. The minister’s contribution to the probability theory was considered remarkable by George Boole, John Maynard Keynes, Ronald Aylmer Fisher, etc.

Similar in point of impact and retrospective, in the same statistical thinking which shaped the early scientific methodology (which gradually generated statistical physics, alongside of physics), the interpreter or statistical price index, which today helps us to assess inflation, was authored by an Anglican minister, demography and economy cannot be conceived without Rev. Thomas Robert Malthus, and without Adolphe Quetelet and his statistics there would be no social physics. But the examples that start here are really lacking some finiteness for the restricted space of a mere article…

There is also a complementary, and as natural a form of this trend, namely that scientists of past centuries who, due to the fact that they believed in God and carefully read the Bible at an early age, found in its pages, at the moment of the full maturity of their creative development, an inexhaustible resource to generate new areas of scientific interest, new scientific disciplines, new ways of observation and research of outer reality, of the world in general (McGarr, and Rose, 2006)...

A synopsis illustrating the contribution of scientists who, starting from the faith and religious content of the bible,

founded new scientific disciplines Table 1

SCIENTIFIC DISCIPLINES SCIENTISTS Dimensional analysis and model analysis Lord Rayleigh (1842-1919) Comparative anatomy and paleontology of vertebrates Georges Cuvier (1769-1832) Physical astronomy and celestial mechanics Johann Kepler (1571-1630)

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Galactic astronomy William Herschel (1738-1822) Bacteriology Louis Pasteur (1822-1895) Systematic biology Carolus Linnaeus (1707-1778) Infintesimal calculation and dynamics Sir Isaac Newton (1642-1727) Chemistry and gas dynamics Robert Boyle (1627-1691) Isotopic chemistry William Ramsay (1852-1916) Antiseptic surgery Joseph Lister (1827-1912) Electrodynamics and statistical thermodynamics James Clerk Maxwell (1831- 1879) Electromagnetic Michael Faraday (1791-1867) Electronics Ambrose Fleming (1849-1945) Energy studies and thermodynamics Lord Kelvin (1824 -1907) Entomology Henri Fabre (1823-1915) Genetics Gregor Mendel (1822-1884) Non-Euclidian geometry Bernhard Riemann (1826-l8 66) Gynecology James Simpson (1811-1870) Hydraulics Leonardo da Vinci (1452-1519) Hydrography Matthew Maury (1806-1873) Hydrostatics Blaise Pascal (1623- 1662) Ichthyology Louis Agassiz (1807-1873) Fluid mechanics George Slokes (1819-1903) Optical mineralogy David Brewster (1781-1868) Oceanography Matthew Maury (1806-1873) Paleontology John Woodward (1665-1728) Pathology Rudolph Virchow (1821-1902) Stratigraphy Nicholas Sumo (1631-1686) Computer science Charles Babbage (1792-1871) Field theory Michael Faraday (1791-1867) Reversible thermodynamics James Joule (1818 – 1889) Thermokinetics Humphrey Davy (1778-1829)

Source: Morris, H. M. (1993). The biblical basis for modern science. New York: Baker book House, Grand Rapida, pp.56 – 80.

A large number of inventions were created by other scientists who also professed faith in God and found the Bible an inexhaustible source of inspiration for all their famous inventions and discoveries (e.g., throughout the twentieth

century American scientists who confessed their faith in God consistently represented 4/10 out of the total number of scientists).

A synopsis illustrating the contribution of scientists who, starting from the faith and religious content of the bible,

generated new devices and technologies Table 2

INVENTIONS SCIENTISTS Autoinduction, galvanometer and electric motor Joseph Henry (1797-1878) Barometer and absolute temperature scale Blaise Pascal (1623 -1662) Transatlantic cable Lord Kelvin (1824 -1907) Kaleidoscope David Brewster (1781-1868) Global catalogue of stars John Herschel (1792-1871) Chloroform James Simpson (1811-1870) Fermentation control, law of biogenesis, pasteurization, vaccination and

immunization Louis Pasteur (1822-1895)

Inert gases William Ramsay (1852-1916) Electric generator Michael Faraday (1791-1867) Safety miner’s lamp Humphrey Davy (1778-1829) Law of gravity and reflection telescope Sir Isaac Newton (1642-1727) Calculating machines and actuarial tables Charles Babbage (1792-1871) The scientific method Francis Bacon (1561-1626) Classification system Carolus Linnaeus (1707-1778) Double stars William Herschel (1738-1822) Tables of ephemerides Johann Kepler (1571-1630) Telegraph Samuel Morse (1791-1872) Thermionic valve Ambrose Fleming (1849-1945)

Source: Morris, H. M. (1993). The biblical basis for modern science. New York: Baker book House, Grand Rapida, pp. 81 – 98.

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A note relating to the duality and complementarity of the

spirit of the relationship between religion and physics is in order to go back to the present. The analysis of the phenomena of statistical, religious, social, economic, etc. physics (in general, of complex physics) requires consideration of both the corpuscular and the wave aspects. These are obviously contrary, yet they can be said to be also complementary, in that they complement each other in describing quantum phenomena.

This is actually Niels Bohr’s complementarity principle… Another interesting facet of complementarity between science and religion is that of judging the relationships between science and faith through the reductionist lens of the ideologies that are commonly known by the name of creationism and evolutionism. A purely scientific approach to these issues is generally considered foreign to the phenomenological essence of both creationism and evolutionism, and substantially departs from the spirit of patristic tradition.Although, according to some opinions, there are a lot of facts that testify to creation, many other approaches accept evolution. The theories that accept evolutionary theories coexist and share the opinion, or the impression that it is now a scientific fact; on the other hand, creationism is as much an accepted reality. There are so many creationist–evolutionary complementarities.

Today’s scientists realize the limits of reason and the current instrumental means of investigation, knowledge and insight into the secrets of the real world, and felt acutely the need for complementarity with theology and the instruments of transfigured mind. Their existence and appearance does not mean giving up reason, but rather an opening to other states of reason than those usual in positivist culture and science.

The new horizon of knowledge, currently manifested in the scientific community, is moving towards theology and spirituality, which together represent a prompt and efficient step, as well as an aspect of multidimensionality of the approaches, solutions, experiments and interpretations. The new type of theology has initiated a specific identity approach in this century of internet communication, in order to more clearly approach the new sciences as well as the new technologies.

Another interesting complementarity links the Eucharistic studies and approaches and sciences (Magnin, 1993).

The Eucharist is not simply a gesture of worship, according to a devoted servant of faith as a form of knowledge, it grows to be much more than that, i.e. a new way of being human in the light of the Resurrection of Christ. (Nesteruk, 2003). Through this novel cognitive approach, Eucharistic approaches acquire (and lend) competence and divine inspiration. The Eucharist teaches the scientist to receive and give, as a gesture yielding fruits in the coordinates of grace of the scientific knowledge common to human civilization as a whole. Science can be perceived as a method of religious experience: "Scientific activity can be treated as a Eucharist work of cosmic dimensions (a cosmic liturgy). Thus, science can be seen as a way of being of religious experience, a view accessible to those scientists involved in the ecclesial community, but yet unproved to those outside of this type of community " (Ionescu, 2008).

The interference relationship between scientific and religious knowledge, a relationship of the future already present in the contemporary world, was felicitously anticipated by Galileo’s famous statement: "Let us measure what can be measured and make measurable what is still not…".

4. AN EXAMPLE OF COMPLEMENTARY BETWEEN RELIGION AND SCIENCE, OR OF THE INTERFERENCES OF RELIGION WITH ECONOMICS, ECOLOGY AND SOCIOLOGY IN THE NEW HUMAN ECOLOGY

Developed as part of the Chicago school, in the second and third decades of the last century, human ecology is one of the first rigorous systemic sociological approach that took into account the natural environment in explaining social phenomena (promotion of human ecology belongs to Robert E. Park, Roderick McKenzie and Ernest W. Burgess). Univeral recognition of the new direction was fully accomplished after the 202 Summit in Johannesburg, South Africa.

Ecology and solidarity became inseparable elements thereafter, and since ecology can only be a genuine sign of human solidarity which "obviously includes protecting and cultivating the earth’s resources" (according to the Vatican document at the World Summit for Continued Progress, in Johannesburg). The new approach must needs be based on "strong ethical values, otherwise there is a risk of total lack of direction and foundation on which the continued progress under investigation can be built, and sustained", as the essence of development. The concept of continuous / continued progress is linked to sustainable development and life quality, and demands a process that involves meeting the needs of the present without compromising the ability of future generations to meet their own needs. Human ecology is circumscribed to a new perspective of integral and systemic human development.

By and large, the comprehensive concept of human ecology consists primarily in ensuring and protecting ethical conditions in human action on the environment. "It should also be noted that the first and fundamental structure for human ecology is, and will remain the family, in which humans receive their first formative ideas about truth and kindness, and where they learn what loving and being loved mean, and thus what actually being a unique person means"; they shape their matrix or receptacle for the future intellectual energies, a matrix that will be completed in subsequent educational and cultural processes. In this context, particular attention should be paid to the social ecology of human education, of scientific research or of human labour in general. (Săvoiu and Sulescu, 2011). To change the current perspective, according to which the world’s poor are rather a problem than some potentially productive and creative actors in society, it will be crucial to create new opportunities in employment, education, health care or even adequate housing.

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Human ecology is not only about economic development, be it sustainable, or only the quality of life described in terms of ecological processes, but also (and mainly) about social processes, focusing on education, research, life-long cultural training, processes which, through a conceptual transformation, have been biologized in order to explain social reality in terms borrowed from the natural sciences based on a holistic and systemic thinking. New patterns of consumption and production will have to be examined and promoted in accordance with the principles of human dignity and solidarity, from ana angle specific to human ecology (Săvoiu, 2011). Global recession, just as the new crisis that is looming, are the results of the slow pace of change along the logically expected lines of human ecology. Contemporary human ecology redefines human community, humakind itself, within the concept of anthropoecosystem, as a spatial distribution of man’s living environment, and encompasses in its subject matter and area of investigation looking into a human population interacting with the environment, drawing the repertoire of the specific, concrete issues impacting on human life such as the inclemency of the climate, natural reserves and the hydrological regime of water sources, the chemical composition of the water from these sources, the nature of the landscape, vegetation features, the social and economic standards, the customs and traditions, the degree of environmental pollution, the degree of sanitation in people’s housing, providing people with homes, specificity of their activities, food, etc. Human ecology redefines the dignity of the individual in contemporary society, as the very basis of the phenomenon of uniqueness of man as agaisnt the rest of Creation, that of having been made in the image and likeness of God, without however attracting individual selfishness.

"This similarity shows that Man, the only creature on earth that God wanted for Himself, can fully discover himself only in sincere selflessness and abnegation", according to the opinion expressed by the Vatican. One can only agree with the previous sentence, as long as self-denial ultimately ensures the welfare of others and of future generations, or in other words the continuity of progress.

And to reinforce the above ideas, one may recall that the European Community governance is already focused on the principle of subsidiarity, according to which if a state is unable to meet its development needs, the other members of the Community are obliged to come to the rescue, which can be translated as an inference of human ecology in modern human communities.

The top priority of today’s humanity remains therefore doing everything in their power to activate and initiate the advanced consciousness, imminent and quick to manifest in people’s lives on a global scale, in order that the flourishing may be facilitated and accelerated of a civilization that embodies the holos or the global wisdom of mankind, so that generations living nowadays can reveal a world in which the entire human family can live in harmony with nature on this priceless planet, under the divine grace and having faith in "the very God of peace [who] will sanctify you wholly, and I pray God your whole spirit and sould and body be preserved blameless unto the coming of our Lord Jesus Christ." (Epistola întâia a Sfântului Apostol Pavel către Tesalonicieni, cap 5. 23).

5. A FINAL REMARK

As an expression of maximum complementarity of the theories concerning the reality of the surrounding world, physics, in its specific disciplines (from statistical physics to superstring theory, from quantum mechanics to nuclear physics, etc.), combines matter and energy through the particle-wave duality, and places within the compass of uncertainty the exclusive alternatives of spirit and matter. If econophysics and sociophysics represent modelling extensions of physics with respect to the economic and social phenomenon, human ecology is, as exemplified in the previous section, the first multidisciplinary intersection of religion and science.

There are two features that can suggest the complete outline of the relationship between science and religion: the antinomy and complementarity of the correlative approach. The main modality of knowing the truth in the near or more distant future will be of the antinomic type, simultaneously focusing on an approach of negation and an approach of affirmation (Nicolescu and Stavinschi, 2002) yet equally and ultimately focused on the complementarity of overcoming the contradictions and questions pending between today’s science and religion worldwide.

The hierarchy and association of science and religion are defined in the most rigorous manner by Petre Ţuţea: "Science moves asymptotically to the absolute. Science is the seat of usefulness. Religion is the seat of transcendent and essentially unique truth, as the sole principle of all things. "

6. REFERENCES

[1] Dawkins, R. (2006). The God Delusion. New York: Houghton Mifflin Harcourt, p. 83.

[2] Dulgheru, E. (2012). Hexaimeronul, iubirea lui Dumnezeu şi fizica modernă, Lumina de duminică, Săptămânal de spiritualitate şi atitudine creştină, 27 Iunie 2010, http://www. ziarullumina.ro/articole;1292;0;40942;0;Hexaimeronul-iubir ea-lui-Dumnezeu-si-fizica-moderna.html [Accessed on July 12th, 2012]

[3] Gould, S. J. (2002). Rocks of Ages: Science and Religion in the Fullness of Life. New York: Ballantine Books, pp. 23-31.

[4] Ionescu, R., (2008). Despre trăirea euharistică ca şansă de normalizare a raporturilor dintre ştiinţă şi teologie în contemporaneitate, Teologie şi stiinţă, 28 Aprilie 2008, http://www.apostolia.eu/articol_8/despre-trairea-euharistica-ca-şansa-de-normalizare-a-raporturilor-dintre-ştiinţa-şi-teologie-in-contemporaneitate.html?action=print [Accessed on July 15th, 2012].

[5] Magnin, T. (1993). Quel Dieu pour un monde scientifique, Ed. Nouvelle Cité, Paris, p. 12.

[6] McGarr, P. and Rose, S. (2006). The Richness of Life: the Essential Stephen Jay Gould, London: Jonathan Cape.

[7] Morris, H. M. (1993). The biblical basis for modern science. New York: Baker book House, Grand Rapida.

[8] Nesteruk, A. (2003). Light from the East. Theology,Science and the Eastern Orthodox Tradition, Minneapolis: Fortress Press, p.2.

[9] Nicolescu, B. Stavinschi, M. (2002). Ştiinţă şi religie, antagonism sau complementaritate. Editura XXI: Eonul Dogmatic, Bucureşti.

[10] Săvoiu, G., Sulescu, D., (2011). Noua economie şi impactul

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tendinţelor internaţionale în demografie şi religie. Proceedengs International Conference „The Role of Euroregions in Sustainable Development in the Context of World Crisis: Siret-Prut-Nistru Euroregion”, Iaşi, Ed. Tehnopres, Iaşi, vol VIII, pp. 11-20

[11] Săvoiu, G.(2011).Riscuri şi incertitudini în teoria economică sau despre necesitatea unei noi teorii economice

multidisciplinare. Progrese in teoria deciziilor economice in condiţii de risc şi incertitudine -Ed. Tehnopress, Iaşi Vol VI, pag.109-134.

[12] Tipler, F. J. (2008). Fizica nemuririi. Dumnezeu, cosmologia modernă şi învierea morţilor, Editura Tehnică, Bucureşti, p.5

[13] *** Biblia, Epistola întâia a Sfântului Apostol Pavel către Tesalonicieni, cap 5. 23.

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NONLINEAR MODELS FOR THE FRACTAL EVOLUTION OF CITIES AND TOWNS

Mircea Gligor

National College “Roman Voda”, Roman, Neamt

e-mail: mrgligor@yahoo.com

Abstract: Some of the main ideas of the fractal city theory are briefly reviewed, and their applicability is tested for the medium and small-size Romanian urban settlements. Particularly, the diffusion-limited aggregation with dendritic-like growth (modelling The Central Place Theory of Christaller and Beckman) was proved to be in disagreement with the urban area development. Instead, the diffusion-limited aggregation with correlated percolation and self-organized criticality mechanisms are found to fit well the urban perimeter growth. Finally, the streets of a small Romanian town (Roman) were found to display the statistical structure of a scale-free network. The last model allows us to simulate complex phenomena like epidemic/rumour propagation and to find the most efficient lines of the urban development.

Keywords: nonlinear model, cities and towns evolution, fractals, urban development,

1. HISTORICAL FRAMEWORK

More than seven decades ago, Englewood Cliffs from New

Jersey published a pioneering book by Christaller (1933), where several key questions were for the first time posed: “What type of dynamics describe the growing of the urban locations?” and, further: “Are there laws which determine the number, size and distribution of towns?” The Christaller’s theory – the so-called central places theory, later developed by Beckmann (1968), describes the urban morphology in the terms of the Euclidean geometry. The main idea is that the urban development is structured around a central business district.

The applicability of the central places theory is drastically limited by the exclusive using of Euclidean varieties as lines and surfaces. The modelling of the urban perimeter in Euclidean terms leads to results in strong discrepancy with the empirical evidence, especially for the large towns and cities.In the second half of the XX century, B. Mandelbrot (1975) opened the door for a more realistic description of the natural and social phenomena by introducing the mathematical varieties with fractional dimensions, usually called fractals. In the fractal theories, the dimension has a higher degree of generality than in Euclidean it has.

