Octogon Mathematical Magazine Celebrates 20 Years of ...matsefi/Octogon_pre/volumes/... ·...

OCTOGON MATHEMATICAL MAGAZINE

Vol. 20, No.1, April 2012, pp 3-31

Print: ISSN 1222-5657, Online: ISSN 2248-1893

http://www.uni-miskolc.hu/∼matsefi/Octogon/

3

Octogon Mathematical MagazineCelebrates 20 Years of Publication

D.M. Batinetu-Giurgiu and Neculai Stanciu 1

Dedicated to the 20th Anniversary of the Octogon MathematicalMagazine

ABSTRACT. This paper is a tribute to the journal Octogon Mathematical

Magazine who is celebrating its twentieth year of publication.

The first mathematical journal of the town Brasov (Brasso, Kronstadt)was founded by Mihaly Bencze in the year 1978, named Gamma. MihalyBencze was the editor-in-chief and the members of the editorial board werethe following: Constantin Ionescu-Tiu, Jozsef Sandor, Alexandru Lupas,Florentin Smarandache, Jozsef Benko, Alexandru Blaga, Zoltan Tuzson,Florin Popovici, Viorel Gh. Voda, Ovidiu Pop, E. Grosswald (USA), LeroyF. Meyers (USA), Francisco Bellot (Spain). Mihaly Bencze contributed toGamma with 9000 Proposed Problems, 150 Open Question and 250 articlesduring 12 volumes between 1978-1989. In April 1989 the Gamma journal wassuppressed by the Romanian Communist party for unclarified reasons, andtill 1983 it had a latency period functioning as a prohibited journal.

In 1993, Mihaly Bencze, laid down bases of the Octogon MathematicalMagazine written in English and became the legal successor of the formerGamma journal. During these years Octogon Mathematical Magazine ispublished two times a year in April and October.

Retrospective vs. Perspectives of the famous Octogon MathematicalMagazine, Remind vs. Remember the Past (see e.g. [1])Vol.1, No. 1, April 1993:

1Received: 02.04.20122010 Mathematics Subject Classification. 01A60, 01A61.Key words and phrases. Biography, bibliography.

4 D.M. Batinetu-Giurgiu and Neculai Stanciu

Editor: Mihaly Bencze. Associate Editors: Laszlo Zsido (Italy), FlorinPopovici (South Africa), Florentin Smarandache (USA), Jozsef Benko(Romania); Szilard Andras, Szabolcs Boros, Endre Fejer, Szilard Fekete,

Szilard Frohlich (USA), Andras Gyerko, Lehel Kovacs, Cornel Prahovean,Laszlo Tothpal. Front cover: Jakab Abraham. DTP: Fulgur Ltd., Brasov,Romania. Printed by NOVOTYP in Miercurea Ciuc. Copyright FulgurPublishers.

Contents: 4 Articles; 19 Proposed Problems; 5 Open questions.

The Present in an age of progress

Vol. 20, No. 1, April 2012:

Editor-In-Chief: Mihaly Bencze.

Editorial Board: Sefket Arslanagic (University of Sarajevo, Sarajevo,Bosnia and Herzegovina), D.M. Batinetu-Giurgiu (Editorial Board of GazetaMatematica, Bucharest, Romania), Jose Luis Dıaz-Barrero (UniversitatPolitechnica de Catalunya, Barcelona, Spain), Zhao Changjian (China JiliangUniversity, Hangzhou, China), Constantin Corduneanu (University of Texasat Arlington, Arlington, USA), Sever S. Dragomir (School of ComputerScience and Mathematics, Victoria University, Melbourne, Australia), PeterKortesi (University of Miskolc, Miskolc, Hungary), Preda Mihailescu(Mathematisches Institut, Universitaet Goettingen, Germany), Gao Minghze(Normal College of Jishou University, Hunan Jishou, China), Josip Pecaric(University of Zagreb, Zagreb, Croatia), Ovidiu T. Pop (National CollegeMihai Eminescu, Satu Mare, Romania), Themistocles M. Rassias (NationalTechnical University of Athens, Athen, Greece), Jozsef Sandor (Babes-BolyaiUniversity, Cluj-Napoca, Romania), Florentin Smarandache (University ofNew Mexico, New Mexico, USA), Laszlo Zsido (University of Rome, TorVergata, Roma, Italy), Shan-He Wu (Longyan University, Longyan, China).

DTP: Jozsef Wildt Mathematical Association & Edit Aranyi. Front cover:Lehel Kovacs.

Contents: 29 Articles; 890 Proposed Problems (PP.); 111 Open Questions(OQ.)

The number of all articles in these 20 years is 2360.

The number of all proposed problems in these 20 years is 20145.

Octogon Mathematical Magazine Celebrates 20 Years of Publication 5

The number of all open questions in these 20 years is 4151.

Topics covered: general, inequalities, history and biography, mathematicallogic and foundations, combinatorics, number theory, general algebraicsystems, real functions, integrations, geometry, and others in all areas ofpure and applied mathematics.

Aims and scope: Octogon Mathematical Magazine publishes high qualityoriginal research papers and survey articles, proposed problems and openquestions.

The Octogon Mathematical Magazine promote mathematical culture inthe world of the mathematical sciences and to facilitate the exchange ofresources.

The publishing process in the Octogon Mathematical Magazine beginswith the author’s idea for the work itself, continuing as a collaborationbetween the author and the editor as the work is created. As such, editing isa practice that includes creative skills, human relations, and a precise set ofmethods.

The title of the top editor at many publications may be known as theeditor in chief, executive editor, or simply the editor. A frequent andesteemed contributor to a magazine may acquire a title of editor at-large orcontributing editor.

