MINISTERUL EDUCAŢIEI, CERCETĂRII ȘI INOVĂRII

UNIVERSITATEA DIN ORADEA

FACULTATEA DE ŞTIINŢE

ABSTRACTS BOOKLET

INTERNATIONAL CONFERENCE

ON SCIENCES (Mathematics and Computer Science section)

November 12­13, 2009

organized by

University of Oradea, Romania

International Conference on SciencesNovember 12-13, 2009, Oradea, Romania

Organized byUniversity of OradeaFaculty of Sciences

Abstracts brochureMathematics and Computer Science sections

http://stiinte.uoradea.ro/conf2009/internationala/ICS2009.html

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Local organizing committeeRectorat of the University of Oradea Antal Cornel - RectorJurcut Teodor - Vice-rectorCurila Sorin - Scientific Secretary of the University

Faculty of Sciences Filip Sanda Monica - DeanGal Sorin - Vice-deanFodor Alexandrina - Scientific Secretary of the FacultyOros Horea - Conference Secretary

Scientific committee - Mathematics

• Dumitru Acu, Romania

• George Anastassiou, USA

• Mircea Balaj, Romania

• Adrian I. Ban, Romania

• Barnabas Bede, USA

• Alexandru M. Bica, Romania

• Daniel Breaz, Romania

• Gratiela Cicortas, Romania

• Sorin G. Gal, Romania

• Daniel Pasca, Romania

• Liviu H. Popescu, Romania

• Emil Schwab, USA

• Mihail Ursul, Romania

Topics in Mathematics

• Algebra and Applications

• Numerical Analysis and Applications

• Differential Equations and Applications

• Mathematical Analysis

• Probabilities

• Statistics

• Algorithms

Scientific committee - Computer Science

• Florian M. Boian, Romania

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• Mitica Craus, Romania

• Ioan Despi, Australia

• Dan Dumitrescu, Romania

• Mircea Marin, Japan

• Horea Oros, Romania

• Victor V. Patriciu, Romania

• Constantin Popescu, Romania

• Daniela Elena Popescu, Romania

• Pantelimon Stanica, USA

• Athanassios D. Styliadis, Greece

• Michael Gr. Vasssilakopoulos, Greece

Topics in Computer Science

• Internet Protocols

• Internet Based DataBases

• Software for Parallel and Distributed Systems

• Mobile and Wireless Computing

• Cryptography and Data Security

• Distributed Database

• Multimedia

Organizing committee

• Constantin Popescu

• Alexandru Bica

• Adriana Catas

• Eugen Laslo

• Alina Alb Lupas

• Delia Merca

• Horea Oros

Editorial board of this booklet

• Mircea Balaj, University of Oradea (mbalaj@uoradea.ro)

• Sorin G. Gal, University of Oradea (galso@uoradea.ro)

• Horea Oros, University of Oradea (horos@uoradea.ro)

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Contents

On a subclass of analytic functions defined by differential Salagean operatorAlina Alb Lupas, Adriana Catas 7

Enterprise software development using the REA modelAdrian Alexandrescu 7

Applications to discrete Morse theory: The collapsibility of CAT(0) hexagonalcomplexes of dimension 2Dorin Andrica, Ioana-Claudia Lazar 8

Some remarks on circle - valued morse functionsDorin Andrica, Dana Mangra 8

KKM families of set-valued mappings and their applicationsMircea Balaj 9

New numerical method for Hammerstein integral equationswith modified argumentAlexandru Mihai Bica 9

Low Degree Toom-Cook Multiplication in Characteristic ThreeMarco Bodrato 10

A solution for viscous flow on a vertical planeEmilia-Rodica Borsa, Diana Luiza Borsa 10

Univalence criteria for some general integral operatorsDaniel Breaz, Virgil Pescar, Nicoleta Breaz 11

Computing the Hilbert polynomial with NORMALIZWinfried Bruns, Bogdan Ichim 11

Some inclusion relations for a certain family of multivalent functions involvingnonhomogeneous Cauchy-Euler differential equationAdriana Catas 12

Convergence of the proximal point algorithm for variational inequalities withregular mappingsCorina L. Chiriac 12

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On the approximation by Jakimovski-Leviatan operatorsAlexandra Ciupa 13

Existence of solutions to quasilinear elliptic problems with boundary blow upDragos-Patru Covei 13