Cities are large physical objects animated and driven by human behaviour. By far the most interesting and difficult questions about them are about how the two connect: exactly how is the physical city linked to the human city? The consequent question is: what are the consequences of the physical form of the city for its human form, that is the

patterns and dynamics of the economic, social, cultural and cognitive life that goes on in the city.

Living cities have intrinsically fractal properties, in common with all living systems. The pressure to accommodate both the automobile and increased population growth led twentieth-century urbanists to impose anti-fractal geometrical typologies. The fractal properties of the traditional city were erased, with disastrous consequences for the urban functionality.

As it was already shown in literature (Salingaros, 2001), older, pre-modernist cities are fractal, because they work on all scales. Mediaeval cities are the most fractal on the smaller scales up to 1 km, whereas 19th century cities work better on larger scales. Urban typologies used throughout history up until the twentieth century lead automatically to a fractal structure. But, the urban morphology is a product of the particular transportation system laid down by the government when the city was initially built. Later modifications to the transportation system lead to changes in city structure.

A city's life comes from its connectivity (Salingaros, 1998). In the present paper we discuss the connective properties of several undirected graphs to gain some insight into how city life arises. The simplest and most studied network with undirected edges was introduced by Erdös and Rényi (ER model) (Erdös & Rényi, 1959). In this network:

(i) the total number of vertices, N, is fixed; (ii) the probability that two arbitrary vertices are connected

equals p. One sees that, on average, the network contains pN(N −

1)/2 edges. The degree distribution is binomial:

k1Nk1Nk p)(1pCP(k) −−− −= (1)

so the average degree is:

1)p(Nk −= For large N, the distribution described in Eq. (1) takes the

Poisson form:

k!k)kexp(P(k)

k−=

Therefore, the distribution rapidly decreases at large

degrees. Such distributions are characteristic for classical random networks (Dorogovtsev & Mendes, 2002).

As we shall see in the next section, the growing networks often self-organize into scale-free structures. A little change of parameters controlling their growth removes them from the

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class of scale-free structures. This is typical for the general self-organized criticality phenomena. Reasons for power-law distributions occurring in various systems, including urban systems, were a matter of interest of numerous empirical and theoretical studies. The models of networks growing with preferential linking can be reduced to the sandpile problem: at each increment of time, m new particles are distributed between the increasing number (by one per time step) of boxes according to some rule. Here, the boxes play the role of vertices. The particles are associated with edges. The probability that a new particle gets to a particular box depends on the filling of this box and on the filling numbers of all other boxes.

In Subsection 2.1 we simulate the urban growth by various models. We find that the sandpile model and Diffusion-Limited Aggregation (DLA model) with correlated percolation may fit the urban area of a small town. The problem of urban streets network is analysed in Subsection 2.2. Following some statistical data, we find that for a small town, the scale free network (simulated by Barabasi-Albert model of preferential attachment) fits better the data than the exponential (random) network.

The growth of a human settlement is essentially a self-organized process. A connection between self-organized criticality and urban growth may be performed by formulating an old sociological model (the Simon model) for networks in terms of vertices and edges (Bernhold & Ebel, 2001). This approach is based on two steps:

(i) At each increment of time, a new edge is added to the network.

(ii) a) Also, with probability p a new vertex is added, and the target end of the new edge is attached to the vertex.

b) With the complementary probability 1 − p, the target end of the new edge is attached to the target end of a randomly chosen old edge.

In fact, both the original Simon model and the preferential linking concept are based on a quite general principle: popularity is attractive. Popular objects attract more new fans than the unpopular ones.

2. RESULTS 2.1 Numerical simulations of the growth process

The simulation follows the slightly modified cellular-

automata model (Bak et al. 1987, Pica Ciamarra and Coniglio, 2006): the model is defined on a lattice, which we take for simplicity to be the two dimensional square lattice. There is a positive integer variable at each site of the lattice, called the height of the sand pile at that site. The system evolves in discrete time. In the first version (Fig. 1), all the grains are initially contented into the central site; then, the grains are added to the neighbouring sites with a power-law decay probability. In the second version (Fig. 2), one starts from a uniform distribution of heights. At each time step a site is picked randomly, and its height zi is increased by unity. If the site height is larger than a critical value zc, the site relaxes by toppling whereby zc grains leave the site, and each of the four neighbouring sites gets zc/4 grains. In case of toppling at a site

at the boundary of the lattice, grains falling “outside” the lattice are not removed from the system, but they are added randomly to the highest ones. This process continues until all sites are stable.

As shown, in the DLA model, only a large central place or large cluster is generated (Fig. 1). The classical DLA model begins with an initial green "seed" in the center of the world. The particles move around the world randomly. When a particle hits a green square, it "sticks" and turns green (and a new particle is created to keep the process going). However, a real urban area is rather composed of central places that are spatially distributed following a certain hierarchy, thus the sand pile model (Fig. 4) offer a more realistic description of the urban perimeter (Fig. 3).

Such a structure may be also simulated by DLA with correlated percolation (Makse et al., 1995, 1998). Like the main DLA model, this model demonstrates diffusion-limited aggregation, in which particles moving (diffusing) in random trajectories stick together (aggregate) to form beautiful treelike branching fractal structures. There are many patterns found in nature that resemble the patterns produced by this model: crystals, coral, fungi, lightning, and so on (Witten Jr. and Sander, 1983)

Figure 1 A numerical simulation of a growth process in a dendritic-like structure, from the DLA model. The growth begins in the centre and extends to the periphery

(a)

12

(b)

Figure 2 The result of the numerical simulation of a growth process in the sand pile model after (a) n = 102; (b) n = 103 simulation time steps.

Figure 3 Structure of Roman in 2012. The residential and economic unit coordinates are obtained by dividing the map in 250 × 250 screen squares (See Ref. Roman – Interactive map). The surrounded zones are the ones at which the centrality indices (see Appendix) have the largest values.

Figure 4 The urban growth model simulated by DLA model with correlated percolation. The image is provided by a simulation using Netlogo applet (Wilensky, 2006) with the

parameters: wiggle-angle: 60°; number of particles: 2500; ticks: 1221.

2.2 The streets of the town.Exponential or scale-free network?

The network metaphor in the analysis of urban and

territorial cases has a long tradition especially in transportation /land-use planning and economic geography. All the previous approaches – though under different terms like “accessibility”, “proximity”, “integration”, “cost”, “connectivity”, or “effort” – focus on the idea that some places (or streets) are more important than others because they are more central (Latora and Marchiori, 2004). The study of centrality in complex systems, however, originated in other scientific areas, namely in structural sociology, well before its use in urban studies; moreover, as a structural property of the system, centrality has never been extensively investigated metrically in geographic networks as it has been topologically in a wide range of other relational networks like social, biological or technological (Crucitti et al., 2006).

Let us discuss the simplest random network in which the number of vertices grows (Barabasi and Albert, 1999; Barabasi, Albert and Jeong, 1999). At each increment of time, let a new vertex be added to the network. It connects to a randomly chosen (i.e., without any preference) old vertex. Let connections be undirected, although it is inessential here. The growth begins from the configuration consisting of two connected vertices at time t = 1, so, at time t, the network consists of t +1 vertices and t edges. The total degree equals 2t. One can check that the average shortest-path length in this network is lnt∝l like in classical random graphs.

It is easy to obtain the degree distribution for such a network. We may label vertices by their birth times, s =

0; 1; 2; ... ; t. Let us introduce the probability, p(k; s; t), that a vertex s has degree k at time t. The master equation

describing the evolution of the degree distribution of individual vertices is:

t)s,p(k,1t

11t)s,1,p(k1t

11)ts,p(k, ⎟⎠⎞

⎜⎝⎛

+−+−

+=+

with 1,)1,0,( ktskp δ=== , k,1δ1)tt,sδ(k, =≥= . This accounts for two possibilities for a vertex s:

(i) With probability 1/(t +1), it may get an extra edge from the new vertex and increase its own degree by 1.

(ii) With the complimentary probability 1 − 1/(t + 1), the vertex s may remain in the former state with the former degree. Notice that the second condition above makes the master equation non-trivial.

The total degree distribution of the entire network is:

∑=+

=t

0st)s,p(k,

1t1t)P(k,

Using this definition and applying ∑ to both sides of

above master equation, we get the master equation for the total degree distribution:

=

t

0s

13

k,1δt)P(k,t)1,P(kt)tP(k,1)t1)P(k,(t +−−=−++

The corresponding stationary equation (i.e. at t → ∞) takes the form: k,1δ1)P(k2P(k) =−−

It has the solution of an exponential form:

kkP −∝ 2)(

Figure 5 The distribution of degrees for N = 71 vertices in Roman (histogram). The continuous line fits to power distribution (scale-free network) while the dashed line fits to the exponential (random growing network). The Pearson coefficients RSQ are given in inset (See Ref. Roman – Interactive map).

At least several important large growing networks in nature

are scale-free, i.e., their degree distributions are of a power-law form. The natural question is how they self-organize into scale-free structures while growing. What is the mechanism responsible for such self-organization? For explanation of these phenomena, the idea of preferential linking (preferential attachment of edges to vertices) has been proposed (Barabasi and Albert, 1999; Barabasi, Albert and Jeong, 1999).

We have demonstrated above that if new connections in a growing network appear between vertices chosen without any preference, e.g., between new vertices and randomly chosen old ones, the degree distribution is exponential. Nevertheless, in real networks, linking is very often preferential.

We describe here the simplest situation: The probability that the edge is attached to an old vertex is proportional to the degree of this old vertex, i.e., to the total number of its connections. At time t, the total number of edges is t, and the total degree equals 2t. Hence, this probability equals k/(2t). One should emphasize that this is only a particular form of a preference function.

For the BA model, the master equation takes the following form:

t)s,p(k,2tk1t)s,1,p(k

2t1k1)ts,p(k, ⎟

⎠⎞

⎜⎝⎛ −+−

−=+

with the initial condition k,1δ1)t0,sp(k, === and the

boundary condition . k,1δt)t,p(k, =

The master equation for total degree distribution:

[ ] k,1δt)kP(k,t)1,1)P(k(k21t)tP(k,1)t1)P(k,(t +−−−=−++

and, in the limit t → ∞, the equation for the stationary

distribution:

[ ] 1,)1()1()(21)( kkPkkkPkP δ=−−−+

In the continuum k limit, this equation is of the form:

[ ] 0)(21)( =+

dkkkPdkP

The solution of the last equation is . 3kP(k) −∝ Thus, the preferential linking provides a scale-free network

and the exponent of degree distribution is −3. An empirical study was performed on N = 71 nodes in

Roman. The results are shown in Fig. 7. One can easily see that the urban streets structure is fitted better by the scale-free network than the exponential network. In Fig. 8 the urban streets structure is simulated by preferential attachment mechanism.

14

Figure 6 The urban streets structure simulated by preferential attachment mechanism. The image is provided by a simulation using Netlogo applet with the parameters: number of nodes: 142; ticks: 146.

3. CONCLUSIONS

In the present paper some basic ideas of the fractal city theory have been briefly reviewed. The universality of intrinsic fractality has been proved once again using particular statistical data.

Particularly the question of urban perimeter growth was pointed out. While an increasing amount of literature is devoted to the large cities structure and distribution, a relatively low interest has been so far given in the study of medium and small-size urban locations, especially those situated in the developing countries. Generally here are not mega-polis-like cities and the most urban centres are formed by merging some small units (villages). We found that self-organized criticality (the sand pile model) fits the urban perimeter better than the classical Central Place Theory. Nonetheless, the best fit of urban area has been performed by means of the Diffusion-Limited Aggregation with Correlated Percolation (DLACP) model.

Finally, the urban streets network was modelled starting from two models: the growing exponential network and the scale-free network. The last was simulated by means of Albert-Barabasi mechanism of preferential linking and it seems to fit better the empirical data than the first model, at least for small towns.

The study of urban perimeter growth and urban streets network may be useful in order to identify the most „central” points of the towns as well as to predict the further development of the towns in terms of cost and efficiency. Knowing the structure of the network we can analyse, also, complex phenomena such as the epidemic contamination spreading, and the fashion/fear/rumour propagation.

APPENDIX: Various centrality indices Let us consider now N = the number of nodes/vertices in

the streets network of the town. We consider a link as a street starting from an intersection situated next to the vertex.

a) Degree and closeness centrality Degree centrality is based on the idea that important nodes

have the largest number of ties to other nodes in the graph. The degree of a node is, as previously mentioned, the number of edges incident with the node, i.e. the number of first neighbours of the node. Defining the degree of node i as:

∑∈

=Nj

iji ak

the degree centrality (CD) of the node i can be defined as

(Nieminen, 1974):

1N

a

1Nk

C Njij

iDi −

=−

=∑∈

The normalization adopted is such that CD takes on values

between 0 and 1, and is equal to one in the case in which a node is connected to all the other nodes of the graph.

The simplest notion of closeness is based on the concept of minimum distance or geodesic dij, that is, the smallest sum of the edges lengths throughout all the possible paths in the graph from i to j in a weighted graph, and reduces to the minimum number of edges traversed, in a topologic graph.

The closeness centrality of point i (Freeman, 1979) is:

∑≠∈

− −==

ijNj

ij

1i

Ci d

1NLC

where Li is the average distance from actor i to all the other actors. CC is to be used when measures based upon independence are desired. Such an index is particularly meaningful for connected graphs.

b) Betweenness centrality Interactions between two non-adjacent points might depend

on the other vertices, especially on those on the paths between the two. Therefore points in the middle can have a strategic control and influence on the others. The important idea at the base of this centrality index is that a vertex is central if it lies between many of the other vertices. This concept can be simply quantified by assuming that the communication travels just along geodesics. Namely, if njk is the number of geodesics linking the two vertices j and k, and njk (i) is the number of geodesics linking the two vertices j and k that contain point i, the betweenness centrality of actor i can be defined as (Freeman, 1979):

15

∑≠

≠∈

=−−

=

ikj,kj

Nkj, jk

jkBi n

(i)n2)1)(N(N

1C

The betweenness centrality of the node i takes on values between 0 and 1, and it reaches its maximum when node i falls on all geodesics.

c) Efficiency and Straightness centrality Efficiency and straightness centralities originate from the

idea that the efficiency in the communication between two nodes i and j is equal to the inverse of the shortest path length dij (Latora and Marchiori, 2001). In particular, the efficiency centrality of node i is defined as:

∑

∑

≠∈

≠∈

=

ijNj

Euclij

ijNj ij

Ei

d1

d1

C

where is the Euclidean distance between nodes i and j along a straight line.

Euclijd

The straightness centrality is a variant of the efficiency centrality that originates from a different normalization (Vragović et al. 2005). The straightness centrality of node i is defined as:

1N

dd

C ijNj ij

Euclij

Si −=

∑≠∈

This measure captures to which extent the connecting route

between nodes i and j deviates from the virtual straight route. d) The overlapping index Another measure of the two countries connection strength

is the overlapping coefficient (Gligor and Ausloos, 2008) defined for an unweighted network as:

2)1)(N2(N)k(kK

O jiijij −−

+= , i ≠ j,

where N is the number of vertices, ki and kj are the degrees of the two considered nodes, and Kij is the number of common neighbours. For an unweighted network, Oij does not account the edge directly linking i and j but rather to what extent the two nodes “overlap” by means of their common neighbours.

4. REFERENCES

[1] Bak, P., Tang, C. and Wiesenfeld, K. (1987). Self-organized

criticality: An explanation of 1/f noise. Physical Review Letters, 59, 381-384.

[2] Barabasi, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. Science, 286, 509; Preprint: http://arxiv.org/abs/cond-mat/9910332 Last accessed: 14.10.2012.

[3] Barabasi, A.-L., Albert, R. and Jeong, H. (1999) Mean-field theory for scale-free random networks. Physica A, 272, 173; Preprint: http://arxiv.org/abs/ cond -mat/9907068 Last accessed: 14.10.2012.

[4] Beckmann, M. J. (1968). Location Theory. New York: Random House.

[5] Bernhold S. and Ebel H. (2001). World Wide Web scaling exponent from Simon’s 1955 model. Physical Review E, 64, 3 035104(R).

[6] Christaller, W. (1933).Central Places in Southern Germany. New Jersey, Prentice-Hall: Englewood Cliffs.

[7] Crucitti, P., Latora, V. and Porta, S. (2006). Centrality measures in urban networks, Physical Review E, 73, 3, 036125. Preprint: http://arxiv.org/abs/physics/0504163 . Last accessed: 14.10.2012

[8] Dorogovtsev S.N. and Mendes J.F.F. (2002). Evolution of networks. Advances in Physics 51, 1079.

[9] Erdös, P. and Rényi, A., (1959). On random graphs Publications Mathematicae, 6, 290.

[10] Freeman, L. C. (1979). Centrality in social networks: conceptual clarification. Social Networks, 1, 215-239.

[11] Gligor, M. and Ausloos, M. (2008). Clusters in weighted macroeconomic networks: the EU case. European Physical Journal B, 63,533-539.

[12] Latora, V. and Marchiori, M. (2001). Efficient behaviour of small-world networks. Physical Review Letters, 87,198701.

[13] Latora, V. and Marchiori, M. (2004). A measure of centrality based on network efficiency”, Preprint: http://arxiv.org/abs /cond-mat/0402050 Last accessed: 14.10.2012.

[14] Makse, H. A., Havlin, S. and Stanley, H. E. (1995). Modelling urban growth patterns. Nature, 377, 608-612.

[15] Makse, H. A., Havlin, S. and Stanley, H. E. (1998). Modelling urban growth patterns with correlated percolation. Physical Review E, 58, 7054-7062.

[16] Mandelbrot, B. (1975). Les objets fractals: forme, hasard et dimension. Paris: Flammarion.

[17] Nieminen, J. (1974). On centrality in a graph. Scandinavian Journal of Psychology, 15, 322-336.