The top editor sometimes has the title executive editor or editor-in-chief.This person is generally responsible for the content of the publication. Anexception is large newspapers, who usually have a separate editor for theeditorials and opinion pages to separate news reporting and editorial content.The editor-in-chief sets the publication standards for performance, andmotivates and develops the staff.

The editor-in-chief is also responsible for developing and maintaining thepublication budget. In concert with the publisher and the operatingcommittee, the editor-in-chief is responsible for strategic and operationalplanning.

The editor-in-chief is effectively the head of this magazine and hasconsiderable influence on its content. One of the great strengths of thepresent editorial team of Octogon is the ability of its members to cooperateon as a whole even if this team is a network of the fourteen universities, oneNational College and one from the editorial board of Gazeta Matematica,Bucharest, Romania.


Mihaly Bencze

Hard work, that is his secret: work, work and hard work on his part withthe blessing of having supporting parents and his family. But, this is not anisolated story - biographies of many great mathematicians testify how theywere successful because of perseverance and hard work. There is, of course,another side to the coin: since the hard-work habit is a valuable one, but itis not enough Genius is five percent inspiration and ninety-five percentperspiration. He has both: inspiration and perspiration, so what you candeduce from here?

Excellence in research is to put in as much hard work as the project mayrequire. Mihaly Bencze received his Ph.D in mathematics from CraiovaUniversity in 2010. To work on problems in mathematics and achieve successneeds determination and not to give up when hurdles arise. We all know howsome students tend to relinquish mathematics when it gets difficult. MihalyBencze is: the organizer of Rubiks contest (1980) , the president ofassociation Wildt Jozsef, the scientific leader of Fulgur publisher of Brasov(since 1993), the founder of the International Hungarian mathematicalCompetition, the founder of the Wildt Jozsef International MathematicalCompetition. Also he is editor-in-chief of 8 journals, editor to other 18


magazine and mentor for other 10 journals.

His creative work is amazing: has published over 800 articles, 12 booksand over 14.000 proposed problems and open questions in almost all thejournals with columns of Problems all over the world.

Mihaly Bencze has received the following awards:

•Man of the year 2003 (American Biographical Institute, USA), 2003.08.22

•Exclusive Nomination for The Contemporary Hall of Fame (AmericanBiographical Institute, USA), 2003.10.3

•American Medal of Honor (Governing Board of Editors of the AmericanBiographical Institute, USA), 2003.10.17; Man of the year 2004 (AmericanBiographical Institute, USA), 2004.07.01

•Nomination as International writer of the year 2004 (InternationalBiographical Centre, Cambridge, England), 2004.08.13

•International Peace Prize (United Cultural Convention, USA), 2004.12.03;

•International Peace Prize (United Cultural Convention, USA), 2005.02.04;

•Man of Achievement Award (American Biographical Institute, USA),2005.07.03;

•American Medal of Honor (Governing Board of Editors of the AmericanBiographical Institute, USA), 2005.07.24;

•Nomination as International Professional of the year 2005 (InternationalBiographical Centre, Cambridge, England), 2005.08.19;

•Man of the year 2005 (American Biographical Institute, USA), 2005;

•Top 100 Communications 2006 (International Centre, Cambridge,England), 2005.11.04;

•DiplomaA 110 years since the foundation of the Gazeta Matematicaawarded by the Board of the Society of Mathematical Sciences in Romania(S.S.M.R), in 2005

•Ezustgyopar dıj (Romaniai Magyar Pedagogusok Szovetsege, TelekiOktatasi Kozpont, Szovata, Romania), 2005.10.15;

•The Global Year of Excellence 2006 (International Centre, Cambridge,England), 2006.07.09;

•2000 Outstanding Intellectuals of the 20’s Century (International Centre,Cambridge, England), 2006.10.06;

•Man of the year 2006 (American Biographical Institute, USA), 2006;

•The World Medal of Freedom (American Biographical Institute, USA),2006.08.10;


•Gold Medal for Romania (American Biographical Institute, USA),2006.12.15;•Farkas Gyula-emlekerem (Kolozsvar Csıkszereda, Sapientia Egyetem,Romania), 2006.11.25;•Apaczaidıj (Romaniai Magyar Pedagogusok Szovetsege, Teleki OktatasiKozpont, Szovata Csıkszereda, Romania), 2006.12.12;•Gheorghe Lazar-diploma, I. fokozat, 2007;•International Peace Prize 2007 (The United Cultural Convention of USA) ;•Prize Beke Mano (Bolyai Janos Matematikai Tarsasag, Budapest, Ungaria),2008.•Prize Apaczai (Uniunea Democrata a Pedagogilor Maghiari din Romania,Centrul Teleki, Sovata, Miercurea Ciuc), 2008.10.18;•Prize Apaczai silver grade (Uniunea Democrata a Pedagogilor Maghiari dinRomania, Centrul Teleki, Sovata, 16 October 2010)•Miniszteri Elismero Oklevel (Nemzeti Eroforras Miniszteriuma, Dr. RaethyMiklos, Budapest, Ungaria, 12 March 2011.)

The fact that Mihaly Bencze, is a model for many pupils, students,teachers and colleagues was proved in this paper and others to (e.g [6] and[7]). It has been a great pleasure for us to have developed on ongoingfriendship with such a modest and such a refined and talentedmathematician.

Another important feature of his character is the fact that he does notupset anyone, not ever judge people, is always happy and respect all - andthat means for him to be human.


Sefket Arslanagic

Sefket Arslanagic has born in 1942 in Trebinje (Bosnia and Herzegovina)where he was attended the primary school and secondary school(gymnasium). Between 1963-1967 he was a student of the Faculty of sciencesand mathematics of the University of Sarajevo. He received his mastersdegree in 1982 in University of Zagreb (Croatia). In the winter of 1999 hereceived his Ph.D. from the University of Sarajevo, with a dissertation Theaspects of the work with mathematically gifted students (MGS).