Solving a Cauchy problem with MATHEMATICAMircea Dragan, Simona Dragan, Sorin Muresan 14

Hillam algorithm to locate fixed pointsRaluca Efrem 15

The thermal dilatation of a silicon porous plateRemus D. Ene, Florica Ioana Dragomirescu 15

Norm extensions on the generalized semidirect productDorina Fechete, Ioan Fechete 16

On the geometrization of the Rheonomic Lagrangian mechanical systemsCamelia Frigioiu, Katica (Stevanovic) Hedrih 16

New properties for the p variables Stancu operatorsLoredana-Florentina Galea 17

The variational method of Schiffer-Goluzin in an extremal problem from theclass of the univalent functionsMiodrag Iovanov 17

Remarks on some metrical fixed point theoremsTania A. Lazar 18

Mk-type Estimates for maximal multilinear commutator ofBochner-Riesz operatorHuang Mingliang, Liu Lanzhe 18

A problem of approximation of the system reliabilityBogdan Gheorghe Munteanu 18

Numerical remarks on the Cauchy problemSorin Muresan, Octavia Nica 19

Study of nonlinear perturbation of the Laplacian via generalization contractionIon Marian Olaru 20

Strong differential subordinations and superordinationsGeorgia Irina Oros, Gheorghe Oros 20

Best subordinants of the strong differential superordinationGheorghe Oros, Adela Olimpia Taut 21

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Periodic solutions of second-order differential inclusions systems with (q,p)-LaplacianDaniel Pasca 22

Remarks on a mathematical approach of the vertical wind turbine with identicalbladesSonia Petrila, Balazs Albert 23

Optimization consideration on a parachute problemTitus Petrila, Balazs Albert 23

The behavior of the positive solutions of a nonlinear difference equationGheorghe Radu, Gheorghe Anton, Bogdan Gheorghe Munteanu 24

Topological classification for linear autonomous ODELiviu Horia Popescu 25

Hybrid models with time delay for the social diffusion. Numerical simulationAndrea Sandru, Dumitru Opris 25

Concomitants of order statistics for bivariate pseudo-gaussian distributionSaman Shahbaz, Muhammad Qaiser, Arif Rafiq, Ana Maria Acu 26

The calculus of variations for processes with independent incrementsNadia Mirela Stoian 26

On nonuniform stability for stochastic cocycle on Banach spacesDiana Stoica, Ludovic Dan Lemle 27

On a certain differential inequalityRoxana Sendrutiu 27

On necessary optimality conditions for Pareto minima in set-valued optimizationproblems with geometric constraintsRadu Strugariu 28

A note on a subclass of analytic functions defined by Ruscheweyh derivative andgeneralized Salagean operatorAlina Alb Lupas, Daniel Breaz 28

Some applications of sums of random variables in non-life insuranceMihaela Covrig, Daniela Ioana Todose, Emilia Titan 29

On some computational methods in risk theoryIulian Mircea, Mihaela Covrig 29

Author index 30

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On a subclass of analytic functions defined by differentialSalagean operator

Alina Alb Lupas, Adriana Catas

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: dalb@uoradea.ro, acatas@uoradea.ro

Abstract: By means of the Salagean differential operator we define a newclass BS(n, µ, α) involving functions f ∈ A. Parallel results, for some relatedclasses including the class of starlike and convex functions respectively, arealso obtained.Keywords: Analytic function, starlike function, convex function, Salageandifferential operator.2000 Mathematical Subject Classification: 30C45

Enterprise software development using the REA model

Adrian Alexandrescu

“Ovidius” University of ConstantaMathematics and Informatics DepartmentE-mail: adi alex cta@yahoo.com

Abstract: The REA (Resources-Events-Agents) model describes the eco-nomic processes, using a set of concepts: economic resource, economic agent,economic event, commitment, contract, etc. REA was originally proposed asa generalized accounting model, by William E. McCarthy of Michigan StateUniversity, in 1982. Since then, the original REA model has been extendedby McCarthy and Guido Geerts to a framework for business systems. REAbecame the foundation for several interchange standards. The paper proposesa development process for the enterprise software, using the concepts of theREA model.Keywords: Enterprise Ontology, Enterprise Software Application, Concep-tual Modeling, Software Engineering

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Applications to discrete Morse theory: The collapsibility ofCAT(0) hexagonal complexes of dimension 2