[18] Pica Ciamarra, M., and Coniglio, A. (2006). Random walk, cluster growth, and the morphology of urban conglomerations. Physica A, 363, 551–557.

[19] Salingaros, N.A. (1998). Theory of the Urban Web, Journal of Urban Design 3, 53-71.

[20] Salingaros, N.A. (2001). Fractals in the New Architecture, Archimagazine. Ed. online: http://www. archimagazine.com/ afrattae.htm. Last accesed: 14.10.2012.

[21] Roman-Interactive map https://maps.google.ro/maps .Last accesed: 14.10.2012.

[22] Vragović, I., Louis, E. and Dìaz-Guilera, A. (2005) Efficiency of informational transfer in regular and complex networks. Physical Review E, 71, 036122. Preprint: http:/ /arxiv.org/abs/cond-mat/0410174 Last accessed: 14.10.2012.

[23] Wilensky, U. (2006).NetLogo DLA Simple model http://ccl. northwestern.edu/netlogo/models/DLASimple. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. Last accessed: 14.10.2012

[24] Witten Jr., T.A., & Sander, L. M. (1983). Diffusion-limited aggregation. Physical Review B, 27, 5686-5697

16

GROSS DOMESTIC PRODUCT AND EXTERNAL COSTS: THE CASE OF SUSTAINABLE MANAGEMENT IN SERBIA

Jelena, Z. Minović1, BožoM. Drašković2

1,2Institute of Economic Sciences, Belgrade, Serbia

1e-mail: jelena.minovic@ien.bg.ac.rs and 2bozo.draskovic@ien.bg.ac.rs Abstract. This paper defines a complicated calculation

model of sustainable development. Social welfare can be expressed quantitatively by GDP growth. The empirical data on changes in Serbian GDP growth in the period: 2002-2011, served as a base values on which the assumed correction of external costs was applied. For our analysis we used numerical simulation approach. Our results show that variable GDP has the sixth-degree polynomial form with the empirical Serbian data in observed period. Consequently, the results show the viability of the economic and ecological development in the framework of our assumptions. We defined the external costs or social costs of externalities as "the costs of nature", and they are structured so that they make the sum of losses of the environment due to exploitation of non renewable resources, pollution and the necessary investments for the elimination of pollution costs. Additionally, the paper presents utility function that includes both market and non-market assets, or consumption of these assets by an individual.

Keywords: GDP, external costs, sustainable development, utility function, numerical simulation.

1. INTRODUCTION The external costs and their inclusion, as a correction

factor, to the calculation of the commercial effects of the companies, at micro level, respectively the negative impact of unsustainable use of natural environmental the macro level, still represents the research challenge. However, the marginalization of external costs leads to maximizing the benefits and profits for market factors whose target function is to maximize profits. The problem of calculating the external costs, especially their negative impact on the relations between economy and ecology requires further research and analyses. Specifically, in economic science and its relationship with the border areas of other sciences, ecology, in this case, the problems of negative external effects that arise due to human economic activities have been scrutinized for a long time. Most often, the problem of negative externalities is related to the question of free pollution of the environment and so-called social or general expense. We will try to analyze the problem of external costs calculation that arises during the economic activities. They are most often defined as external social costs, presenting the negative consequences in terms of pollution or environmental degradation. These costs are most often, not born by market representatives, who tend to maximize profit by economic

activity, so the costs themselves become the “cost of nature” which synonymous is “external social costs”.

In this paper, we expand the content of the concept of negative externalities and include two more, in our opinion, important segments. The first makes free or insufficient nature paid use of renewable and nonrenewable natural values and natural capital. The second segment makes the costs that must be paid for the elimination of consequences of natural environment pollution in order to return, if possible, the status quo ante. These segments are defined as a concept “costs of nature”. The measure of social and economic development is generally expressed through gross domestic product (GDP). In the past decades, the methodologies for calculation of GDP growth or decrease were also developed. The defect of applied methodologies for GDP calculation is that they do not include the “cost of nature”. Respectively, the costs are partly erroneously encompassed in the calculation, but as a factor of GDP growth, instead of as a correction factor that decreases the statistically calculated GDP growth. This approach opens the possibility for the development of measurement methodology for sustainable growth.

It should be noted that the exploitation of natural resources is unilateral process in which the natural capital, through human activities and implementation of technology, is transformed into created capital-processed nature, and further into its cash forms and financial capital. This capital is spent in short or long time horizon, even in cases when some of its parts are not used at all. Generally it is one-way process. There are some exceptions when the reverse flow is possible which means that the cash equity, along with the use of created capital- technology, is engaged as capital investment for continuation or self-continuation support to some of environmental segments. Speaking about positive external flow, we only speak about the cases when the nature itself has ability to regenerate and establish the status quo ante.

The paper is structured as follows: Section 2 presents literature review; Section 3 introduces the concept of utility and utility function, in Section 4 a model of sustainable development on the case of Serbia is presented and numerical simulation for solving this model is applied, and Section 5 is Conclusion.

2. LITERATURE REVIEW Tobin (1981) defines the structure of material wealth of a

society as follows: “Material wealth of a country consists of

17

its natural resources, inventory of goods and net claim from the rest of the world”. Accordingly, the material wealth of a country presents the cumulative structure of: natural resources, generated goods made by labor and capital, and net surplus or deficit resulting from international trade.

According to the presented approach, the material wealth of a country represents the cumulative structure: natural resources, labor and capital goods, and generated a net surplus or deficit resulting from international trade.

Ponting (1993) described case of exploitation of natural resources – phosphates from islands Ocean and Naurua in Polynesia during the first half of the twentieth century. The empirical case of exploitation of natural capital from the above islands is de facto complete and simple model that accurately shows then on-inclusion problem of negative externalities in the calculation of economic efficiency.

Hotelling (1931) described the economics of exhaustible resources. He examined the small tax effect on social value of the resource. The author showed that even a small tax on a monopoly resource significantly reduces social utility. The Hotelling’s Rule is connected with using nonrenewable natural resources such as mineral resources, land and other natural resources that do not possess the ability to regenerate. Hotelling’s Rule, which still occupies a central place in the economy of natural resources, demands (so that the exploitation or extraction of nonrenewable resources in the course of time be optimal), net cost of resources to grow in the future at the same or a minimum rate at which the interest rate increases (Hotelling, 1931). The net price represents the difference between sales and market price and costs of resource exploitation. 3. UTILITY FUNCTION

The concept of utility or usefulness is complex. There are

two aspects of understanding. Due to the difficulty of its synthesis, the concept is not operational enough for analytical expression of natural values and benefits that arise from them. The economic approach is based on the anthropocentric factor – the consumption of goods and services by an individual represent happiness and benefit for some individual. Goods are divided into: market goods (consumer goods such as food, beverages, another products and services) and non-market goods (such as clean air, charity work, and enjoying nature).

The utility function includes commercial and non-market goods or consumption of goods by individuals. All goods that are used for consumption represent the market basket of the individual. The value of market goods consumption can be directly monetary expressed through product of quantities and prices, while on-market goods are directly evaluated and often cannot be expressed monetary. Social utility or welfare could rise even when one social group has the growth of consumption of goods or profit at the expense of other social groups that experience the declining consumption of market goods and the deterioration of the environment (Robinson, 1964). The taxes could be viewed from two aspects. The standard tax concept defines percentage burden (increase) of market goods which affects the growth of their prices and

reduced demand for them, reduce consumption, leading to a reduction of individual utility. The taxes do not affect the utility of non-market goods. No standard approach is related to the consumption of natural resources, resources or environmental pollution. These are fees, they are not a standard tax, but they have a similar function as the standard tax. Thus, they increase the cost of goods, reducing demand for them, and lead to less consumption.

The function of individual utility can be expressed in the following term (Drašković, 2010):

( )s s ss

U C Z c= − s∑

(1)

where: Us,- function of individual utility Cs– total consumption Zs – average consumer basket of market and non-

market goods in time t cs – consumption, expenditure as “production” of

polluted air, contaminated water and land s – individual or economic agent.

Total consumption Cs makes the difference between the total sum of individual consumption of market and non- market goods. The consumer basket of market and non-market goods Z, presents a pleasure (welfare, utility) for individual (so called positive externalities). Then, shown benefit is decreased for social cost of negative externalities, cs representing the natural environment pollution, that arise from a negative function of the consumption process of goods by individuals (Drašković, 2010).

In the theory of social choice preferences themselves, are of crucial importance. Urošević (2008) states that it is important when the preferences can be described as an ordinal utility function. The ordinal utility function U reflects the aggregate of all consumer baskets Z on the aggregate of all real numbers R, so that (Urošević, 2008):

U(x) > U(y) ⇔ x > y

U(x) = U(y) ⇔ x = y (2) It is assumed that on the market there are N consumer

goods. The vector x =(x1, xN) ∈RNdefines arbitral consumer basket of consumer goods. Z is arranged aggregate of all consumer baskets which can be formed from existing N consumer goods. The index means that an economic agent “prefers strongly x in relation to y” where as the index x = y means that a consumer is indifferent in choosing between the two consumer baskets (Urošević, 2008)

x yf

The function of utility U reflects the preference relation on the aggregate Z on the standards arrangement of real numbers aggregate, where the consumer basket, which corresponds to higher level of utility is preferred in relation to the basket which utility level is lower (Urošević, 2008). 4. THE NUMERICAL SIMULATION OF THE SUSTAINABLE MANAGEMENT

There is a large number of sustainable development

definitions which can be reduced to one of the most common,

18

from the standpoint of essential meaning, quite acceptable, and it is a formulation that is exposed in the Bruntland Commission Report (WCED, 1987), in which sustainable development is defined as: "Development that meets present needs, without the danger of the future generations not to be able to meet their needs."This means that there are two general aspects. The first is that the current generations do not exhaust the natural resources by using them up during this time, hence not leaving natural resources for the future generations. Another aspect is that the present generations must take care not to contaminate the environment, hence leaving the future generations with the environment of less quality or its usefulness of quality, that which the current generations enjoy.

The standard methodology for calculating the gross domestic product (GDP), on the level of individual countries, reflects the state of economy of a country. The calculation results in aggregate sizes, which are expressed for each of the individual years. Economic science has not found a better method. Lack of existing methodologies, calculations and showing the movement of GDP from an environmental standpoint, is that it does not include, in a proper way neither the benefit nor gifts of nature, i.e. natural capital. Furthermore, the calculation also does not include the nature cost that is expressed as pollution and, partially as environment damage. Namely, when it comes to cost and expenses for eliminating the consequences from environmental accidents, these costs are calculated so that they are expressed as the incentives for GDP growth. The problem of GDP calculation, which does not include the costs appropriately and nature as a source of wealth and as a space for waste by-products of economic activity, duly indicates the paradox included in the application of sustainable development.

We constituted a sustainable development model using Serbia as an example, which we are presenting here under. In constituting the model historic data on the movement of the size of GDP in Serbia for the period from 2002 to 2011 was used. Values are expressed in Euro, at the current exchange rate. Following assumptions were introduced:

nominal value of the reported GDP is not realistic, because it does not include the costs of nature and the cost that is necessary to remedy the damage that is imposed to the environment and which represent negative externality, the growth of nominal GDP is projected at a rate of 3.5%, the calculation should be based on the assumption that the

cost of nature and cost of removing the damage caused by economic activities should to be add, and their sum results as a subtrahend of the officially reported GDP. The result should demonstrate development sustainability

or the price that has to be paid for the development to be sustainable.

Social welfare can be expressed quantitatively by GDP growth. The amount of GDP represents the total amount of consumption, satisfactory use of measurable material goods and services. The value of GDP in Euro is observed at the site of the Statistical Office of Republic Serbia (http://webrzs.stat.gov.rs/WebSite/).

In Figure 1 we drew the values of GDP from 2002 through 2011, with blue dots. The red line in Figure 1 represents the trend line for which we got to be sixth degree polynomial form. This means that the GDP variable has a multifunctional

character and in its calculation at least six different factors should be included. In the best case GDP (marked as y) would have the sixth-degree polynomial form, whereby the assessed coefficients of the given polynomial form are presented in Figure 1. The determination coefficient, R2, is quite high (98.3%) which means that the trend line fits well to the actual data values for GDP.

Figure 1. Real Value of GDP in EURO (blue dots). Red

line represents the trend line.

Source: Statistical Office of the Republic of Serbia, and

authors’ calculation In case that there is no impact of pollution as a negative

factor that reduces the benefit, social welfare (GDP) will grow continuously in the considered period. The average GDP growth rate in the perceived period was 3.5% per annum. The stated continued growth does not take into account the problem of benefit distribution in the society itself, amongst the social groups that make up its structure.

We will introduce the assumption that there are harmful effects of the economic activities that generates goods and services as a necessary utility segment, i.e. GDP growth. The detrimental consequences of c (costs) are air and water pollution, reduction of biodiversity and the like. Investments which should be introduced to repair the damage of these negative effects we marked with I (investments). We will examine the effect of the negative harmful effects due to environmental pollution, as well as the effect of investments in order to repair the damages, on reduction of GDP growth, or usefulness.

We postulate the following form for the GDP function (GDP*):

* *1 (1 )t tGDP GDP I c GDP+ = ⋅ − − ⋅ (3)

Then, we estimate the coefficients I (investments), and c (costs) which best approximate the given GDP using the following optimization program:

( )2*

, t tI c tMin GDP GDP−∑

(4)

where GDP is real GDP given by the market, and GDP* is given by the model (equation 3). However, equation (4) shows the management of sustainable development in the observed case.

19

It should be noted that we assumed that GDP depends on the costs and investments in a linear manner, even though the actual data suggests the fact that the GDP function would be best to approximate by polynomial form sixth degree. For simplicity and lack of publicly available information, linear dependence was used.

In Table 1 we presented the real value of GDP in Euro and theoretically calculated value obtained using the equation (3). We assumed that the coefficients I (investment) and c (damage) are constant, and they are derived by running numerical simulation by clicking on the "Solver" (see Figure 2) in the software package Microsoft Excel, and by solving the optimization problem given by equation (4). The program itself executes simulation and optimization and gives values for the given parameters.

Actual Theoretical Value of GDP

Table 1. GDP(in Euro) GDP* (GDP-GDP*)2

2002 16028 17974.5 3788864 2003 17306 19294.8 3955443 2004 19026 20706.7 2824845 2005 20306 22197.5 3577879 2006 23305 23800.5 245513 2007 28468 25436.7 9188574 2008 32668 26993.8 32196155 2009 28957 28514.0 196242 2010 28006 30418.5 5820196 2011 31140 32605.5 2147623

sum 63941334 Notes: GDP = actual value in Euro, observed on site of the Statistical Office, GDP * = theoretical value that is calculated after calculating the damage and necessary investments to removing the damage. Source: Statistical Office of the Republic of Serbia, and authors’ calculation.

After running the numerical simulation shown in Figure 2, the program gives the value of damage 5.38% (c = 5.38%), while the value of investments -12.14% (I = -12.14%) in order to satisfy the optimization problem set by equation (4).

Figure 2. Obtaining parameter values of damage and

investment by solving the optimization problem

Source: Authors’ estimation.

Average growth of GDP's real value in the observed period was 3.5% per annum. We get that the value of damage is greater than GDP's growth, and that the rate of investment must be much higher than GDP's growth, in order to eliminate the damage. So, if one assumes that the GDP's growth rate is constant and is 3.5%, we find that the damage is 5.38% and that the rate of investment has to be much higher, in order to repair the damage, and it should be 12.14%.

Once again, the numerical simulation was re-launched for the same function GDP*, represented by equation (3), but now with slightly modified optimization problem. Specifically, unlike the previous case where the minimization of the sum squares, the differences of real and theoretical given GDP represented management of sustainable development, now the management of sustainable development will be expressed by equation (5) which is the minimization sum difference of real and given theory of GDP. Thus, we estimate the coefficients I, and c which best approximate the given GDP using the following optimization program:

( )*

, t tI c tMin GDP GDP−∑

(5)

In Table 2 we presented the real value of GDP in Euro and the theoretically calculated value obtained by using equation (3). We assumed that the coefficients c and I are constant, as was in the previous case, and they are obtained by running the numerical simulation by clicking the "Solver" (see Figure 3) in the software package Microsoft Excel, and by solving the optimization problem given by equation (5). The program itself executes simulation and optimization and gives values for the given parameters.

The actual and theoretical value of GDP

Table 2. GDP(in Euro) GDP* GDP-GDP*

2002 16028 17958.0 -1930.0 2003 17306 19244.7 -1938.7 2004 19026 20616.6 -1590.6 2005 20306 22059.7 -1753.7 2006 23305 23606.7 -301.7 2007 28468 25176.0 3292.0 2008 32668 26652.3 6015.7 2009 28957 28076.9 880.1 2010 28006 29875.8 -1869.8 2011 31140 31943.2 -803.2

sum 0.0 Notes: GDP = actual value in Euro, observed on site of the

Statistical Office, GDP * = theoretical value that is calculated after calculating the damage and necessary investments to removing the damage. Source: Statistical Office of the Republic of Serbia, and authors’ calculation.

20

Figure 3. Obtaining parameter values of damage and investment by solving the optimization problem

Source: Authors’ estimation.

After running the numerical simulations shown in Figure 3,

the program gives the value of the damage – 4.16% (c = – 4.16%), while the value of investments – 4.11% (I = – 4.11%) in order to satisfy the optimization problem set by equation (5).

Average value of real GDP growth in this period was 3.5% per annum. We get that the value of damage and investment is greater than GDP growth in absolute value. So, if one assumes that the GDP growth rate is constant and is 3.5%, we find that the damage is – 4.16% and the rate of investment has to amount to – 4.11% in order to repair the damage.