He was a mathematics teacher in Gymnasium in Trebinje and a lecturer ofmathematics in University of Mostar (Bosnia and Herzegovina). In the timeof war in Bosnia and Herzegovina he was between 1993-1996 as the banishedperson in Berlin (Germany) where he was a participant and a lecturer inSeminar for mathematics and didactic of the Mathematical Institute ofHumboldt University in Berlin.

Starting September 1996, he worked at the Faculty of sciences andmathematics in University of Sarajevo where he is now a professor ofelementary mathematics and the methods of mathematics. In recognition ofhis work with gifted students, he was named by the Mathematical


Association of Bosnia and Herzegovina for the president of the Section forthe work with MGS.

He has published more than 600 (six hundred) mathematical problems in15 scientific journals. He is Editor in Chief of the mathematical journalTriangle (Bosnia and Herzegovina) and also member of the editorial boardsthree scientific journals. He has published 35 books and more than 400papers in journals all over the world.

Dumitru M. Batinetu-Giurgiu

D.M. Batinetu at the General Meeting of The Romanian MathematicalSociety (RMS) which was held in Bucharest on 17 March 2012, at BucharestUniversity

D.M. Batinetu was born on the 27-th of January, 1936, in the heart of theValley of Burnazului Danubian in the commune Pietrosani, the district ofVlasca, Romania. He is a dedicated problem solver (in the years 1954, 1955and 1956 he won the first prize for his activity of solving the most difficultproblems published in the Gazeta Matematica) and problem proposer (hepublished and proposed for publication over 3500 problems for variousmathematics magazine, contests, Olympiads or mathematics camps; also heis one of the Romanian teachers who proposed problems for I.M.O., e.g. the


12-th I.M.O. held in Budapest in 1970), who left strong marks on theproblemist community. His mathematical work covered a very wide range oftopics including almost all possible areas of mathematics ( see for exampleupdated list and the references from [2]), and now is devoted to inequalities.Even after retiring he has found more time to work on mathematicalproblems. His proposed problems and proposed solutions are alwayswell-organized, not only that, but he submits proposals regularly, which arealways well thought out and explained. There is no doubt that he is one ofthe best and prolific of Romanian problemist of the second half of the 20-thcentury. D.M. Batinetu is the third in the top contributors to GazetaMatematica, between two patterns of Gazeta Matematica. During his manyyears teaching high-school mathematics he defined (introduced) quite a fewconcepts in mathematics, namely: “Lalescu sequences, Lalescu functions,Lalescu well-balanced functions, Eulers type sequences, Ioachimescusequences, Ioachimescu constant, Ghermanescu sequences, Wallis sequences,Benczes sequences and others (see e.g. the excellent monograph Siruri,published by the Albatros Publishing House, in Bucharest, in 1979). Thisbook was a good starting point in the study of Matematics Analysis, formany young and distinguished mathematicians.

The most precious prizes to him are:

•Diploma of Excellence for the long mathematical valuable activity atGazeta Matematica and inside the S.S.M.R., awarded by S.S.M.R. in 2007.•Diploma The Centenary of Society of Mathematical Sciences in Romania,awarded by S.S.M.R in 2010.

The fact that D.M. Batinetu-Giurgiu, is a pattern for many students andteachers was proved also in the paper [2]. It has been a great pleasure for usto have developed on ongoing friendship with such a sensitive human beingand such a refined and talented mathematician.


Jose Luis Dıaz-Barrero

Jose Luis Dıaz was born in 1954 in La Sierra de Cazorla (Spain). He is adoctor in Mathematics receiving his degree from Polytechnical University ofCatalonia, with a doctoral dissertation entitled Characterization ofPolynomials by Reflection Coefficients.

Currently, he is in charge of bringing talented students to Centro deFormacin Interdisciplinaria Superior (CFIS) at Polytechnical University ofCatalonia (BARCELONA TECH) where he is a vice-dean. He is teachingMath courses at Polytechnical University of Catalonia since 1980. He ismember of several mathematical societies such as American MathematicalSociety, Fibonacci Association, Mathematical Association of America, RealSociedad Matematica Espanola, Romanian Mathematical Society andSocietat Catalana de Matematiques. He is also member of the OlympiadCommittee of the Spanish Royal Mathematical Society and an active trainerof Spanish students that attend to International Mathematical Contest atHigh School and University levels every year.

He has published more than 130 papers in many scientific journals andabout 600 problems and solutions in almost all the journals with columns ofProblems all over the world. Currently, he is co-editor of the columnProblemas y Soluciones of the Gaceta de la Real Sociedad MatematicaEspanola, co-editor in chief of Mathproblems, and the column Math


Competitions Corner of Octogon Mathematical Magazine.

He was awarded with a Top Cited Article 2005-2010 by Else-vier for hispaper entitled An improvement to Ostrowski root-finding method publishedin Applied Mathematics and Computation Vol. 173, No. 1, (2006) 450456.

He likes too much to walk through the mountains and to cookMediterranean cuisine recipes.

Zhao Changjian

Zhao Changjian has born in 1965 in Binzhou (China) where he wasattended the primary school and secondary school. Between 1984-1986 hewas a student of the Faculty of sciences and mathematics of the University ofBinzhou. He received his masters degree in 1995 in the East China NormalUniversity. In the spring of 2005 he received his Ph.D. from the University ofShanghai, with a doctoral dissertation Extremal Problems in Convex BodiesGeometry. He is a reward-gainers of the excellent PhD dissertations in


Shanghai.

Now, he is a mathematics professor. 1986-1998 lecturer in Binzhouteachers college. 1999-2004 associate professor in Binzhou University. 2005-professor of mathematics in China Jiliang university. 2006-2008 visitingscholar in department of mathematics of the university of Hong Kong. 2009-visiting professor in department of mathematics of the university of HongKong.

His projects: NSFC: National Natural Sciences Foundation of China(10791205). ZNSFC: Zhejiang Natural Sciences Foundation of China(Y605065). FEDZPC: Foundation of the Education Department of ZhejiangProvince of China (20050392). AMMYFSPC: The Academic Mainstay ofMiddle-age and Youth Foundation of Shandong Proving of China (200203).

He has published more than 150 papers in many scientific journals all overthe world (such as Proc. Amer. Math. Soc; Geom. Dedicata; Appl. MathLetters, and Sci. China.). He is the members of the editorial boards twoscientific journals (Theoretical Mathematics & Applications and GeometricalMethods in Science and Technology).

Constantin Corduneanu

Constatin Cordunenu has born on the 26-th of July, 1928, in Iasi,Romania. He is a famous researcher and teacher - one of the most known


Romanian mathematician of all the times. He graduated at Al. I. CuzaUniversity of Iasi, Faculty of Mathematics, in 1951 and obtained his Ph.D inmathematics at the same university in 1956.

Constatin Corduneanu is an Emeritus Professor at the University of Texasat Arlington, U.S.A. His association with Al. I. Cuza University of Iasilasted until 1977, a period in which he held position of assistant, lecturer,associate professor, professor, Dean of mathematics and Vice-Rector forresearch and graduate Studies, as well as some research positions with theMathematical Institute of the Romanian Academy in Iasi. He is the foundingEditor of Libertas Mathematica and for three years the newly createdinstitution which is known today as the University of Suceava, where he hasserved as a Rector over the period 1966-1967.

The researcher Professor C. Corduneanu, during his 60 years of activity,wrote over 200 articles and many books. His works have been mentioned inthe bibliography of researchers over 5500 times. He is corresponding memberof the Romanian Academy from 1974, and doctor honoris causa of thefollowing universities: Ovidius of Constanta, Alexandru Ioan Cuza of Iasi,Transylvania of Brasov, Stefan cel Mare of Suceava.

He had many other activities (see e.g. [4] and [5]), such as participating invarious national or international conferences (more than 100), paying shortvisits and talking about his research work in over 60 universities or instituteson all the continents except Australia and in over 20 countries (includingChina, Japan, Russia, Ukraine, England, France, Italy, Germany, Hungary,Poland, Portugal and Chile).


Sever S. Dragomir

Sever Silvestru Dragomir is professor at the School of Engineering andScience, Victoria University, Melbourne City, Australia. He obtained hisPh.D in mathematics at the Faculty of Mathematics, West University ofTimisoara, Romania.

Research Interests

Pure Mathematics:1. Classical Mathematical Analysis2. Convex Functions3. Best Approximation4. Numerical Integration5. Geometry of Banach Spaces6. Operator Theory7. Variational Methods8. Volterra Integral Equations9. Qualitative Theory of Differential Equations

Applied Mathematics:1. Information Theory and Coding2. Risk Theory3. Guessing Theory


4. Adaptive Quadrature Rules

5. Adaptive Cubature Rules

6. Numerical Methods for Differential Equations

7. Numerical Methods for PDEs

8. Game Theory

9. Kolmogorov Complexity

Peter Kortesi

Born in 1951 at Tg. Mures, has graduted the Bolyai Farkas SecondaryGrammar School, and got his diploma as mathematician at the Babes-BolyaiUniversity Cluj. He was teaching mathematics at the Vocational SecondarySchool No. 4. at Tg. Mures and delivered lectures at the Bolyai FarkasSecondary Grammar School as well. Since 1988, when he has moved with hisfamily to Hungary he is teaching at the Institute of Mathematics of theUniversity of Miskolc. His research interest is related to the study oftopological separation axioms in topological and algebraic structures, and tothe didactics of Mathematics. He has organized numerous internationalconferences like the junior Mathematical Congress (1996, 2000, 2002, 2006,2008, 2010, 2012), the Conference on the History of Mathematics andTeaching of Mathematics (2004, 2006, 2008, 2010, 2012) or the InternationalGeoGebra Conference and Workshop (2011, 2012). He is the coordinator ofthe CEEPUS Network Active Methods in the Teaching and Learning ofMathematics and Informatics involving about 30 universities form 10countries He is the president of the Junior Mathematical Society Miskolc,


and the leader of the GeoGebra Institute of Miskolc, He published theMathematical journal Pi, the Dynamical GeoGebra Journal, and is amember of board of the Creative Mathematics.

He is doctor in mathematics and currently is the secretary of the BorsodDivision of the Janos Bolyai Mathematical Society, the co-chair of theDepartment of Analysis and the network coordinator of the CEEPUSNetwork H 127 (www.uni-miskolc.hu/ceepush127).

He was the local chair of the 10th SEFI European Seminar onMathematics in Engineering(http://www.uni-miskolc.hu/uni/dept/gepesz/matematika/sefi-seminar/)and he was the organizer of the 3rd Conference History of Mathematics andTeaching of Mathematics(http://www.uni-miskolc.hu/uni/dept/gepesz/matematika/hmtm/).

Preda Mihailescu

He was born on May 23, 1955 and is a Romanian mathematician, bestknown for his proof of Catalans conjecture. After leaving Romania in 1973,he settled in Switzerland. Mihailescu studied mathematics and informatics inSwitzerland, receiving his Ph.D. from ETH Zurich in 1997. His thesis,Cyclotomy of rings and primality testing, was written under the direction ofErwin Engeler and Hendrik Lenstra.

For several years, Mihailescu did research at the University of Paderborn,


Germany. Since 2005 he is a professor at the Georg-August University ofGottingen.