The main challenges for the overall environment policy in countries that are in transition are to establish adequate mechanisms and institutions for financing and assisting in solving priority environmental problems. These mechanisms and institutions should be designed to promote the development of market-based mechanisms in accordance with the mechanism of the "polluter pays" (Drašković, 1998).

5. CONCLUSION

The paper defines utility function that includes both

market’s and non-market’s assets, or consumption of these assets by an individual. Then, a complicated calculation model of sustainable development was introduced. The numerical simulation approach was applied in our analysis of Serbian GDP growth in the period: 2002-2011.

Our results showed that variable GDP has the sixth-degree polynomial form. We have simplified the external costs during our analysis and have further defined them in two aspects. One aspect relates to the free cost of nature that is presented as a benefit for the participants of economic activities, those who seek to maximize their own benefits (profits) and have an interest to minimize these costs. Thus, participants have an interest not to settle these costs. The other aspect of external costs, whereby the market participants, led by their own interests avoid to present the

costs that occur, as expenses for removing damages inflicted on nature. Both aspects of external costs, i.e., their sum, should be presented as a deduction in relation to reported changes in real GDP.

Implementing this procedure, during our analysis we noticed, using the example of Serbia, that the results on the basis of the starting assumptions, conditions for sustainable development are not met. However, the integration between the economy and ecology, both at micro and macro level still remains, in a satisfactory manner an unresolved problem of internalization of external costs.

6. ACKNOWLEDGEMENTS

This paper is part of research projects numbers 47009

(European integrations and social and economic changes in Serbian economy on the way to the EU), 179015 (Challenges and prospects of structural changes in Serbia: Strategic directions for economic development and harmonization with EU requirements), financed by the Ministry of Science and Technological Development of the Republic of Serbia. All remaining errors are the authors’ responsibility. 7. REFERENCES

[1] Drašković, B. (1998). Economics of natural capital, valuation and protection of natural resources, Institute of Economic Sciences, Belgrade, Serbia.

[2] Drašković, B. (2010).„Essay on the value of natural-resources, costs and methods” Chapter in the Monography Environmental Challenges of Serbia, Ekodos Library, Open University, Subotica, pp. 88-89.

[3] Hotelling, H. (1931). „The Economics of Exhaustible Resources“, Journal of Political Economy, 39, pp. 137-175.

[4] Ponting, C. (1993). A New Green History of Word, The Environment and the Collapse of Great Civilisations, Odiseja, Belgrade, Serbia (2009).

[5] Robinson, J. (1964). Economic Philosophy, Harmondsworth, Middlesex: Penguin Books.

[6] Tobin J. (1981). Financial mediators, source The New Palgrave, Finances, translation of work collection from English into Russian language, Moscow, Russia (2008).

[7] Urošević, B. (2008). Finansijskaeknomija, 1st issue, Faculty of Economics Center for publishing University of Belgrade, Belgrade.

[8] WCED (World Commission on Environment and Development). (1987). Our Common Future. New York: Oxford University Press.Official the Statistical Office of the Republic of Serbia web site:http:// webrzs.stat.gov.rs/

21

TRAIT ANALYSIS OF INVESTMENT PACKAGES AS EOQ BY USING COMPUTATIONAL TECHNIQUE: A CASE STUDY OF

INSURANCE COMPANIES

S.S.Mishra1, Prem Prakash Mishra2 and S.K.Sharma3

Dept. of Mathematics and Statistics Dr. RML Avadh University, Faizabad (UP) India1,2

Dept. of Comp. Sc., GU, Assam, India3

e-mail: 1sant_x2003@yahoo.co.in

Abstract: In this paper, an attempt has been made to analyze the traits (availability, demand, security and growth) of investment packages as EOQ with regard to three important insurance companies of India. Computing technique developed on the basis of σ – score, multiple correlation and regression have been employed to numerically demonstrate the model.

Keywords: investment package, multiple correlation and regression, σ – score, traits. 1. INTRODUCTION

Investment packages offered by various insurance of finance companies can be treated as inventory items because it embodies market values (it can be sold and bought as materialistic items) with the security and growth vide (Acoff et al. al.,1968). Availability of insurance plan is vital for all countries. The security of the fund is of particular concern for any insurance company like LIC, ICICI and Bajaj Allianz etc. as in (Marquis and Long, 2001) using a 1993 survey of over 22,000 private employers in 10 U.S. states, found that changes in insurance price affect decisions to offer insurance, and that the share of employers offering insurance rose a mere 2.5% if insurance premium fell by 40%.

This relative lack of sensitivity of coverage to a large decrease in premium may mean that smaller employers resort to complex and highly ingenious ways of financing the increasingly costly health care coverage of their employees. They included co-insurance and also considered the provisions under Section 105 of the U.S. Tax Code that allows employers to create Medical Expense Reimbursement Plans (MERP) and write off the cost of Medi-gap insurance, co-payments for office visits and medications, return trip mileage for doctor’s office visits, hearing aids and braces.

Under state’s Children’s Health Insurance Program (CHIP) for minor dependents of eligible single parents and the parents obtaining a single plan through the employer; and the small employer granting economic incentives to Medicare-eligible employees to declare Medicare as the primary medical care insurance. The insurance plans like medical insurance, money insurance, vehicle insurance etc play most important role to manoeuvre human life .Since each and every person wants to insure and secure his life

from the forth coming risks. Risk can have several economic meanings such as risk describe the possibility of harmful event occurring or being induced. Such event may cause substantial damage. Second, risk refers to the variation, variance or volatility of economic indicators such as exchange rates or future investment returns. These movements may induce costs to some economic factors. In (Mark, 2003), discussed that cyber insurance provider potential source of risk to accurately predict insurance premiums and deductibles because no historical data available on cyber insurance policies and security violations, insurance providers find it difficult. In (White-Means, Okunade, and Stafford, 1993) there is new thought about the evidence of differences in the job-lock behaviours for women and men could signal differences in the implications for job mobility, medical insurance coverage, the health care system’s access policy designs, and the resulting gender-specific health outcomes.

Researchers Monheit and Cooper (1994), and Gruber, and Madrian (1994) used a voluntary job-switch dummy variable is the dependent variable, and proposed to use a continuous variable as the dependent variable to capture job-lock behaviour of workers. Dummy variables by nature constrain the informational contents of data. Therefore, although “voluntary job switch” could be a proxy of job-lock, this phenomenon could be alternatively captured using a continuous measure, such as the tenure of workers on a job.

Our novel measure, being continuous, would enable computation of marginal effects with respect to continuous independent variables, such as, years of education or number of children living at home. A worker may elect to continue work at his/her current employment with a longer rather than a shorter duration of tenure (resulting from frequent job switches), if indeed that particular worker has to satisfy the waiting period to qualify for health insurance, or more importantly when pre-existing health conditions are excluded from insurance coverage in a new job. In other words, medical care benefits are the least portable among employer-subsidized benefits in the worker’s compensation package. Sullivan and Nozaki (1984) and Hui Sam (2008) employed the multiple regression analysis (MRA) for developing energy prediction equations from the results of building energy simulation.

For minimizing the number of simulations to generate the data a randomized approach to MRA is proposed. Several researchers, as in Benjamin, Guttery and Sirmans (2004), focused on the case study to the basics of real estate

22

appraisal and multiple regression analysis, and also include the market comparison technique as well as advantage and disadvantages of using multiple regression analysis.

In (Sander et al. 1993) provided the data for deriving algebraic expressions using multiple regression analysis, a set of simulation results is usually generated by varying the input parameters of building energy simulation.

Higher proportion of women tend to participate in health insurance, life insurance, retirement plans, and maternity (paternity) leave than men, has been elaborated as in Okunade and Wunnava (2002).

Using the logistic multiple regression method, in Lee (2005), the spatial relationship between landslide-occurrence location and landslide-related factors was calculated. A statistical program was used and calculated the correlation of landslide to each factor.

As we know that trade-off refers to the different types of expenditure by both the private sector and governments. Such butter versus guns decisions include the trade-offs between different types above.

Security driven improvements may even facilitate trade in the long run. Additional investments in secure facilities and modern technologies can reduce transaction costs. Security cost pressures could potentially induce reforms in trade-related institutions and infrastructure with beneficial effects on trade and growth. Better trade facilitation due to deregulation of trade-related sectors, harmonization of customs services and coordination across countries would increase trade among 75 countries by 377 billion USD (World Bank 2003).

Analysis of public policy choices in the security economy from an economic perspective and discussed the role of public goods for national and global security and identifies the importance of the first and second-order indirect effects of insecurity on economic activity, which include the behavioral responses of agents and the government to security measures (Bruck,2004). While in the United States the government required insurance firms to offer terror insurance, in Germany for instance the government helped subsidise a monopolist public private partnership re-re-insurer to cover potential terror risks.

The US scheme has suffered from insurance firms offering the obligatory terror insurance but doing so at premiums that are unattractive to most firms. Thus the insurers fulfil their legal obligations without incurring risky and potentially unprofitable terror risks discussed as in Kunreuther, Wolgast and Ruprecht (2002).

Therefore, this may represent an instance where public intervention and even subsidies are necessary for maintaining some market forces, rather than using regulation. World Bank elaborated that security regulations imply shifting economic resources between actors, including between sellers and buyers and between private and public agents. The existence of such a burden will reduce the efficiency of the market and hence growth. Regulation may be more targeted, thus reducing unnecessary security measures. Security measures have been discussed as in (World Bank 2004) and find new ways to communicate, to produce and to deliver goods. Security measures may deter or identify criminals thus reducing the

exposure to risks and hence making the measures superfluous in the long-term. This may be true. It is, however, not clear if these developments will actually occur. A key policy focus should thus be the monitoring of security spending, the security situation, the security policies and their effects on the economy to adjust measures over time as appropriate.

Overall, security spending and security measures do have strong effects. It is less clear that these effects significantly restrict growth, trade and other economic activities. However, security policies appear to have a differential impact, depending on the nature of the economy. In the long-term, there operate strong forces which will alleviate the negative economic effects of security policies. In Hobijn, (2003), it is open to empirical analysis if and how soon the negative effects of insecurity will wear off in the long-term. Increases in efficiency may be obtained by better regulation and implementation.

In the context of the analysis of the impact of social security systems on saving and growth, the different treatment of population growth in the neoclassical and Classical models leads to a fundamental difference in the predicted growth path. Long-run equilibrium growth rate is determined completely by the capitalist saving function, sometimes called the Cambridge equation and second version of the Pasinetti Paradox: changes in workers’ saving affect the level, but not the growth rate, of capital in the long run. Applied to social security, this result implies that an unfunded system relying on payroll taxes reduces workers’ lifetime wealth and saving, creating level effects on the capital stock without affecting its long-run growth rate. His model is offered as an analytical framework for the review of current topics in fiscal policy, in particular identifying the social security reserve fund as a potential vehicle for generating capital accumulation and effecting a progressive redistribution of wealth vide for example Marglin (1984), and Michl and Foley, (2004).

In Kunreuther, and Heal, (2003) pointed out that on the demand side, people tend to under-estimate the risks of natural disasters or terrorist attacks when it comes to making insurance decisions. This “it-will not- happen-in-my-backyard” mentality represents another obstacle for developing an insurance market for disastrous events.

In this paper, a real case study of investment packages as EOQ has been conducted and their demand has been analyzed and computed with respect to their traits such as availability, security and growth.

Stratified random sampling approach has been employed to collect the data from various strata of population under consideration. Analysis and computing of the data has been carried out on the basis of psychological statistics, σ − score, multiple correlation and regression techniques. 2. NOTATIONS

In this paper the following notations are used throughout the paper: D = σ−score of demand

23

A = σ−score of availability

G = σ−score of growth

S = σ− score of security

σ1 = Standard deviation of σ −score of demand

σ2 = Standard deviation of σ −score of availability

σ3 = Standard deviation of σ − score of growth

σ4 = Standard deviation of σ − score of security

rgs = Correlation between growth and security

rda = Correlation between demand and availability

rds = Correlation between demand and security

3. DESCRIPTION OF THE MODEL

For the measurement of psychological data which are rather abstract in nature as compared with physical or biological characteristics. For scaling of the psychological data various devices, many of them based upon the use of the normal probability curve, have been used. Psychological scale is an interval scale and not a ratio scale since there is no absolute zero point. In this case, a number test items, say n, all designed to test the same trait, and are administered to a large group of individuals who are selected at random out of those for those whom final test is intended. We can find the proportion i p for the ith item ( i = 1, 2, 3…n) successfully, i.e.

sindividual ofNumber

correctly itemth answering sindividual ofNumber ip

i=

In the construction of the scale we assume that the trait (availability, demand and security, growth) being measured is distributed normally about some mean μ = 0 and standard deviation σ. Under the group provides a better scale, known as σ scale. Here the minimum ability to answer this item correctly under the assumption that the ability is distributed normally N (0, σ2). If pi is the proportion of the individuals answering ith item successfully then its difficulty value is given by σzi where zi is determined from the following relation:

P( Z > zi ) = pidt

t

e =∞

∞−

−

∫ 2 2

12

π (1)

i = 1,2,...,n and where Z ~ N(0,1)

Let us suppose that the observation of the trait say X is N (0,1). Suppose that the individuals with trait values in the interval ( x1 − x2 ) are given a rating A by the customers.

The scale value corresponding to this rating A is defined to be the average trait value of all these individuals and is accordingly given by the formula:

Scale value =Φ−Φ

−−

==

∫

∫

)1

()2

(

2

1

2/2

2

1

2x

1x

(u)du

(u)du 2

x

1x

u

xx

x

x

ueπ

φ

φ

=

)2(x - )1(x

)1()2( xx Φ−Φ

φφ (2)

The numerical score for rating is now obtained by shifting

the origin in the scale value to -3.0 as an arbitrary origin, multiplying each σ -value so obtained by 10 and rounding them to the nearest integer. We get the score of each trait (availability, demand, security, growth) for different grades.

We find out mean, standard deviation of each variable trait from its corresponding scores and also correlations between pair of variables. After that we compute multiple correlation coefficient of the demand which is associated with availability, security and growth. Let us consider a distribution involving random variable demand, availability and security, growth.

Then the regression of demand (D) on availability (A), security (S) and growth (G) is:

D = a + b12.34 A+ b13.24S + b14.23 G (3)

Without loss of generality, we can assume the variables

D, A and S, G have been measured from their respective means, so that:

E (D) = E (A) = E (S) = E (G) = 0 (4)

Put these values in above equation we get,

D = b12.34 A+ b13.24S + b14.23 G (5)

The coefficients b12.34 , b13.24 and b14.23 are known as the

partial regression coefficients of D on A and D on S and D on G respectively, e1.234 = b12.34 A + b13. 24 S + b14. 23 G is called the estimate of D as given by the regression equation (5) and the quantity:

D1.234=D−b12.34 A−b13.24S−b14.23G is called the error of estimate or residual.

We apply the least square principle for knowing the value of b’s which is given as:

b12.34 = 112

121-

ωσ

ωσ and

24

b13. 24 = 113

131-

ωσ

ωσand

b14. 23 = 114

141-

ωσ

ωσ; where

1gsrgargdr

sgr1sarsdr

agrasr1adr

dgrdsrdar 1

ω =

1gsrgar

sgr1sar

agrasr1

11ω =

1dsrdgr

sgr1sdr

agrasradr

12ω =

1gargdr

sgrsarsdragr1adr

13ω =

gsrgargdrsgr1sdr

asr1adr

14ω =

where: rda = rad , rds = rsd and rdg = rgd are the correlation coefficients of demand with availability, security and growth respectively. Similarly, other correlation coefficients ras = rsa, rag = rga and rsg = rgs are the correlation coefficients between various traits are defined.

Hence the regression equation of demand is given as

(D - D )× 1

11σ

ω + (A- A ) ×

2

12σ

ω+ (S - S )×

3

13σ

ω +

(G - G )× 4

14σ

ω = 0

where D, A, S, G are the sigma-score of demand,

availability and security, growth respectively and D , A

and S , G are the mean of the σ − scores of D, A and S, G respectively.

In the notation subscripts before the dot are known as primary subscripts and those after the dot are called the secondary subscripts. The order of the regression coefficient is determined by the number of secondary subscripts are written is immaterial but the order of the primary subscripts is important. The sensitivity analysis has been done with the help of computer programming in C++ language. 4. COMPUTING ALGORITHM

The following computing algorithm has been developed to compute all the necessary steps: Step 1: begin

Step 2: input all variables for computation of sigma-score

Step 3: input all variables necessary for computation of

correlation matrix

Step 4: input holding cost, setup cost (ordering cost) of

different investment packages

Step 5: compute sigma-scores of D, A, S and G

Step 6: compute mean of sigma-scores of D, A, S and G

Step 7: compute standard deviations of D, A, S and G

Step 8: compute the regression equation of demand for

various companies

Step 9: compute the EOQ of different insurance packages

Step 10: end.

5. SAMPLING OF DATA COMPUTATION OF MODEL PARAMETERS

Random samples were taken out in the stratified populations of various districts of Uttar Pradesh a largest province of India. This case study based on large sampling (more than 500 size of the sample) keeping in a view adequate represents of the population. Sampling units are randomly selected across the whole population. Though it is very difficult to gauge the psychological standing of investors, a sound and widely used scientific technique computing based on sigma statistics, multiple correlation and regression analysis has been rigorously used. For each company, we use separate data sheet and information for entering their choice according to sampling units’ experience and knowledge.