In the summer of 1999, I heard of Catalans conjecture and obtained thefirst partial results, which had some impact. Two years later, in the fall of2001, I finished its proof. (Preda Mihailescu)

In 2011 Preda Mihailescu demonstrated other famous conjecture, i.e.Leopoldts conjecture for CM fields.And he will not stop here:

I work at a theory in mathematics that will catch very well; it will beuseful and welcome. It is under examination and professionals take time toverify it. If things are as I see them, there will be a deep simplification thatthe mathematicians will definitely enjoy. (Preda Mihailescu)

Gao Minghze

Gao Mingzhe has born in 1937 in Anxiang county of Hunan province(China) where he was attended the primary school and secondary school.Between 1962-1967, he was a student of the Department of Mathematics ofthe Hunan University where he received graduate. He was a mathematicsteacher in middle school between 1967-1978. Starting September 1979, heworks at Section of Mathematics in Xiangxi Education College fornationalities, where he was a lecturer between 1983-1986 and an associateprofessor between 1987-1998, where he won Zeng Xianzi Education Fund


Prize awarded by Ministry of Education in 1997. Since July 1999 he is aprofessor in Normal College of Jishou University. He was a reviewer ofAmerican Mathematical Reviews and membership of AMS. And he is namedinternational mathematician by UNESCO at Asia-Pacific area in September2005.

He established some new methods and new theory which the inequalitiesare studied by means of matrix theory and the weight function and analytictechnique, so that he made many achievements in studying foundationmathematics, such as some applications and the generalizations, extensionsand improvements of the famous Hilbert inequality, Hardy inequality, Holderinequality, Fan Ky inequality and Heisenbergs inequality etc.

He has published more than 200 papers in many scientific journals all overthe world (such as Proc. Amer. Math. Soc; ZAA (Germany); J. Math. Anal.Appl.; StudiaScientiarumMathematicarum Hungarica; MIA (Croatia);Integral Transforms And Special Functions, etc.).

Josip Pecaric

Josip Pecaric on the right with his wife Ankica Pecaric


Josip Pecaric (born September 03, 1948) is a Croatian Academician,mathematician and the professor of mathematics at the University of Zagreb,Croatia. He has written and co-authored over 800 articles on mathematics inmathematical journals, books, and conference proceedings. Josip Peari wasborn in Kotor (Boka Kotorska) on September 03, 1948 (In his documents itis written September 02, 1948) where he finished elementary and high school.Then he started studying at the University of Belgrade’s Faculty ofElectrical Engineering and he completed his masters degree in electricalengineering under the supervision of mathematics Professor Dobrilo Tosic.After that he decided to dedicate himself to pure mathematics.

In 1976, when Gradimir Milovanovic finished his doctoral degree, ProfessorDobrilo Tosiac gave him the copy of Milovanovic thesis and together withGradimir Milovanoviac he wrote his first two articles in 1976. ProfessorDragoslav Mitrinovic then invite him to work on his doctoral thesis. Hefinished the work on his thesis by 1979 but he succeed to get degree only in1982 because of series of attacks on his work.

He is one of the leading world experts in the theory of inequality, so inworld reference journals (in USA and Germany) he is called a great name inthe theory of inequality. He is the Editor-in-Chief and founder of theinternational journal Mathematical Inequalities and Applications, and theEditorial Board consists of about 60 of the most well-known world scientistdealing with the subject. He is a referee for about 60 international journalsand several publishing houses. In addition to his scientific work, academicianPeari is known for his journalistic activities. He is the author or co-author of250 newspaper articles, and 22 books dealing with journalistic or historicaltopics.


Ovidiu T. Pop

Ovidiu T. Pop, born on 4 March 1957 in Zalau, Salaj.

He is a teacher of mathematics at ”Mihai Eminescu” National College inSatu Mare, Romania.

Ovidiu T. Pop received his Ph.D. in mathematics in 2006. He is theauthor of more than 100 problems published in Gazeta Matematica - Seria Band of other problems and papers which appeared in Gazeta Matematica -Seria A, Revista de Matematica din Timisoara, Recreatii Matematice,Creatii Matematice, etc.

He has also published 125 papers, out of which 60 are research papers.

His research fields include the theory of linear positive operators.

In addition, he is co-author of 4 books and of more than 40 othermathematical books.

He has also written a monography of ”Mihai Eminescu” National Collegein Satu Mare and has published some essays.


Themistocles M. Rassias

Themistocles M. Rassias (born on April 2, 1951, in Pellana, Peloponnese,Greece) is a Greek mathematician, and a professor at the National TechnicalUniversity of Athens (E ), Greece. He has published more than 220 papers,6 research books and 30 edited volumes in research Mathematics as well as 4textbooks in Mathematics (in Greek) for university students. His researchwork has received a large number of citations by several mathematicians. Heserves as a member of the Editorial Board of several mathematical journals.

He received his Ph.D. in Mathematics from the University of California atBerkeley in June 1976. Professor Stephen Smale and Professor Shiing-ShenChern have been his thesis and academic advisors, respectively.

His work extends over several fields of Mathematical Analysis. It includesGlobal Analysis, Analysis on Manifolds, Calculus of Variations, NonlinearFunctional Analysis, Approximation Theory, Functional Equations,Inequalities, Metric Geometry and their Applications.

He has contributed a number of results in the stability of minimalsubmanifolds, in the solution of Ulam’s Problem for approximatehomomorphisms in Banach spaces, in the theory of isometric mappings inmetric spaces and in Complex analysis (Poincar’s inequality and harmonic


mappings).

Some of his research work has been established with the scientificterminology: (i) HyersUlamRassias stability of functional equations. (ii) TheAleksandrovRassias problem for isometric mappings.

Jozsef Sandor

He was born in 1956, Farcad (Forteni), near Szekelyudvarhely (Odorheiu-Secuiesc), Jud. Harghita, Romania. Elementary schools at Farcdand Bikafalva (Tureni); Middle school: Szkelyudvarhely. In 1980 graduatedat Babes- Bolyai University of Kolozsvar (Cluj). He worked at Nagyszeben(Sibiu) between 1980-1983, at Szekelyudvarhely between 1983-1996. From1997 he works at Babes-Bolyai University; from 1999 as an AssociateProfessor of Department of Mathematics.

His main research fields are : Mathematical analysis (convexity,generalizations and its applications in optimization theory; special functions,inequalities and applications; means and their applications); Number theory(elementary, asymptotic and algebraic study of arithmetic functions; numbertheoretical inequalities and applications; prime number theory andconnections; diophantine approximations, irrationality and transcendance;Diophantine equations); Geometry ( classical geometric theorems and


geometric inequalities; geometric inequalities and their applications); Historyof mathematics (Bolyai research; history of Transylvanian mathematics,XXth century history of mathematics).

He published 15 books of mathematics, the well known being Handbook ofNumber theory I, II at Kluwer Acad.Publ. (1996) and Springer Verlag (2005,2006)[ I. written in cooperation with D.S. Mitrinovic and B. Crstici; II. Incooperation with B. Crstici]; as well as Geometric theorems, diophantineequations and arithmetic functions (USA, 2002), with more editions. In 1988he published a book in Hungarian: Geometric inequalities (Ed.Dacia), whichevoked a large interest and has been cited by international journals andbooks. He has published along the years many scientific papers in prestigiousjournals from Romania, Hungary, Bulgaria, Croatia, Serbia, Montenegro,Bosnia, Kosovo, Polonia, Slovakia, Czech Republic, Germany, Switzerland,France, Netherlands, England, Portugal, Iran, India, China, Korea, Taiwan,Australia, Canada, Australia, USA. He also published methodical-scientificpapers , mostly in journals from Romania , Hungary, England and USA.Though he published many papers, he prefers quality in place of quantity,and originality of ideas.

Florentin Smarandache

Dr. Florentin Smarandache is a polymath: as author, co-author,translator, co-translator, editor, or co-editor of 160 books and 200 scientificpapers and notes.

Actually he is a Renaissance man since he published in many fields, such


as: mathematics (number theory, statistics, non-Euclidean geometry),computer science (artificial intelligence, information fusion), physics(quantum physics, particle physics), economics (cultural economics,poly-emporium theory), philosophy (neutrosophy a generalization ofdialectics, neutrosophic logic a generalization of intuitionistic fuzzy logic),social sciences (political essays), literature (poetry, prose, essays, novel,dramas, children plays, translations), arts (avant-garde/experimentaldrawings, collages, paintings).

He works as a Professor of Mathematics at the University of New Mexico,Gallup Campus, USA. On 22 September 2011, CERN researchers havepartially proved Smarandache Hypothesis that there is no speed barrier inthe universe, since the muon neutrino traveled faster than light.

Received the 2011 New Mexico Book Award for algebraic structures togetherwith Dr. W. B. Vasantha Kandasamy.Received in 2011 the Doctor Honoris Causa diploma (Adjunct Professor)from Beijing Jiaotong University and from Academia DacoRomana fromBucharest.Received the 2010 Telesio-Galilei Gold Medal for Science at the University ofPecs, Hungary. He is also a member of Romanian-American Academy ofScience.


Laszlo Zsido

Curriculum:

Place and date of birth: Brasov/Romania, February 22, 1946.

He participated for Romania at 5-th IMO held in Wroclaw, Poland in 1963,where obtained the Gold medal.

Master Degree at the University of Bucharest/Romania in 1968.

Other degrees: PhD at the University of Bucharest/Romania in 1973.

1968-1979: Research Fellow at several research instituts inBucharest/Romania.

1979-1980: Research Fellow at the University of Muenster/Germany.

1980-1990: Professor at the University of Stuttgart/Germany.

From 1990: Full Professor of Mathematical Analysis at the University ofRome ”Tor Vergata”.

Scientific activity:

Research in the field of Functional Analysis, mainly in Operator Algebrasand Spectral Theory of Linear Operators;

Other research fields: Harmonic Analysis, Generalized Functions, ErgodicTheory.

Scientific publications: more than 70 papers and 2 monographs.


Shan-He Wu

Position: Professor; Director of department of information and computationscience.

Address: Department of Mathematics and Computer Science, LongyanUniversity, Longyan, Fujian 364012, People’s Republic of China.

Email address: [email protected]

Editorial Responsibilities:

1. Octogon Mathematical Magazine

2. International Journal of Computational and Applied Mathematics

3. International Journal of Information Science and Computer Mathematics

4. Mathematical Reviews

5. Fujian Middle School Mathematics

Professional Societies:

1. A member of the American Mathematical Society, USA

2. A member of the Research Group in Mathematical Inequalities andApplications, Australia

3. A director of Chinese Society of Inequalities and Applications, P. R. China

Academic Interests:

1. Classical Mathematical Analysis

2. Theory of Mathematical Inequalities

3. Theory of Mathematical Mean Values


4. Theory of Convex Functions

5. Theory of Special Functions

6. Mathematics Education

Refereeing Services: for 16 other scientific journals of mathematics.