After getting all the data based on above indices, we get the sigma score for traits (availability, demand, security and growth). The sigma-score of traits for LIC, ICICI and Bajaj Allianz are shown in the table (1), table (2) and table (3)

25

respectively. Difficulty score of any trait or sigma score of trait increases then the trait value will decrease i.e. if the difficulty scores of demand increases then the demand value will decrease. In similar manner, the difficulty score of availability decreases then the available quantity will increase, and the difficulty score of the growth decreases it means the growth of the fund will increase. While collecting the data through interview, three insurance companies operating in India i.e. LIC, ICICI and Bajaj Allianz are targeted to study. Four important traits such as availability, demand, security and growth have been associated with investment of each company and each trait has got five options or choices to be responded by each respondent. These choices include very-high, high, medium, low and very-low. Any one choice is supposed to be answer by each respondent. The following computation tables are given as follows:

Computation for LIC Table 1.

Traits Scores Mean S.D. Demand 56 4 14 16 24.5 22. 942 Availability 48 13 19 18 25.5 11.786 Security 52 6 22 24 26 16.462 Growth 47 13 25 15 27 15.885

rda rds rdg Rd.asg 1.0

0.9960 0.9790 0.955

D = 56.208 -0.71972 G – 1. 2134 S – 1.3751 A

Computation for ICICI Table 2.

Traits Scores Mean S.D. Demand 11 14 18 17 15 13.162 Availability 44 27 19 19 27.25 11.786 Security 48 13 15 18 23.5 16.462 Growth 47 12 13 17 23.5 15.885

rda rds rdg Rd.asg

0.99864 0.9371

0.9008 0.9399

D = 33.211-0.52272 S+ 0.27417 A- 0.57015 G

Computation for Bajaj Allianz Table 3.

Traits Scores Mean S.D. Demand 43 15 16 18 22.5 22.94 Availability 38 24 18 21 25.2 8.928 Security 32 23 17 20 22.6 5.683 Growth 49 11 13 19 22 15.29

D = 39.14 + 0.33410 S + 0.26336G -1.30A

6. QUANTITY

The investment package is treated as the inventory and according to the assumption of simple inventory model without shortage with deterministic demand D. There will be a cost through a advertisement the package till its purchase Ch and a contrary cost which is invested on luring the customers towards itself is denoted as Co; For equilibrium, Carrying Cost = Ordering Cost

C h= 2

Q= Co

Q

D ⇔ Q* =

Co2DCh

EOQLIC = Co

Ch A) 3751 1.- 2134S 1.-G 0.71972 - 2(56.208

EOQICICI= Co h0.57015G)C -0.27417A +0.52272S-2(33.211

EOQBajajAllainz =

Co )Ch1.3025A -0.26336G +S 0.33410+(39.14 2

The following computation tables are given for EOQ of three insurance companies: Computation of EOQ for LIC, ICICI and Bajaj Allianz for given security and growth S = 20 and G = 10 Table 4 Availability LIC-Demand ICICI-Demand Baja Allianz-

Demand 20 2.1776 22.064199 21.6998 15 4.1163 21.16765 28.9181 10 10.991 19.796801 35.430599

LIC-EOQ ICICI-EOQ Baja EOQ 1.47566 4.6977 4.658133 2.028867 4.600832 5.377555 4.060505 5.44933 7.290123 Computation of EOQ for LIC, ICICI and Bajaj Allianz for given availability and growth A = 15 and G = 20 Table 5.

Security LIC-Demand

ICICI-Demand

Bajaj-Allianz Demand

8 11.4799 21.7387 27.5425 12 6.6263 19.647909 28.8789 15 2.9861 18.077975 29.88126

LIC-EOQ ICICI-EOQ Bajaj- EOQ

3.3882 4.662488 5.248095 2.57416 4.432596 5.373909 1.728034 4.252029 5.46637

26

Remarks: (i) When σ − score of security increases then the σ − score of LIC-demand and ICICI-demand will decrease but σ − Score Bajaj-Allianz demand will increase. (ii) When σ − score of security increases then the σ − score of LIC-package and ICICI- package decrease but the σ − score of Bajaj Allianz-package will increase. Computation of EOQ for LIC, ICICI and Bajaj Allianz for given availability and security A = 15, and S = 15 Table 6

Growth LIC-Demand

ICICI-Demand

Bajaj-AllianzDemand

20 2.9861 18.07975 29.88126 15 6.5847 20.9305 28.5644 10 10.1833 23.78125 27.247601

LIC-EOQ ICICI-EOQ Bajaj-EOQ 1.728034 4.252029 5.46637 2.566067 4.574968 5.344567

3.1911280 4.876602 5.219023 Remarks: (i) When the σ -score of growth decreases then the σ – score of the LIC package demands as well as ICICI -package demand will increase but Bajaj-Allianz package demand will decrease. So it is obvious that σ -score of EOQ of LIC package and ICICI-package will increase but σ -score of Bajaj –Allianz package will decrease. 7. OBSERVATIONS AND CONCLUSIONS • From table (4) we can say that if only availability of investment packages are increased by each insurance company then demand of ICICI would increase but demand of LIC & Bajaj Allianz would decrease. • From table (5), we observed that if only security of the money is increased by each company then Bajaj Allianz demand would increase, but LIC & ICICI – demand decrease. • From table (6), it is clear that if only growth of the money is increased by each company then demand of the Bajaj Allianz would increase but the demand of LIC and ICICI investment packages decreases. The above illustration shows that indices related to traits of LIC in the public domain are higher than ICICI and Bajaj Allianz. Moreover, traits indices related to ICICI are higher than Bajaj Allianz and Bajaj Allianz has lowest traits-indices in the market. Through this work, we have attempted to show that growth and security have been targeted to have optimal trade off. And, these are key factors for the investments by the customers in the market. Availability of schemes also affects the demand of investments for various investment companies. It has been observed that business and professional classes while investing their money are more tempted the growth of

the fund as compare to security of the same. In another words, we can say that professionals have more capacity to afford the risk and the hence they also tend to gain in their final pay off.

Similarly, middle class having low traditional education often considers security of the fund at top. So for as LIC is concerned, It has maximum demand among the customers because of high security, expected growth and availability of the schemes. Reason may be long established monopoly of the corporation in the field of the investment.

Here it is very interesting to note that about 15% sampling units reported to the interviewer, while the process of sampling, that they have no yet heard the name of Bajaj Allianz and about 5% to 10% sampling units are not well acquainted to ICICI organization. These reasons are because of low education index among customers in the society and least interactive exposer with cross sectional groups of the society. This kind of case studies can easily contribute to the decision making in investment sector as a scientific foundation.

This study further reveals that what is the amount of multiple correlation among various traits (demand, availability, security and growth), and multiple regression among them facilitating the system of comparison for various traits. 8. REFERENCES

[1] Acoff, Russell L. and Sasieni, Maurice W. (1968). Fundamental of Operations Research. Wilely Eastern Limited, First U.S. Edition.

[2] Okunade A.A. and Wunnava, P.V. (2002). Availability of Health Insurance and Gender Differences in “Job-Lock” behavior: from NLSY, Journal of Forensic Economics vol. 15, pp 195-204.

[3] Gruber, J., and Madrian, B. C. (1994). Health Insurance and Job Mobility: The Effects of Public Policy on Job Lock, Industrial and Labor Relations Review, 48(1), pp.86-102.

[4] Hobijn, B., (2003). What Will Homeland Security Cost, Economic Policy Review, vol.8 (2), pp.21-33.

[5] John D. Benjamin, Randall S. Guttery and C. F. Sirmans (2004). Mass Appraisal: An introduction to Multiple Regression Analysis for Real Estate Valuation, Journal of Real Estate Practice and Education, vol.7, pp. 65-77.

[6] Kunreuther, H. and Heal, G.(2003). Interdependent Security, The Journal of Risk and Uncertainty, vol.26, , pp. 231-249.

[7] Kunreuther, H, Wolgast and Ruprecht, (2002). Risk Assessment and Risk Management in an Uncertain World, Risk Assessment, vol.22 (4), pp. 655- 664.

[8] Lee, S. (2005). A Cross-Verification of Spatial Logistic Regression for Landslide Susceptibility Analysis: A Case Study of Korea, A Geosciences Information Center, Korea Institute of Geoscience and Mineral Resources (KIGAM) 30, Gajeong-Dong, Yuseong – Gu, Daejeon, Korea, pp. 305-350.

[9] Marquis, M. S., and Long, S. H. (2001). To Offer or Not to Offer: The Role of Price in Employers, Health Insurance Decisions, Health Services Research, vol.16(5), pp. 935-958.

[10] Marglin S.A. (1984). Growth, Distribution, and Prices, Cambridge MA:Harvard University Press,

[11] Mark, A.H., (2003). Cyber risk exposures challenges

27

insurers, Business Insurance, vol.37 (47), pp.12. [12] Monheit, A. C., and Cooper, P. F. (1994). Health Insurance

and Job Mobility: Theory and Practice, Industrial and Labor Relations Review, vol.48 (1), pp.68-85.

[13] Sander, D. M., et al. (1993). Development of a simple model to relate heating and cooling energy to building envelope thermal characteristics, In Proc. of the Building Simulation 93rd Conference, Adelaide, Australia, pp. 223-230.

[14] Sullivan, R.T. and Nozaki, S.A. (1984). Employed standards Multiple regression techniques for developing simplified energy equations and design tools for building energy to fenestration effects on commercial building energy performance, ASHRAE Transactions,vol.90, pp. 116-123.

[15] Hui Sam C.M., (2008).A Randomized Approach to Multiple Regression Analysis of Building Energy Simulation. Research Report, Department of Architecture University of Hong Kong.

[16] Michl T.R. Foley, D.K. (2004). Social security in a classical

growth model, Cambridge Journal of Economics, volume 28, no. 1, pp. 1–20.

[17] Bruck, T. (2004). An Economic Analysis of Security Policies, German Institute for Economic Research, DIW Berlin, Germany, pp.1-2.

[18] World Bank Reducing Trading Costs in a New Era of Security, In Global Economic Prospects 2004:the Development Promise of the Doha Agenda World Bank: 2004, pp.179 – 203.

[19] White-Means, D.B., Okunade, A.A. and Stafford, P. (1993). What Influences Employees to Choose Optional Benefits, Journal of Compensation and Benefits, vol. 9(3), pp. 37-41.

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VARIABLES IN THE SPECIFIC THOUGHT OF MULTIDISCIPLINARY RESEARCH: THE IMPORTANCE OF EPSILON

Gheorghe Săvoiu1 and Ion Iorga Simăn2

1,2University of Piteşti e-mail: 1gsavoiu@yahoo.com and 2ioniorgasiman@yahoo.com

Abstract: Contemporary variables are more and more

involved into multidisciplinary thinking and research. This paper aims to highlight the importance of variation paradigm in modern scientific research, using a process of passing relatively easy from changing levels, to variability, and finally to variables. The paper describes some of the major characteristic variables in physics, economics, sociology, history, mathematics, statistics, demography, etc. It underlines the importance of the first multidisciplinary variable in econometrics, the residual variable, which is indeed an economic, statistical and mathematical variable at the same time, but also an innovative and historical explanation for reality, followed by other increasingly interesting variables from econophysics and sociophysics. Some final remarks about the new multidisciplinary context and the role of modern multidisciplinary research variables in our investigation close, naturally and symmetrically, the circle of multidisciplinary thought.

Keywords: paradigm, variation process, variability, multidisciplinary, variable, epsilon.

1. INTRODUCTION

Variables in multidisciplinary thinking assume fairly different forms, reconstructing data or databases and investigative databases in a majority of scientific disciplines, virtually all of today’s sciences. Variables have been, and still is, a key concept of modern science and research, generating, apart from databases, specific methods or solutions for validating / invalidating various models that simplify reality as an object of study.

Variation and variability are essential structural components of scientific research, especially the multidisciplinary researches.

An attempt at delimiting the concept of multidisciplinary variable is a difficult process, bringing together some of the most variegated aspects of homogeneity and heterogeneity, information asymmetry and eccentricity, exogenous, explanatory or factorial character, or enhdogenous specificity, either explained or resultative, thus providing the most extensive range of information, going from the historical, demographic, mathematical, statistical, biological and economic ones to the physical, etc. data.

The multidisciplinary variable is a special species of the scientific variable, which finds more and more materializations, ranging from the econometric residual variable to the variable used in econonophysics and sociophysics, the variable in quantum economy, etc. 2. PARADIGM AND VARIABLE – ASSOCIATIONS IN MULTIDISCIPLINARY

The paradigm of variation has the significant merit of

having generated the concept of variable in modern science. Science starts with a new current of thought and "every school or school of thought begins with a paradigm that is used or even constructed" (Kuhn, 1973, 1982), and to "capture the epistemological status of a scientific discipline consists in identifying its main paradigms" (Boudon, 1990).

The practice of any contemporary science is based on a number of paradigms, and multiplying the "defects" and erosion of the "traditional" paradigms leads to new crises, and thus to new solutions.

A good example in this respect is represented by the paradigm of "uility" in classical economics, a paradigm that summarizes some major characteristics of the family group of paradigms: a) ability to identify with the conceptual and procedural core of functional analysis, or the node of the information network of the new science; b a) a new way of thinking, materializing in new principles, methods and techniques for the investigation of reality.

A paradigm facilitates developing hypotheses and finally laws specific to the new science, refocusing its investigational approach towards solutions of a probabilistic, and the new model of scientific thinking, as the ensemble of whole new principles, methods, techniques and research tools, it reaches its own maturity when it was shared "by all the members of a scientific community, and especially by those who practice a discipline" (Merto, 1965), its essence being taught in school or from books, thus turning into a common possession of the scientific world.

A derived linguistic meaning of the paradigm is that of a specific language in which are conceived and translated the theories or their more important subsets, and it comprises a set of the inflected forms of a concept or of a notion, in short a true picture or model of the flexion of the

29

meanings of a category, later reconsidered as elementary, through wear in time (through its gradual assimilation with the part of speech that designates it).

The essence of the paradigm was perceived differently, and is still being resignified in modern science: a) a synthesis or an overview of concepts and issues (Robert Merton); b) a logical model, reduced to an axiomatic structure (Don Martindale); c) a theoretical level combined with a practical level and derived from the effectiveness of practice; d) an experience transposed theoretically and organized economically – efficiently (Ernst Mach); e) a type of operative logic, a code of functional analyses, a

structural hierarchy ordering and classification (Robert Merton); f) a methodological order of iteration of functional analyses; g) a simplification of the study of the contradictory correlation of phenomena and anticipating consequences; h) a refined process within the referential framework of coding the data investigated (laws, theories, applications, instruments – Paul Bran); i) a formal model, a scheme of abstracting the essence of motion and transformation, which capture the dynamics of the integrating system of science within the same coordinates (Nicholas Georgescu-Roegen).

An inflectional picture of the paradigm of variation

Table no. 1 Variation (from Latin: variatio, variationis)

State or status of an element, of a number of features, an individual, a population, a phenomenon to occur in different forms (in a varied form). Passing from one form to another, from one level to another, assortment, diversity, change, transformation, etc.

To vary (from Latin: variare)

To be varied, different, various (in keeping with places, circumstances, situations) Not being similar, not having the same appearance, structure, composition Changing, giving a different shape, transforming Changing the value (state, shape, level)

Variable

Likely to change, changeable, varying, successively assuming different values (states, forms or shapes, etc.).

Variability

(from French: variabilité)

The feature or property of an element, a feature, an individual, a population, a phenomenon to take different forms and aspects or the property of a quantity, size or algebraic function to successively take an infinite set of different values (in economics, statistics, etc.). The tendency of organisms to deviate in a given direction from the original type, the emergence of differences between the individuals of the same species (in biology)

Simple variable A measurable quality (in the sense used by the present article) Bidisciplinary concrete variable (in statistics and mathematics)

A statistical feature having the capacity of changing its value (state or status, type, level) in time, space and organizationally and a mathematical size assuming a value out of a well-defined set with a known probability, generating two major types: a) the (random) discrete or discontinuous variable; b) the (random) continuous variable (the possible values "fill" a finite or infinite interval).

Relationship between variables (represents the essence of physics and

generates modern scientific experiment)

The concept of variable is crucial in experimental physics (e.g. the effect of gravity on falling bodies: fall speed v is influenced, as a dependent variable, by the gravitational field g and height h by the relation: 2ghv = ). A carefully studied physical process results in a relationship, a model, a balance, a duality where variables are ubiquitous (E = mc2) and a physical discovery is expressed mathematically by variables, requiring in-depth study of the behaviour of the dependent variable in different instances, changing the independent variable and

30

thus generating physical experiment.

Non-experimental (historical) variable

A variable in history is characterized precisely by the lack of experimental and the consequences of scenarios in real terms.

Source: Săvoiu, G. (2001), Universul preţurilor şi indicii interpret (Price universe and interpreter indices), Editura Independenţa Economică (Economic Independence Publishers), Piteşti, p. 316-317, recast and completed by the authors.

Variation seems to have originally appeared in

philosophy as the antithesis of Socratic identity, being the natural consequence of the impossibility for multiple identical things to exist (Săvoiu, 2009). The identity formulated by Socrates "ab initio" as an intrinsic quality of reality evolves towards defining through ratio and generates the stationary or the "premise of variation".

Plato, according to whom knowledge, implicitly scientific one, is a subspecies of what may be defined at the same time as true and credible, placed variation in two of the five universal concepts applicable to all things, namely in difference and change, which followed existence and identity, but were placed before resistance.

The logic of falseness and of truth become, within the paradigm of variation, a mere variable of an alternative type. In the modern science of the last half-century, truth has been trying permanently to reach synonymy with objectivity: "Although the term has been used by some to suggest a naive version of vulgar positivism, objectivity is the foundation [essential basis] of any good research." (Kirk and Miller, 1986)

Based on the need for authentication of apparent or related variables, and also on the growing interest for real or free variables, resonance, as an essential principle of variability, developed (Odobleja, 1984).