During these twenty years, apart from those mentioned above havecontributed to The Octogon Mathematical Magazine the followingmathematicians namely: Petrus Alexandrescu, Titu Andreescu, DorinAndrica, Krassimir T. Atanasov, Ovidiu Bagdasar, J. Gibergans-Baguena,Horia Banea, Catalin Barbu, Dorel Baitan, Dan Barbosu, MariaBatinetu-Giurgiu, Paraschiva Bırsan, Gheorghe Boroica, Szabolcs Boros,Vlad Ciobotariu-Boer, Nicolae I. Bratu, Ion Bursuc, Constantin Bue,Chao-Ping Chen, Nu-Chun, Eugen Constantinescu, Adrian Corduneanu,Viorel Cornea, Gheorghe Costovici, Thomas Csinta, Pal Peter Dalyay, GyulaDarvasi, Karoly Dane, Marian Dinca, Marius Dragan, Gheorghe Eckstein,Edit Egri, Paul Erdos, Bela Finta, Louis Funar, Sorin G. Gal, RomantaGhita, Ioan Ghita, Radu Gologan, Mehdi Hassani, Traian Ianculescu, RaduRazvan Ignat, Romeo Ilie, Attila Imre, W. B. Gabor Ivanka, Wei-DongJiang, Walther Janous, Andrei Jorza, Zeljko Juric, Ferenc Kacso, PauloKemp, Vasantha Kandasamy, Murray S. Klamkin, Omran Kouba, BelaKovacs, Jozsef Kramli, Valmir Krasniqi, Pal Aurel Kupan, Alexandru Lupas,Luciana Lupas, Maohua Le, Yin Li, Jian Liu, Florian Luca, I. V. Maftei,Dan Stefan Marinescu, J. Rubio-Massegu, Dorin Marghidanu Dragoljub M.Milosevic, George Miliakos, Nicusor Minculete, Laurentiu Modan, CristinelMortici, Hossein Moshtagh, Ovidiu Munteanu, Nicolaie Musuroia, TanaseNegoi, Memudu O. Olatinwo, Marius Olteanu, Moubinool Omarjee, ZhangQian, Laurentiu Panaitopol, Eugen Paltanea, Ion Patrascu, Lokot V.V.Phenchiva, Mihai Piticari, Alin Pop, Maria S. Pop, Rodica D. Pop, Emil C.Popa, Dan Popescu, Florin Popovici, Cornel Prahovean, Gabriel T.Prajitura, Eduard Puschin, Sorin Radulescu, Razvan Satnoianu, Ilka Sandor,Augustin Semenescu, Yilun Shang, Li Sheng, Neculai Stanciu, KalmanSzabo, Robert Szasz, Gyorgy Szollosy, Harun Siljak, Sabin Tabarca, TatianaTabarca, Marian Tetiva, Gheorghe Toader, Laszlo Toth, Janos Toth, TiberiuTrif, Mircea Trifu, Lucian Tutescu, Zoltan Tuzson, Marcel Tena, Ioan Tincu,Kramer Alpar-Vajk, Georg Weiss, Yu Wenxin, Yu-Dong Wu, Yu-Lin Wu,Yan-Qin Xu, Yu Wu-Yang, Yi Zhuxin and many others to which we have agreat recognition.

Everybody spends a fair amount of time on some scholarly activity. In


most cases, it involves research that is intended to be published in one ormore refereed journals. These mathematicians presented above are alsoexpert writers have written books and articles that describne fascinatingmathematical topics in an interesting manner.

The Octogon Mathematical Magazine has thousand-pages of researchpapers which often becomes the next hundred-pages articles and notes in apopular journals, and this keeps the volume of mathematics manageable,what can be accessible to the students, graduate students or their theachersof a future academic generation.

One might think that such magazine are of interest only the researchersand problem buffs, but this is not quite so. These articles, notes, proposedproblems and open questions created by mathematicians, often withconsiderable qualifications and experience, are used and adapted to becomeaccessible to a wide range of students and to foster some interestinginvestigations to highlight ideas, approaches and results, even if they cannotbe directly imported into general classroom situations, they can often bereworded. Even if the research cannot take into account all variables andcannot answer definitively all of the questions we might ask aboutmathematics, we can expect research in mathematics to be helpful in manyways. The research it can: answer questions, inform us, educate us, promitnew questions, create reflection and discussion, clarify situations, help makeeducational decisions, challenge what we currently do as educators, etc.Above all, despite educational research provides information that thecommunity of educators can use. Also we can use the research to shift fromthe Yesterday mind to the Tomorrow mind (see e.g. [3]).

Finally: The Octogon Mathematical Magazine is an inclusive professionalcommunity of researchers and teachers who promote research inmathematics. The Octogon Mathematical Magazine focuses on promotingresearch-based innovations related to preparation and continued professionalenhancement in mathematics. Target audiences include teachers, researchers,higher education, faculty members, the secondary, undergraduate andgraduate levels .

We are sure we speak on behalf of all lovers of mathematics when we say:

May all of you live long, and continue to write books, to submit articles,proposed problems and open questions to enjoy us.


REFERENCES

[1] The Octogon Mathematical Magazine is Ten Years Old or maybe 25?,Octogon Mathematical Magazine, Vol. 10, No. 1, April 2002, pp. 7-8;[2] Bencze Mihaly and Neculai Stanciu, Dumitru Batinetu-Giurgiu, OctogonMathematical Magazine, Vol. 19, No. 1, April 2011, pp. 125-148;[3] Dr. Terry Bergeson, Rosemary Fitton, Pete Bylsma, Beverly Neitzel andMary Ann Stine, Teaching and Learning Mathematics using Research toShift from the Yesterday Mind to the Tomorrow Mind, www.k12.wa.us;[4] Vasile Berinde, Interview with Professor Constatin Corduneanu, EMSNewsletter, December 2011, pp. 38-42;[5] Laurentiu Modan, Professor Constantin Corduneanu, a life dedicated tomathematics, Octogon Mathematical Magazine, Vol. 16, No.2, October 2008,pp. 1060-1078;[6] Neculai Stanciu, Mihaly Bencze - un matematician prolific - Revistaonline MateInfo.Ro, mai, 2011[7] Themistocles M. Rassias, Mihaly Bencze the Mathematician Is 50 YearsOld, Octogon Mathematical Magazine, Vol. 13, No.1, April 2005, pp. 16-67;*** Wikipedia, the free encyclopedia.

Department of MathematicsMatei Basarab National CollegeBucharest, Romania

E-mail: dmb [email protected] of Mathematics,George Emil Palade Secondary School,Buzau, RomaniaE-mail: [email protected]


Vol. 20, No.1, April 2012, pp 32-33



32

The Last Ten Years of OctogonMathematical Magazine

Jose Luis Dıaz–Barrero 2


No doubt that among the journals publishing columns of problems the onewith largest number of proposals and an entire section devoted to pose openquestions is Octogon Mathematical Magazine being its Editor in Chief, theprolific mathematician Mihaly Bencze, the main contributor to bothsections. Also a lot of papers and notes are published and since the year2005 a section with solutions is included. From now on, a new sectionentitled Math Competitions Corner will present interesting mathematicalproblems proposed previously in High School Mathematical Contests andUniversity Competitions or used by trainers and contestants to prepare MathCompetitions around the world.

Many topics of pure and applied mathematics are the usual subjects of thepapers and notes published in the last decade, but inequalities is withdifference which most frequently appeared. The journal is a good referenceto study or revisit inequalities from and elementary, but not trivial point ofview. A lot of new inequalities, generalizations and refinements of theclassical ones mainly discrete algebraic inequalities were published in the lastten years.

In this period of time no without difficulties the Editor in Chief and histeam of collaborators managed to publish yearly the two issues of the journalcontinuously. About one thousand and half of papers and short notes, fifteenthousand problems and three thousand open questions appeared.Furthermore, the proposals and solutions of Jozsef Wildt InternationalMathematical Competition (editions XIII to XXI) and book reviews werealso published. I encourage them to continue and I want to express mysincere gratitude for their task and hard work in the last decade.


The Last Ten Years of Octogon Mathematical Magazine 33

To continue publishing Octogon the Editor in Chief will be assisted by thefollowing international board of editors: Sefket Arslanagic (Bosnia andHerzegovina), D. M. Batinetu – Giurgiu (Romania), J. L. Dıaz-Barrero(Spain), Zhao Changjian (China), Constantin Corduneanu (USA), Sever S.Dragomir (Australia), Peter Kortesi (Hungary), Preda Mihailescu(Germany), Gao Minghze (China), Josip Pecaric (Croatia), T. M. Rassias(Greece), Ovidiu T. Pop (Romania), Jozsef Sandor (Romania), FlorentinSmarandache (USA), Laszlo Zsido (Italy) and Sanhe Wu (China). I am surethat they will help to keep and to improve the quality of the journal withtheir contributions and accurate comments and suggestions.

Applied Mathematics IIITechnical University of Catalonia (BARCELONA TECH)Jordi Girona 1-3, C2, 08034 Barcelona. SpainE-mail: [email protected]


Vol. 20, No.1, April 2012, pp 34



34

Happy Birthday Octogon!

Constantin Corduneanu 3


When Profesor Mihaly Bencze called my attention to the upcoming 20-thAnniversary of the Matheamtical Magazine OTOGON, I had the idea tovisit the library of our department, where I have displayed several copies ofthe publication, sent to me regularly since April, 1993. I have found allvolumes (two issues each, April and October) on the shelves. Thenmanyvolumes came online, and several times I have shared them with mycolleagues. Starting volume 3, I had the honor to be added to the group ofAssociate Editors, and for a few years I had the privilege to see also thename of the famous and omnipresent Hungarian mathematician Paul Erdos(whom I’ve met several times, for the first time in Bucharest, at the FourthCongress of Romanian Mathematicians, in 1956). It is really amazing to seehow the energy and the dedication of the founder and promoter of theOCTOGON, Professor Mihaly Bencze, from Sacele-Brasov, have producedand supported for two decades (so far) this publication. Indeed, most newjournals start with some support from an authoritative institution or groupof interestedand establishedscholars. But Professor Bencze, from his College,almost by himself, took upon himself the task to publish the OCTOGON,and he succeeded in short time to get an international readership, as well asa large number of authors from most everywhere in the World, whosubmitted their articles to the publication. I take this opportunity toaddress, in the name of people loving the Mathematics, and cultivating themin various forms, the Special Congratulations to Professor Mihaly Bencze, forhis outstanding achievement with this beautiful and useful O C T O G O N !

Needless to say that I had a great satisfaction seeing in this publicationmany names of former students, distinguished colleagues from most of theRomanian Universities, as well as an impressive number of contributors fromaround the World, whom I’ve met in various occasions.



Vol. 20, No.1, April 2012, pp 35



35

After ... 20 years

Ovidiu T. Pop 4


Professor Mihaly Bencze, PHD., was, is, and will always be a fighter. Hewas not defeated by the human wickedness or envy, or by the materialhardships of the existence, and he survived the tribute that he should havepaid to life.

Few from this world have the courage to publish, by themselves amathematical journal. A valuable journal! And why? Because theresponsibility and the effort to make it is huge!Mihaly had the courage, and he did it.Once upon a time

20 years ago, in Brasov, Romania, the first number of the OctogonMathematical Magazine appeared . First, it contained 16 pages, 4 articles,19 proposed problems and 5 open questions.

After that, from one number to another, the journal started to increasethe scientific level and value of the published articles.

Nowadays, the journal includes in the Editorial Board mathematiciansknown worldwide and it has collaborators all over the world. Theseattributes make the journal known at global level.

At this anniversary hour, I wish the Octogon Mathematical Magazine andeveryone who is beside it a sincerely Happy Anniversary!

National College “Mihai Eminescu“Satu Mare, Romania

4Received: 04.01.20122010 Mathematics Subject Classification. 01A60, 01A61.Key words and phrases. Biography, bibliography..

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