The development of logic, and especially the use of mathematical induction, had the unexpressed premise of "limiting independent variation, which translates the same major significance of variation and variability" (Mills, 1959).

The paradigm of the variable gradually became an "isomorphism" or a structural similarity of several scientific disciplines.

The basic variable was used excessively with a different degree of "identity" in physics, mathematics, biology, economics, statistics, demography, chemistry, ecology, management and organization etc., starting from the meaning of variable (a certain value, a specific state or condition, a particular form or a certain level achieved by the function that defines a process or a phenomenon), to the sense of variance, or dispersion, or the fluctuation (equal to the arithmetic mean of the squared deviations and not expressed in measuring units, being found explicitly or implicitly formulated in most statistical methods, e.g. for risk assessment in economic models, etc.).

There were also attempts at renaming variables, as in biology where they have become apparent, but also complex, varieties (a group of organisms, specifically below, which is different from other groups of the same species through characteristic features such as: adaptability, resistance and quality characteristics).

Variety generated phenotypic variation (Vp) seen as the totality of the biological variations, while preserving a principle, developed in the meantime in statistics, viz. the rule or law or summing variabilities (dispersion). Phenotypic variation is the sum of two aggregate components, respectively variation caused by the influences that of the environmental factors (Ve or the environmental variation component) and the variation caused by the contribution of the segregating genes (Vg or the component of genetic variation), so an essential principle in modern genetics was obtained practically Vp = Ve + Vg resonant or interfering with the classical rule of

adding dispersions: )σ()(δ)(σ 2220 +=

Heritability, or the proportion of the total variation that is controlled by heredity (H = h2), is a relationship or ratio between variation caused by multiple genes with additive

effects (Va) and phenotypic variance (Vp): H = h2 = VV

a

p

or H = h2 =V

V Va

e g+ hence :

h = VV

VV V

a

p

a

e g=

+ a relation which is resonant or

interfering with R =)(σ)(δ

20

2

=)σ()(δ

)(δ22

2

+

In parallel, statistics and mathematics generated a bidisciplinary variable of their own, by the emergence of probability theory (Bernouli, 1713).

Variability and variation in the biological sciences were a prime example of evolution from the type of thinking through the unidisciplinary variable to thinking through multidisciplinary impact variables, based on specific and generally applicable rules:

Prima regula: Variation (variability) does not exist on its own, but coexist in a "mesonic" manner with stability (heredity).

Secunda regula: The total variance is the sum of two components, bringing together key, explanatory and non-essential or residual factors.

Tertia regula: The proportion of the total variance that is "controlled" by a key or essential factor is a determinable ratio.

Quarta regula: Various partial variations are correlative, and there is the possibility to establish the

31

existence, the direction and the intensity of the relationship between variations.

Quinta regula: Evolutive processes contain both correlative and non-correlative variations, and insofar as the system where they occur is closed and there is a measuring unit of universal character, the amount of the variations is relatively constant and the regressive evolution is irreversible or entropic (Săvoiu, 2009).

Specifying quantity immediately led to measure in the Hegelian sense, but also paved the way for the appearance of the first variable of the bidisciplinary type, namely the statistical-mathematical variable. A more comprehensive discussion on the first bidisciplinary variable or on variation and variables in mathematics and statistics requires treating the continuumu and the discontinuum.

"Treating variables as constant", F. Edgeworth emphatically stated in 1932, "is the characteristic error of the... non-mathematician"(Georgescu-Roegen, 1998).

Information, which appears, in the opinion expressed by Nobert Wiener, as a continuous or discontinuous sequence of measurable events, distributed with respect to time, emphasized the perpetual mixing of discontinuum and continuum information. "The whole precedes the parts," Leibnitz said, revealing continuity in the whole.

Yet the same whole represents, in today’s systems theory, much more than the mere sum of its parts…

Intuitively, the continuum is the generator of differences, and ultimately, of variation. The continuum represents that structure, composition, organization, dialectical overlapping of the constituting elements that leaves virtually no empty space, and the constitutive elements are neither divided nor separated from one another. Spatial and temporal continuum is synonymous with overlapping rather than the indivisibility of its component entities. A very precise definition of the continuum is illusory, on account of the very impossibility to completely avoid discontinuum or the essential property of any entity to be discretely distinct.

The opposition continuum-discontinuum lies in the contrast between the continuous and discrete variable. As a synthetic summary of the paradigm of statistical-mathematical variation, the statistical series, a key concept in statistical thinking, is defined as "expressing a variable in relationship to the variation of another" (Georgescu-Roegen, 1930).

Variation and variables in physics, considered jointly, raised the whole range of issues of the experiment. The variable in physics was defined as a certain class of size that was quantified or measured. A first classification of the above divided variables, in both statistics and physics, in four types: a) nominal (categorical); b) ordinal; c) of the interval type; d) of the ratio type.

The first two types were mostly qualitative, and the last two quantitative (numerical), gradually ensuring the supremacy of quantitativeness over qualitativeness, followed by redefining the qualitative by the quantitative (Thorndike said that "everything that exists is in a certain amount", and McCall went further, saying that "everything that is in a certain amount can be measured").

The classification variables in modern physics has evolved gradually, retrieving other typologies already developed in statistics and mathematics, from the independent to the dependent variable, or transiting towards the canonical variables of a mechanical system under analysis (where each pair of variables (pi, qi) are called canonically conjugate and have the property that a change of variable pi in qi, and qi in pi, does not change the form of the equations of motion, to form the complexity of the quantum, etc. type variables.

Other variables were variously specified in their own disciplines’ own universe. The main characteristic feature of the economic variable is its duality, captured between the value that varies continuously (Adam Smith) and invariable measure of value (David Ricardo).

Adam Smith, the author of The Wealth of Nations and therefore the father of economics as a science, focused his reasoning on values that vary continuously ("Digression concerning the variations in the value of silver"), while David Ricardo chose the opposite extreme, that of stability, as being precisely what transforms a commodity made over a period of production, in its capacity as the arithmetic mean of production, into an invariable measure of value, a standard of measure, invariable as to the changes in relative earnings.

The historical variable involves another specific aspect, there being no experiment in history and its remarkable practical consequences for assessing the impact, the hierarchy and the confrontation of this variable, which is interesting especially in the evolution of science.

Unlike physics, history is not an experimental science. Consequently, history "cannot measure the weight of

each element (or factor) contained in it." (Boia, 2010). At the beginning of its analyses, history collected small "causes", whereas the contemporary historians working in accordance with a method guide themselves by the big causes, according to structural approaches.

The drama, or the special feature of the historical variable is related to the impossibility of predicting or of simulation. This variable, either simple causal (small causes) or major causal explanatory, does not provide, within its space of application, any modality, any way to check the validity of the solutions put forward in the model of historical analysis exploited and valued as such. There is no experiment in history, yet there do exist repetitive errors, similar endings or similar resultative variables (Boia, 2010).

The economic variable, to a much lesser extent, and mostly the historical variable are variables whose probabilistic ending is hard to identify, impossible to simulate, and inexplicable in reevaluating after the fact.

It is not time, but the large number of the variables that seems to be the cause of this rigorous unpredictability and reasonable validation in the universe of such variables as the economic and historical ones (especially the aspect of mutual compensation of most of these variables over certain periods of time, or the mutual cancellation of an infinite horizon of small causes, as some historians graphically put it).

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The demographic variable, as a resultative variable, has the broadest causal horizon and the most complex causality possible. The dynamics, the structure, the partial offsetting of the immigration and emigration flows, and plenty of other elements that contribute to the knowledge of this variable call for exclusive multidisciplinary manners of data sampling, processing and interpretation, modelling and forecasting or simulation.

In turn, this complex variable, which has become explanatory in a model or specific analysis, requires multidisciplinary decomposition to be able to identify the true causes and correctly distribute probabilities within a major decision-making context, significantly modified from a priori to a posteriori. 3. THE ECONOMETRIC VARIABLE EPSILON – A PIONEERING MULTIDISCIPLINARY VARIABLE

Induction, practiced simultaneously in several areas

(multidisciplinary subjects), was the factor that perfected the process of disjunction into explanatory (exogenous) variables, and explained (endogenous) variables, paving the way to better delimiting the multidisciplinary complex variable.

Inductively bringing together elements of the exclusively historical or chronological, geographical or spatial variables, with elements of structural logic content, a three-dimensional statistical variable was first created, then, through investigating, in economic processes and phenomena, their characteristic variability with various mathematical methods, the first complex multidisciplinary variable was obtained, namely the econometric variable, with special focus on the exceptional vitality of the variable epsilon.

Whenever the statistical and mathematical methods, techniques and tools are used to analyze the economic processes and phenomena, the only term that can felicitously describe such a scientific approach is the concept of econometrics, and the variable resulting from such an approach is certainly the first one that is truly multidisciplinary.

"Experience has shown that each of these points of view, i.e. that of statistics, of economics and of mathematics, is a necessary but not sufficient condition for an effective understanding of the quantitative realities of modern economy; it is their unification that ensures efficiency. Econometrics is precisely this unity" (Frisch, 1933).

ogene (factoriale), completând restul influenţelor printr-o variabila reziduală (aleatoare).

Specification in the econometric model practically begins by specifying the endogenous (resultative) variable and the exogenous (factorial) variable, completing the remaining influences through a residual (random) variable.

This is perhaps the most important variable for multidisciplinary research, which is, in fact, the first alternative, that of gathering a group of variables under a

common name and permanently studying to what extent the aggregate and the offset effect of residue expands and contracts, i.e. require reconsidering the previous model and describing a new one.

In order to understand the rapidity with which this first multidisciplinary variable evolved by the name of residue or epsilon in the most common notations (εi), annexing the whole econometric model, one can analyze carefully what contribution it had to the construction and validation of the model as such in the simplest econometric model of unifactorial regression (Săvoiu, 2011)

For instance, the specific assumptions of the model of classical multifactor regression are outlined below in order to explain the exceptional importance of this first multidisciplinary variable, from H1 to H11.

H1: The linearity of the model (the simple model of classical unifactorial regression is most commonly a linear model in both its parameters and the exogenous variable xi, according to the relation: yi = E (yi|xi) + εi, or detailed yi = α + β (x i) + εi where: i= 1,n.

H2: The absence of measurement errors in the values xi observed (the values of the exogenous, predictable variable, specifically deterministic in the statistics of the classical type, xi are collected and recorded without error, regardless of the experiment);

H3: The mean value of the errors equal to zero or clearly tending to zero: E (εi |xi) = E(εi ) = 0 or the residual variable average is null, confirming the fact that, on average, the model is well specified);

H4: The homoscedasticity of the model or the constant variance of the residual variable (the variance of residue εi for the given values of xi is constant: : var (εi |xi) = E[εi – E (εi |xi)]2 = E (εi

2|xi) = σ2 (the homoscedasticity of the model also implies a constant variance for yi,, i.e. var (yi |xi) = σ2 , and once this relationship is not satisfied, it will lead to the conclusion that the model is heteroscedastic);

H5: Independent residual values or uncorrelated errors (for any two values xi and xj of variable x, with i ≠ j, these are independent values if there is no correlation (correlation is zero), so the following statistical-mathematical relationship is valid: cov (εi , εj |xi , xj) = E{[εi – E (εi |xi)] [εj– E (εj |xj)]} = E [ (εi |xi) (εj |xj)] = 0;

H6: The independent residual variable as to the exogenous variable xi (covariance between xi and εi is zero: cov(xi,εi) = E{[xi–E(xi)][εi–E(εi)]} = E[εi(xi–E(xi)] = E(xi ,εi) – E(xi)E(εi) = E(xi,εi) = 0, thus the residual variable is independent as to the exogenous variable xi);

H7: The number of observed data n greater than the number of estimated parameters in the model (the number of observations n greater than the number of exogenous variables);

H8: Variability in the values of exogenous variable xi (the values of xi are not all identical, or var (xi)

= : (n–1) is a positive finite number is a

hypothesis that usually has a clear visibility or can be verified by calculation if necessary);

2n

i=1ˆ(xi –x)∑

H9: The model of regression, correctly specified (specifying the endogenous variable and the exogenous

33

variable, filling the rest of the influences with a residual variable and correctly identifying the mathematical function of the model, which thus became specified or signified);

H10: The normally distributed residual variable (its variable εi is normally distributed εi~N(0,σ2).

H11: Identifying multicollinearity and removing it by means of the residue or the multidisciplinary variable epsilon, calculated systematically.

Two features are crucial for this first multidisciplinary variable:

a) the multidisciplinary variable essentially brings together the rest of the variables that are not modelled or not included into the fundamental investigation, having a character of component uncertainty, or structural uncertainty, yet possessing the value of signal of the degradation of the econometric model underlying the theory, at the level of this variable;

b) the multidisciplinary variable is no longer exclusively a component of the data corpus (database or data bank in the classical sense), but an active instrument of testing, analysis and validation/invalidation of the model, of the theory, and ultimately of the realities as such.

If the essential nature of the paradigm is methodological rather than ontological in classical science, and the relevance of the paradigm depends on the coverage of the structure of the specific phenomena studied, the multidisciplinary variable supplements, by testing, analysis and validation/invalidation, the quality of the research and the theory, which is generated, in the modern universe, more and more difficultly otherwise than in a multidisciplinary manner.

4. CONCLUSIONS Over the past editions of EDEN I, II and III, the focus

was placed on some particular aspect out of those considered essential in trans- and multi-disciplinary scientific approach in the field of contemporary academic research and education, from the distinctively historical and methodological aspects, to the model of investigation specific (the unifying character of multidisciplinary modelling is strongly emphasized here), from dissipation in econophysics, sociophysics, quantum economy, etc., to the specific multiverse of trans- and multi-disciplinarity.

The present contribution looks into the profundity of the multidisciplinary multiverse, highlighting the fact that the very core of multidisciplinary research is identified not only by significant methods and original models, but also, and mainly, by what might be called perhaps its greatest contribution, as a type of research and innovative specificity: the multidisciplinary variable.

If the method is constantly improved and the model is captive towards one or more theories in point of

multidisciplinarity, it is the multidisciplinary variables that lend density to a number of economic laws and theories, while also mutilating the fundamental freedom of the model or method, and acting in the spirit of the originality of the measuring, and then getting deep knowledge of the new phenomena of marked multidisciplinary character.

The present times have confirmed a process of multiplication of the econometric variable as a pioneering multidisciplinary variable. The econometric residual variable is multiplied with regard to the econophysical variable, the model lacks restrictions, the residue, or the unstable epsilon, becomes more and more complex, and the results are increasingly interesting and original.

Physical thinking contributes, by formalizing the multidisciplinary variable in the new discipline of econophysics, then in the equally original discipline of sociophysics, or the impressive trend of quantum economy, in a more or less unexpected manner, to the understanding of economic, social and demographic issues, to determining the equations that simplify and the methods that describe phenomena such as production, market, migration, traffic or transport, the financial world, etc.

The multidisciplinary variable is reluctant to work in areas where there are less reliable and short-term datasets, dominated as it is by the desire to unify things against the background of a physical tradition, while at the same time relativizing, capitalizing on experiments having to do with genuine conceptual revolutions. The more rigorous delineation of the subject matter, through the contribution of the multidisciplinary variable, contributes to a better validity and adequation of specific models, an active discussion of the role and potential of econometrics, of the rival modelling sciences that integrate the universal thinking of physics (econophysics, sociophysics, quantum economy, etc.) into higher education and scientific research in Romania.

As final remarks on the general characterization through the paradigm of variation and the multidisciplinary variable, the following can be noted:

a) the paradigm remains either the essential core of concepts, laws, methods and variables, supported by thinking patterns or sets of principles, ways, methods and specific variables construed by rules defined by means of theoretical and practical knowledge,

b) the paradigm of variance and of the multidisciplinary variable is the priority in relation to any other (subsumed under it);

c) the paradigmatic excesses appear once the paradigms are isolated from the methods and their specific variables, which easily converts separate, unidisciplinary classical theories into theorizing without pragmatic, which lead to gradual loss of the sense of reality.

Without multidisciplinary variation and without multidisciplinary residual epsilon variables, the attempt to depart from, or shun reality through unidisciplinary "scientific" knowledge, or under the influence of a single scientific paradigm, could hardly be identified, let alone improved or diverted.

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The authors of this paper can finally state that they know they do not know, as the only Socratic certainty; however, that can only bring them the greatest joy, as the new multidisciplinary variable is the very seed of our ignorance along the long, maybe endless, yet so exciting way to scientific knowledge, and also the evidence that, more and more obviously, knowledge acquired must be continuously turned into yet other knowledge, thus increasing the multidisciplinary nature of knowledge…

5. REFERENCES

[1] Bernoulli, J. (1968). Ars conjectandi: opus posthumum. Accedit Tractatus de seriebus infinitis, et epistola Gallicè scripta de ludo pilæ reticularis. Basileæ, Impensis Thurnisiorum, 1713, Culture et civilisation, 1968, University of Califonia.

[2] Boia, L., (2010). Tragedia Germaniei 1914 -1944, Ed. Humanitas, Bucureşti, pp. 64-65.

[3] Boudon, R. (1990). Texte sociologice alese, Bucureşti, Ed. Humanitas.

[4] Bran,P. (1995). Economia valorii, Bucureşti,Ed. Economică. [5] Frisch, R., (1933), Editor's Note. Econometrica 1,pag.1-4 [6] Georgescu–Roegen, N. (1979). Legea entropiei şi procesul

economic, Ed. Politică, Bucureşti. [7] Georgescu – Roegen, N. (1998), Metoda statistică Elemente

de statistică matematică, editată în 1930, ediţia a II-a, Ed. Expert, Bucureşti. [8] Ionescu, N. (1993). Curs de istorie a logicii, Bucureşti, Ed.

Humanitas. [9] Kirk, J.Miller, M. L.(1986). Reliability and validity in

qualitative research, Beverly Hills: Sage Publications. [10] Kuhn, T. (1973). Structura revoluţiilor ştiinţifice, Bucureşti,

Ed. ştiinţifică şi enciclopedică. [11] Kuhn, T. (1982). Tensiunea esenţială, Bucureşti: Ed.

ştiinţifică şi enciclopedică. [12] Merton, R. (1965). Elements de theorie et de methode

sociologique, Paris: Ed. Plon. [13] Mills, F. (1959), Metode statistice, Bucureşti, Editura D.C.S. [14] Odobleja, Ş. (1984). Introducere în logica rezonanţei,

Craiova, Ed. Scrisul românesc. [15] Săvoiu, G. (2001), Universul preţurilor şi indicii interpret,

Editura Independenţa economică, Piteşti, pp.316 -317. [16] Săvoiu, G. (2009). Paradigma şi prioritatea acesteia în

raport cu metoda, în cadrul gândirii statistice. Limbaj şi context, Anul 1, vol. 2, Ed. Alecu Russo State University of Bălţi [Accessed on July 15th, 2012] http://www.usb.md/ limbaj _context/volcop/2/2.pdf

[17] Săvoiu, G. (2011). Econometrie, Bucuresti, Ed.Universitară

35

PROFILE METHOD – AN EXAMPLE OF MULTIDISCIPLINARY APPLIED METHOD

Gheorghe Săvoiu1, Mladen Čudanov2 and Mariana Vladu3

1University of Piteşti, Romania, 2 University of Belgrade, Serbia, 3University of Tiraspol, Moldova e-mail: 1gsavoiu@yahoo.com, 2mladenc@fon.rs

Abstract: The paper describes the practical use of

the method of statistical profiling in various disciplines, underlining the importance of this new method concept as applied to multidisciplinary approaches. The method is described briefly in the introduction and applied in the third section, after the second section has detailed the multidisciplinary innovative management process. The practical results of applying the method in innovative educational systems are further detailed, based on both the specifically multidisciplinary nature of this type of processes, and the profile method applied. A final remark ends the paper in a structuralist, schematic and optimistic manner.

Keywords: statistical profile, the profile method, innovative educational process, management in innovative educational processes, profiled skills.

1. INTRODUCTION

Along with the models and variables, even the methods can become multidisciplinary, in their use within several specific disciplines, or simultaneously within a multidisciplinary reality.

As part of this picture, one can define methods that can be applied in a multidisciplinary manner, being able to implement the method or approach mostly in multidisciplinary areas.

The profile method, as presented and applied in this paper, confers powers to shape permanent individual profiles of the real outer environment, of the educational, human, entrepreneurship, etc. milieux.

The aspects of the applied, practical diversity are not sufficient, as the method becomes consistently applicative in a multidisciplinary manner only after its validation as a method applied to realities approachable only in the multidisciplinary manner. The methods, applied in this way, induce the need to put them to better use, to implement and generalize their results by original techniques and instruments, which are simple but effective.

The statistical profile method is one of the simplest solutions, which can thus become the very method of decision-making management, by profiling, at the interference region with the multidisciplinary decisional management area, or, in the special case presented in this paper, the method of shaping and training management skills in innovative educational processes through profiles.

The argument of the conceptual simplification of the applied multidisciplinary method is given by one of the statements made by Ştefan Odobleja (1984) that "it is not

the object or the subject, but the method that determines science".

The nature of the managerial phenomenon reveals at least three dimensions, namely the presence of the unknown or the limit lent by the latter to the object observed (in the sense of an innovative educational process exposed to a managerial decision, or an educational entity facing an objective problem), the limit of the observer’s power or competence (i.e. the teacher manager), and especially the limit of the method used in the management process (equipment, instrument).

The relativity of the comprehensive type of knowledge or of comprehensive analysis, limitation as a result of the indistinguishable, imperceptible presence of the unknown, always gives other managers or management theorists the opportunity to identify, seek and try new solutions.

The new method, which is applied here in a multidisciplinary manner, as the approach of management by profiling, is a management and leadership method by which the function of information and decision-making sees hypertrophy and decision can be completely influenced by the profiles used as a support.

The approach based on the method of profiling is also a synectic solution. Gordon’s Synectics is suitable and indicated for selecting a single idea or a for identifying an original solution, and generates stages that have already become classical in innovative educational processes: forming the synectic group, presenting the problem, setting the synectic itinerary, developing the problem solving model, and finally testing and application of the model (Săvoiu G., Jaško O., Dulanović Z., Čudanov M., Crăciuneanu, 2008; Săvoiu, Jaško & Čudanov, 2009).

The typology of the profiles that can be used is extremely diverse, from temporal or dynamic profiles to local / territorial or hierarchical profiles, from coordination profiles defined by differences and gaps to intensity profiles, from structural profiles and average profiles, to the profiles centred on extreme (minimum or maximum) values, from demographic profiles, to statistical profiles, from climatic or geographic profiles to innovative educational profiles, a.s.o.

Various specific operations can be defined by using profiling, from the intersection of some of them, to the reunion of others meeting or the complementary of a profile, as operations similar to those in set theory.

A standard profile involves both a selection of the profile design variables, as an operation subsequent to dispersion analysis, and a final sequencing of the profile variables in accordance with the values of the determination coefficient for the characteristic features considered to be explanatory,

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or likely to be able to tackle the newly emerged management problem that requires prompt decision.

To briefly illustrate the applied multidisciplinary applicative nature of the new method, one can have recourse to the dominant demographic profile resulting from the natural involvement of demography into the interstices, or on its borders with other sciences, sometiems even penetrating into the body of some of them.

The demographic profile of the unemployed and the offender are only two examples of the multidisciplinary or interdisciplinary intersections of demography and economics or criminal law.

The demographic profile of the unemployed in the Romanian economy, in the year prior to its accession to the European Union, is outlined by significant statistical issues: a) in 6.6 out of 10 cases, the unemployed has already had a job; b) they originate mainly from industrial enterprises with large financial losses, especially in the category of companies having undergone or going into liquidation; c) in almost 6 cases out of 10 the unemployed is male; d) in about 7 cases out of 10 they live in urban areas; e) they belong to the 15-24 age group with a probability three times higher than any other age group; f) the average unemployment period exceeded 21 months; g) in 62 cases out of 100 the highest education level completed is secondary school, etc.

The demographic profile of the prisoner in Romania, in the same pre-accession year, as a result of the analysis of the prison population, also emphasizes various aspects as important and defining as the ones above: a) one person in custody pending trial out of two is 21 to 30 years of age; b) one in three inmates has been convicted to terms between 3 and 5 years; c) 54 inmates out of 100 male inmates are from urban areas; d) 64 out of 100 female inmates are from the same urban environment; e) 45 out of 100 male inmates have completed secondary/middle school, 14 have completed vocational school, 12 graduated high-school, 18 completed primary school, and 9 are illiterate; f) 38 out of 100 female inmates have completed secondary/middle school, 5 have completed vocational school, 20 graduated high-school, 16 completed primary school, and 17 are illiterate, etc. (Săvoiu, Manea and Simoni, 2008).

If we operate an intersection of the two profiles, most of the offenders and criminals are from the demographic profile of the unemployed, and this is an example of a process of intersection with profound social and managerial implications.

Supposing a managerial decision is envisioned to use probation as a solution to reduce prison spending, but also for the gradual integration of offenders and criminals into the social and economic environment, it will be found that both the above profiles can be significant as an informational support, and an operation of reuniting the two profiles will be needed.

The outstanding valences of the profiling method as an expression of the multidisciplinary applied approaches, and the growing utility of profiling projections and forecasts continuously extend the area of its various uses, and as a result of the finding that statistical profile has real qualities of managerial decision support.

2. THE MANAGEMENT OF INNOVATIVE EDUCATIONAL PROCESSES

"Change is the law of life. Those who look only to the

past or the present will certainly miss the future," said, almost 60 years ago, none other than John Kennedy.

In its contemporary sense, innovation is increasingly pragmatic, and more quickly turned into actuality. The innovation efforts become practical innovation in relatively fewer cases in relation to the expectations, and when they fail, especially in the educational processes, the cause is the managerial decision-making difference or the managerial culture gap between the aspirations of the teacher manager and the capacity of the innovative educational organization or entity.

Roy Rothwell, in his book "Managing Innovation and Change", published in 1991 and reprinted in 2002, 2003 and 2004, makes a retrospective analysis of the innovative, especially industrial, process (which the synoptic view intended by the present contribution adapted and integrated in the educational process), identifying no less than five successive generations that contributed to the maturation of both the process itself and its management:

a) the generation of teachers managers of the first two postwar decades (the first generation of "technology push", focused not so much on the new concept of research and development, or "R&D", which was in the early stages of of large-scale implementation of industrial innovation, and less educational innovation); b) the generation of the second half of the '60s, and also of the '70s (a generation experiencing the first attempts at rationalizing the technological and financial changes, no less than the increasing importance of long-term "R&D", and in the innovative educational processes, according to the opinions, relatively belated in relation to the staging of the original, namely those in 1984 of R.L. Daft & K.E. Weick, who practically identified four specific entities in relation to the relationships developed, proceeding from those that initiate a "perspective or visualisation not oriented on a long term", to those receiving the benefit of "conditioned" strategies, then the evolved alternative of the entities capable of making "discoveries in learning with a strategic impact", and, finally, to those able to "adopt original educational strategies"); c) the generation of the decade of the 80s (now the innovative axis describes innovation itself as a network meant to adapt to the internal and external environment of the educational entity, bringing together business and academic or research communities, and the educational entities in an administrative context, according to Rothwell and Zegveld, in 1982 and 1985); d) the generation of the decade of the 90s (when the computer-assisted educational processes become dominant, based on simulations and databases, innovative educational technologies, etc., as the 1992 paper of Rothwell indicates); e) the new generation after 2000 (where internet communication, social networking groups become educational components whose importance in the process is more and more significant, and the new information

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In education and the economy alike, "the most common source of error is ignoring side effects and long-term consequences," the authors of the ten principles of economic thought and economics emphasized in full fairness.

solutions focused on tablets and integrated phones are likely to be gradually assimilated, and educational space and time dilated, thus resizing the new innovative educational processes).

Henry Chesbrough, a professor at Berkeley University, seems to have been the first to use the term open innovation (in 2003), later taken over in a book containing the new innovative concept in its very title (Open Innovation, 2003), which generically redefined the fifth generation described above, and the new innovative educational system is increasingly linked to the concepts of networking, managerial IP, collaboration across networks and educational systems, corporate entrepreneurship of the new technologies, the absolute domination of the R&D, the more extended stock of basic knowledge and the information which is distributed exponentially, the need for an increasingly mobile and better educated workforce, and also for continuous educational processes, etc.

In terms of the innovative educational entity, management studies have long considered side-effects as a negative phenomenon (De Jong, Vanhaverbeke, Kalvet & Chesbrough, 2008).

The paradigm of open innovation ensures the premises for the entities to be able to benefit from the side effects by acquiring external knowledge, deliberately or through outsourcing of internal knowledge.

In a way, increased side effects suggest that it takes political interference to a lesser and lesser extent, yet, in a world of open innovation, political interventions have become more important than before.

The OP (Open Innovation) model is closely related to the model of innovation systems. Both models were developed in various disciplines of managerial content (from economy to education, market, quality assurance), and the similarities between these two specific contemporary paradigms or approaches cannot be denied.

In general, open innovation dictates entities and organizations how to make better use the growing stock of their knowledge. Open innovation provides a type of education with a permanent processing of the side effects, which can thus be anticipated (Gwartney and Stroup, 1993).

Similarity and complementarity between

models of open innovation (OI) and systems of innovation (IS)

Table no. 1. Open Innovation (OI)

(Chesbrough, 2003; Chesbrough, West & Vanhaverbeke, 2006)

Systems of Innovation (SI) (Lundvall, 1992; Edquist, 1997; O'Doherty & Arnold, 2003)

1.Entities get better results if they open innovative systemic process, where the external environment is also included.

1.Innovation is the result of complex and intense interactions between various internal and external actors.

2. Open innovation is no longer exclusively belongs to the R&D department. The initial stage of modelling, addressed traditionally, provided an incomplete picture of how innovation could be organized

2.The linear model, where the knowledge relating to activities are divided into supply and demand, is no longer appropriate, and has fewer and fewer of the systems.

3. Entities can benefit from a study of the purpose of input and output elements of knowledge. Dissemination of knowledge especially offers opportunities.

3.Dissemination of knowledge is essential to the functioning of the innovation system, and are very desirable. Functioning of innovation systems can be hampered by failures of capacity and network.

Entities need both internal innovation skills (other than R&D) and skills for connecting with the external environment in order to become competitive.

Functioning of innovation systems can be hampered by limited capability and network failures.

For entities increasingly dependent on external sources, infrastructural arrangements (e.g. intellectual property rights) and other general conditions of the work system are becoming increasingly important.

Functioning of innovation systems can be hampered by institutional failures, and also by the working system.

The increased mobility of the workforce and the presence of a trained workforce are important trends that erode the closed innovation model.

Human and social capital provide the lubricant needed to for the innovation system.

If the innovative entity cannot benefit internally from its innovations, maybe others will.

The social benefits of innovation exceed those of individual innovative actors.

Source: Chesbrough, 2003; Chesbrough, West & Vanhaverbeke, 2006; Lundvall, 1992; Edquist, 1997; O'Doherty & Arnold, 2003

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In a general sense, the similarity as well as complementarity between the two types of models, OI and SI, generating an increasingly extensive scientific literature devoted to innovative educational processes, reveals that previous failures, once discussed and analyzed by innovative systems (IS) can be used to legitimize policies favourable to open innovation (OI).

The paradigm of open innovation implies that entities should develop their internal competencies (e.g. those concerning corporate and entrepreneurship knowledge and experience), as well as their ability to have in-depth knowledge of the external sources (through defining competencies, skills or qualities, or through appropriate behaviour in networks, through collaboration, etc.).

Training decision-making skills (technical, interpersonal, relating to self-improvement) in innovative educational processes is therefore an important point of open innovation approaches.

A clear answer to a question about which might be the most effective manner of training decision-making skills in a truly innovative entity, which designs and provides the best experience, through exceptional qualities and knowledge, on a particular behavioural pattern dominated by sociability, principledness, responsiveness, courtesy, proper dress and morality, can be given only if the key instruments, techniques and methods are analyzed and selected, combined in the management of innovation processes, out of the wide range of managerial methods.

Once the decision-making skills formed appropriately, they will allow the teacher manager of the educational entity to imagine a future with realism and honesty and try to achieve it, realistically starting from what is currently available. 3. THE METHOD OF EDUCATION MANAGEMENT THROUGH PROFILES

The skills of the manager of an educational process,

resulting from the combination of the three statistical profiles, shaped by the opinions of the golden triangle in any educational system, the Romanian one included (student, parent, teacher) can serve as significant milestones in subsequent systematic training of managers.

To properly shape a complete profile, made up of the reunion of 3 distinct profiles, three samples were collected from the three natural populations involved in innovative educational processes: a sample of pupils / students dominated by students (Epupils and students) n1 = 168 people, (158 high-school students from all classes and 10 students

in the first year), a sample of parents (Eparents) n2 = 22 people, and a sample of teachers (Eteachers) n3 = 16 people. In the research proper, for each single profile different questionnaires were used as far as the total number of questions was concerned; the questionnaires of the three surveys conducted to delimit the statistical profile basically included:

a) Cpupils and students = 14 questions; b) Cparents = 18 questions; c) Cteachers = 21 questions.

Ever since the questionnaires were designed, the option was made to build a radial profile, and thus several individual options were possible for the same question in terms of methodology; finally, the result was analyzed in terms of maximum frequency with which a certain response was declared (grading both the unique answer and the two or three response variants identically, in order to have the maximum range optionally in the radial profile).

There are several questions in each questionnaire that clarify, from the very outset, the importance of the teacher manager in the innovation education process, namely in conceptualizing an adequate, quality-oriented education in accordance with the opinion of students, parents and teachers, but only a small fraction of all the questions were designed for the investigations related to training managerial skills in the innovative educational entities, being combined in the intersected profile of the teacher manager of the educational entity, namely only 10 questions, three from the questionnaire designed for the samples of students and parents, and four from the questionnaire devoted to the teachers.

A first question is reunited in the three samples, i.e. everybody’s opinion of about the similarity of content between a good school and a good manager, and another one, addressed to the teachers, concerning the reality of the fact that the manager encourages the initiatives of the other actors in the process (teachers, students and parents) faces, and is reunited with, the decisions and the opinions of the members of the student council, with the important decisions communicated directly, and also with the existence of integrated relations between manager teachers, teachers, pupils/students, and parents.

In the profile built by the pupils/students, correlated with the one built by the parents, the competent manager is placed under the level of the competent teacher, under the level of the school in point of tradition and even competence, and even under that of the competent colleagues, which was in a way natural as an association between student-parent opinions, given the information and the experience of the youngest respondents (Chart no. 1).

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Similarity good educational entity – good school head, and its hierarchy according to the opinion of pupils and students, correlated with that of parents

Chart no. 1

The students’ opinion is strongly influenced by the parents’ opinion of the role and importance of the manager as far as the quality of the innovative process in the educational entity is concerned, which can be seen both from the correlogram and the high value of R2 (the coefficient of determination, or R squared). Separately, the

students’ opinion is no longer correlated, even at medium intensity, with that of their parents (R below 0.2, signifying no correlation, as was natural). Further on, only the pupils’ /students’ sample and their opinions was pursued and analysed.

The strong correlation holding between the students’ and the parents’ opinion of the role of manager competence in

conceptualizing the quality of the innovative educational process

Chart no. 2

Correlation matrix between the pupils’ opinion and the parents’ opinion

PARENTS PUPILS

PARENTS 1.000000 0.889735PUPILS 0.889735 1.000000

Soft Used: Eviews

The teachers’ opinion is independent in relation to the

opinion of the pupils/students and the parents, and it is distinguished by its emphasis on two aspects, situated at near parity: tradition (revealed by competent teachers and

the pupils with results that confirm their skills), but also a teacher manager able to obtain information, material, human and financial resources apt to provide competitive innovative educational processes. The table summary of

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the data from the samples combined from the questions about manager the skills of the teacher manager in

innovative educational processes, is presented below:

Qualitative and quantitative elements of the manager teacher’s statistical profile

Table no. 2. No. Dimensions quantified and described in the statistical profile of management

(positive and negative) Positive values

Negative values

1 Similarity good school–good manager (Epupils) 17,09 - 82,91 2 Similarity good school–good manager (Eparents) 18,18 - 81,82 3 Similarity good school–good manager (Eteachers) 50,0 - 50,0 4 Decisions and opinions of the members of the student council (Epupils) 12,60 -13,92 5 Important decisions communicated directly (Eparents) 13,64 - 68,18 6 Sense of safety, order and discipline (Epupils/ students) 34,18 -52,53 7 Choosing traditional entity (Eparents) 4,55 - 40,91 8 Integrated relationships between manager teacher, teachers, students, parents (Eteachers) 68,75 - 31,25 9 Managerial training of the school head and performance of school Eteachers) 43,75 -56,25

10 Manager encourages the others’ initiatives (Eteachers) 50,0 - 50,0

A profile of the manager, drawn as a result of the reunited opinions of the sample of students/pupils, that of the parents, and that of the teachers is finally summarized along the following 10 dimensions:

1. similarity good school – good manager = 27 out of 158 points (17.09%) – pupils’ opinion (- 82.91% – lack of similarity) highlights a completely negative current dominant of the teacher manager’s skills in the education system tested;

2. similarity good school – good manager = 4 out of 22 points (18.18%) – parents’ opinion (- 81.82% – lack of similarity) expresses the same issue, but according to the parents’ opinion;

3. similarity good school – good manager = 8 out of 16 points (50.0%) – teachers’ opinion (- 50.0% – lack of similarity) shows a parity situation where finally the manager of the innovative educational process is ranged first in relation to tradition;

4. management decisions in the educational entity are in keeping with the opinion of the student council members = 20 of 158 points (12.60%) – students’ opinion (-13.92% –disregard in making decisions) highlights the existing difficulties of communication and consistent integration into the internal environment of the educational entity, when decisions are primarily aimed at management behaviour qualities.

5. decisions that are important to the educational process are communicated directly = 3 out of 22 points (13.64%) – parents’ opinion (- 68.18% – at the most during school in meetings, or none whatsoever) highlights the lack of trust in the actors of the educational process, identifying the need for adequate training of the skills reagarding experience and behaviour;

6. the sense of safety, order and discipline, together with there being no conflicts in the educational entity = 54 out of 158 points (34.18%) – students’ opinion (-52.53% – total absence of the above); all types of managerial skills

are involved here, requiring a more careful and thorough training, starting from skills, and up to knowledge, from experience, to behaviour;

7. choosing the educational entity is done based on it having a tradition = 1 out of 22 points (4.55%) – parents’ opinion, and 9 out of 22 points (- 40.91% because it is close to home (a factor external to the managerial and educational process); analogously, here, too, all the types of managerial skills are involved, requiring more careful training, from the training of the skills, to that of knowledge, experience, and behaviour;

8. the importance of integrated relationships teacher – teacher manager – pupils / students – parents = 11 out of 16 points (68.75%) – teachers’ opinion (- 31.25% – lack of importance of that relationship); this training dimension emphasizes the need for a new vision and perspective, for greater flexibility of thinking, sociability, principledness, courtesy, proper dress and morality, generating tradition in addition to increasingly diverse professional and managerial knowledge at the level of the teacher manager;

9. the school head’s management training has positively influenced the management team’s performance and that of the educational entity = 7 out of 16 (43.75%) – teachers’ opinion (-56.25% – no influence); the result of the statistical measuring shows that more work is needed with a view to training the manager;

10. the manager and the management team encourage the initiatives of the teachers, students and parents = 8 points out of 16 (50%) –teachers’ opinion (50% – doesn’t encourage the initiative of the others); some of the management skills and competence concerning responsiveness is already made, with a favorable impact on the innovative educational process.

A combined image of the two aspects, which are both positive and negative simultaneously, in the combined profile of the three samples, is shown in Chart no. 3.

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Statistical profile of the manager as a result of combined favourable and unfavourable opinions of the samples of students/pupils, parents and teachers

Chart no. 3

Dimensions described in the profile (positive or negative)

1 Similarity good school–good manager (Epupils) 2 Similarity good school–good manager (Eparents) 3 Similarity good school–good manager (Eteachers) 4 Decisions and opinion of student council members

(Epupils) 5 Important decisions communicated directly

(Eparents) 6 Feeling of safety, order and discipline (Epupils) 7 Choosing traditional entity (Eparents) 8 Integrated relations between manager teacher –

teachers – students – parents (Eteachers) 9 Head’s management training and performance of

school (Eteachers) 10 Manager encourages the others’ initiatives (Eteachers)Note: When there is parity, the positive value was

considered to be dominant over time.

Software used: Eviews The same statistical profile can be adequately

represented by means of the polar or radial chart: expressiveness and visibility are more pronounced at an analytical level or per size:

Radial statistical profile focusing on the positive and negative aspects of teacher manager

Chart no. 4. Chart no. 5.

Positive radial profile

0

20

40

60

801

2

3

4

5

6

7

8

9

10

Negative radial profile

‐100

‐80

‐60

‐40

‐20

01

2

3

4

5

6

7

8

9

10

The dimensions transfigured in axes 3, 8 and 10 of the

positive radial profile are the main generators of competitive managerial skills, with some potentialities in dimension 6, while the negative radial profile, which must be interpreted conversely, emphasizes that the most sensitive values are given by axes 1, 2, 5 and 9, with a significant impact in shaping the same so necessary

competences / skills of the school head and his/her management team in today’s Romanian education unit or entity.

The dimensions that have to be added to the statistical profile in the finding experiment to the component representing the opinions of the teachers are also those concerning the simultaneous access to all three main

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classes of skills in current managerial decision-making skills (25% favourable and 75% unfavourable), and also those detailed per classes of managerial skills: a) self-improvement skills (71.8% favorable and – 29.2% unfavorable); b) interpersonal and human skills (66.7% -33.3% favorable and unfavorable); c ) technical skills (37.5% favorable and – 62.5% unfavorable).

The advantages of the statistical method of the profiles applied statically can amplify through dynamic researches, which enable confrontation of the real competences of successive managers and their management teams, according to the information taken from the three key actors of contemporary innovative educational process: teachers, students and parents.

4. SYNTHETIC QUALITATIVE AND GENERAL RESULTS

Skills training is targeted to ensuring a set of qualities, with a greater degree of appropriacy for the actuality of education processes (intelligence, memory, sense of observation, vision and insight, flexibility of thinking, positive character traits, strongly balanced temperament), of some knowledge of practical applicability and quick access from the manager teacher (professional, managerial, economic, psychological, legal, political and ideological), and also by forming a decision-making component based on the experience in the educational process (of the managerial, professional, in the profile of the unit, political type) and a behaviour that is subject to the same innovative educational process (sociability, principledness, responsiveness, courtesy, proper dress, morality), not omitting the factors that can ensure good health to the teacher manager, who will be exposed to great efforts .

Following the analyses conducted using the statistical profile resulting from the three opinion samples, some of the features can be shaped of the process of training management skills in the innovative educational entities with a major impact in the development of this type of professional training particularly important for the innovative educational system.

In a first structural approach to the skills and capabilities that need to be possessed by the future managers in modern educational processes, human skills (especially the native ones) remain essential, while the importance of conceptual and technical skills significantly increases.

The contemporary educational entities in the national system (except for the elite ones, partly resulting from the shaping of a genuine morphic field of performance field, gathered by almost century-old traditions, inherited and maintained by performance management) confirms that the training of technical skills remains the main stumbling block of contemporary managerial decision-making; as a rule, these training efforts are accessed on average by only 4 managers teachers out of 10 (according to the opinions they expressed), usually limited to an effort of self-improvement and not going deeply into the area of advanced management studies, able to generate methodological certainties in the decision-making act.

Of course, there exist training deficiencies in shaping conceptual skills generating, by negative experiences, managerial behaviours suffering from ethical myopia, and even immorality in the framework of educational processes

exclusively aimed at performance, behaviours reported as early as the last century (Longeneker, 1985).

As a reality assessed in a multidisciplinary manner, through the method of the improved statistical profile resulted from the extended analysis of the teacher manager, it points out that, for example, only one in three school principals turns to account competitively his/her interpersonal skills, and only 3 in 10 self-improvement skills are used (virtually, in the combined statistical profile, only one in four managers accesses all three types of skills.

Certainly, at the back of these data it lies hidden the flimsiness of training management skills with all teachers, as the finding experiment emphasized.

I. Training the skills of the manager teacher must draw him/her ever closer to the concept of leadership, and the kind of leadership characteristic of innovative educational processes.

A teacher who possesses managerial skills and is committed, together with his/her management team, to create a new vision, with a unique personal motivation, and connects his/her inner strength in generalizing innovation, can be made into a real leader of the educational process.

As innovative educational leadership nearly always involves the initiation and propagation of change, this makes it the most suitable capitalize in innovative learning processes, virtually becoming the major target of successful training experiments.

Training focuses mainly on the elected leader’s inner strength, which quietly leads an educational organization, which it also develops.

Vision is gradually turning him/her into the main spokesman for the management team, who can substitute the educational entity in moments of decision, finding the appropriate formulas to motivate the organization, to create a joint development, with emphasis on the managerial skills harnessed to the practice of change.

Innovative educational leadership is defined as a sui generis creative activity, and therefore must identify itself with innovative educational processes.

A leader is formed as a supporter of encouraging the initiative and creativity of the people in his/her organization, generating their own ideas about the technical processes of education, and also about the external environment, which can validate or invalidate the educational products, or about the culture and internal processes in the educational organization.

Innovative educational leadership is also, by its very nature, an interpersonal activity. Interpersonal skills are crucial in forming a genuine leader.

Effective educational leaders make use of their time in the spirit of balance, or Paretian optimum, of the 20/80 type. An innovative educational leader decides in no more than 20% of his/her time, but after having communicated,

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for at least 80% of the time, with all the actors in the processes (teachers, students, parents), as well as with the beneficiaries of the educational process itself (companies, institutions, public opinion, etc.)

To do that, a teacher manager should be trained in the spirit of the organization, being able to effectively delegate responsibilities; moreover, they will not allow administrative tasks to consume time that would be better used in face-to-face discussions.

Innovative educational leadership becomes more effective when the people who are network nodes or professional reference points, relevant in the respective educational entity, accept and genuinely appreciate the innovative decisions. The leader is formed and acquires experience proceeding from building an initial consensus, and is gradually developing the courage needed to face the various currents of opinion, whenever this type of response is required. The problem of the teacher manager endowed with leadership skills is solved, and a leader’s training practically is completed when he/she has managed to form the reflex of correctly choosing the time and space for the right decision in order to achieve maximum impact in developing a leadership career. Most successful leaders, who state that were formed gradually, and learned to be in the right place at the right time to be able to take advantage of the particular configuration of their leadership skills within the educational process.

Many of them attribute their success to luck, out of excessive modesty, but in reality they have completed a process of training management skills that has developed leadership skills, which actually defines a true pyramid of leadership, bringing together inner skills by bringing inside (which provide the basis for leadership, the unique and perpetually innovative nature of the leader), leadership skills (which sets apart the leaders of innovative educational processes from common managers by training knowledge, in particular professional, managerial, psychological, economic and legal, as well as by the practical demonstration of the qualities needed to conduct

educational entities focusing on vision and perspective, flexibility of thinking, intelligence, memory, sense of observation, balanced temperament) and professional skills (experience and continuous learning).

II. Another trend needed in the process of training managers on a long-term basis, or innovative educational leaders, seems to be no longer allowing the practical existence of any way of training a teacher manager lacking the completeness of skills, i.e. failing to access all managerial skills, in both the theoretical and experimental stage, as well as in the actual innovative educational processes subsequent to the training.

III. In the interpersonal relationship manager–teachers it is essential to stimulate, by the teacher manager in question, i.e. by the innovative educational leader, the shaping of a critical attitude of the teachers (the finding experiment identified only a 8.2% share of teachers with a critical attitude with respect to management decisions) and the initiatives of the most important actors of the educational process (the analysis of the respondents in the sample answers of the statistical profile identified only 50% favourable responses).

IV. The process of training the teachers managers should be harmoniously included within the broader national process, aiming at actually training as many innovative educational leaders as possible.

5. A FINAL REMARK An integrated innovational educational system can be set

up through multidisciplinary methods, applied based on the essential elements of the innovative educational process; the gist of such an example is described in the figure below; it holds both a conclusive and integrative role, according to the results obtained by the method of the statistical profile, generalized and adapted to educational management.

Structure of an innovative* national educational system meant to train competitive managers Figure 1

EDUCATIONAL SUPPLY Producers of intermediate demand Consumers of educational services

ACTIVE ENTITIES Kindergartens Schools High schools Universities Research institutes Cultural institutions Health institutions Other units providing educational services

LIMITS, INFLUENCES AND AGENCIES IN PROCESS

Elementary classroom management as lower limit; Knowledge and technologies of innovative impact; Psychological and sociological impact on the dynamics of innovation Innovative educational leadership as upper limit

INFRASTRUCTURE Banking capital and investment attracted; Intellectual property; Innovations and innovative educational support Educational norms and standards for innovation

RESEARCH AND EDUCATION Training teachers managers

Innovative competences / skills 1. Qualities (vision and insight, flexibility of thinking, intelligence, memory, sense of observation, positive character traits, balanced temperament, etc.) 2. Knowledge (professional, legal, managerial, psychological, economic, political ideological). 3. Experience (professional, managerial, experience in the educational profile of the entity, in politics, etc.). 4. Behaviour (sociability, politeness, principledness, responsiveness, morality proper dress, etc.); 5. Health (good).

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REFERENCES

[1] Chesbrough, H., (2003). Open Innovation: The new imperative for creating and profiting from technology, Harvard Bussines School Press: Harvard, MA, pp.29-39 and 226

[2] Chesbrough, H., Vanhaverbeke, W. & West, J. Open Innovation: Researching a New Paradigm, (2006). Oxford University Press: Oxford, pp. 220-240.

[3] Daft, R. L. & Weick K. E. (1984). Toward a Model of Organizations as Interpretation Systems, Academy of Management Review, 9 (2), p. 284-295.

[4] De Jong, J. P.J., Vanhaverbeke, W., Kalvet, T. & Chesbrough, H., (2008). Policies for Open Innovation: Theory, Framework and Cases, Research Project funded by Vision ERA – Net, Helsinki, Finland.

[5] Edquist, C. (1997). Systems of Innovation: Technologies, Institutions and Organizations, Pinter Publishers: London, Routledge, pp. 1- 22.

[6] Gwartney, J.D. and Stroup, R. L. What Everyone Should Know About Economics and Prosperity, Published by The Fraser Institute in co-operation with the James Madison Institute, 1993. pp. 5- 125

[7] Longenecker, G.J. (1985). Management priorities and management ethics, Journal of Business Ethics. 4 (1), pp. 65 – 70.

[8] Lundvall, B., (1992). National Systems of Innovation. Towards a Theory of Innovation and Interactive Learning, Pinter Publishers: London.

[9] Odobleja, Ş. (1984). Introducere în logica rezonanţei,

Craiova, Ed. Scrisul românesc. [10] O’Doherty D. & Arnold, K., (2003). Understanding

Innovation: The Need for a Systemic Approach, The IPTS Report, 71 Sevilla, IPTS, pp. 29-36.

[11] Rothwell, R. and Zegveld, W. (1982). Industrial Innovation and Public Policy, preparing for the 1980s and the 1990s. London: Frances Pinter.

[12] Rothwell, R., Zegveld, W. (1985). Reindustrialization and Technology, UK Harlow: Longman Group Ltd,. P.136.

[13] Rothwell, R. (2002). Managing Innovation and Change, SAGE Publication Ltd., London: The Open University Press. 2nd Ed., p.178

[14] Săvoiu, G., Jaško, O., Dulanović, Z., Čudanov, M., Craciuneanu, V., (2008). The value of general methods, quantitative techniques and management models in professionalizing management, Management, no. 13 (49-50) 49-50/2008, Belgrade, pag. 5-12.

[15] Săvoiu, G., Jaško, O., Čudanov, M., (2009). Diversity of scientific quantitative, statiscal, and social methods, techniques and management models in management system, Management (Scyndecs index), no 52, pp.5 -15

[16] Săvoiu, G., Manea, C., Simoni, S., (2008). The Demographic, Sociological and Geographical Profile. The Role of the Profile Method in Contemporary Management, The 14th International Conference Nicolae Bălcescu Land Forces Academy Sibiu, 27-29.1. 2008, vol III, pp. 185-199.

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