Dorin Andrica, Ioana-Claudia Lazar

“Babes-Bolyai” UniversityDepartment of Geometry400084 M. Kogalniceanu 1, Cluj-Napoca, RomaniaE-mail: dandrica@math.ubbcluj.ro, lioana@math.ubbcluj.ro

Abstract: We find necessary and sufficient conditions for the collapsibilityof a finite hexagonal complex of dimension 2. Our main result states thatany CAT(0) hexagonal complex of dimension 2 is collapsible. Our proof usesdiscrete Morse theory.Keywords: Hexagonal complex, collapsibility, CAT(0) inequality, discreteMorse function.2000 Mathematics Subject Classification: 53C21.

Some remarks on circle - valued morse functions

Dorin Andrica, Dana Mangra

”Babes-Bolyai” UniversityDepartment of Geometry400084 M. Kogalniceanu 1, Cluj-Napoca, RomaniaE-mail: dandrica@math.ubbcluj.ro, mdm dana@yahoo.com

Abstract: In this paper we consider the ϕF - category associated to thefamily of circle - valued Morse functions defined on a closed manifold M . It iscalled the Morse-Smale characteristic of manifold M for circle-valued Morsefunctions and it is denoted by γs1(M). In this note we present some basicnotions and results concerning circle-valued Morse functions and we provesome proprieties for γs1(M).Keywords: circle - valued Morse functions; ϕ - category; Morse - Smalecharacteristic.2000 Mathematics Subject Classification: 58E05; 57R70; 57R45.

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KKM families of set-valued mappings and their applications

Mircea Balaj

University of OradeaDepartment of Mathematics and Computer410087 Oradea, RomaniaE-mail: mbalaj@uoradea.ro

Abstract: In this paper we introduce a new KKM concept for families ofset- valued mappings. This permit us to obtain a common fixed point theoremfor a family of set- valued mappings, existence theorems for the solutions oftwo types of vector equilibrium problems, a Ky Fan-type minimax inequalityand a generalization of a known result due to Iohvidov.Keywords: KMM family of set-valued mappings, common fixed point, equi-librium problem, minimax.2000 Mathematics Subject Classification: 47H10, 54H25.

New numerical method for Hammerstein integral equationswith modified argument

Alexandru Mihai Bica

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: abica@uoradea.ro, smbica@yahoo.com

Abstract: A numerical method based on succesive approximations, quadra-ture rule and piecewise linear interpolation, for nonlinear Hammerstein inte-gral equations with variable modification of the argument is obtained. Theconvergence and the stability of the method is proved by the apriori errorestimation obtained in the case of Lipschitzian functions without smoothnessconditions. A practical stopping criterion of the algorithm and a numericalexample illustrating the method are given.Keywords and phrases : nonlinear Hammerstein integral equations withmodified argument, successive approximations, quadrature rule, piecewise lin-ear interpolation.2000 AMS Mathematics Subject Classification : 34K28.

We investigate the nonlinear Hammerstein integral equation of second type, with modifiedargument,

x (t) = g (t) +

b∫

a

H(t, s) · f(s, x (s) , x (ϕ (s)))ds (1)

where g, ϕ : [a, b] → R are given and have the properties: g, ϕ ∈ C[a, b], ϕ ([a, b]) ⊂ [a, b].Supposing that H ∈ C ([a, b]× [a, b]) , f ∈ C([a, b]×R×R), M > 0 is such that |f (s, u, v)| ≤ M,

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for all s ∈ [a, b], u, v ∈ R and g, ϕ, H, f are Lipschitzian in each argument, we construct aconvergent numerical method and a corresponding algorithm to approximate the solution of(1). The method combines successive approximations, trapezoidal quadrature rule and iteratedpiecewise linear interpolation. The interpolation procedure appears only on the points wherethe argument is modified.

Low Degree Toom-Cook Multiplication in Characteristic Three

Marco Bodrato

Centro Interdipartimentle “Vito Volterra”Universita di Roma Tor VergataVia Columbia 2 – 00133 Rome, ItalyE-mail: bodrato@mail.dm.unipi.it

Abstract: The use of Toom-Cook sub-quadratic polynomial multiplicationwas recently shown to be possible also when the coefficient field does not haveelements enough, particularly for F2[x]. This paper focus on how Toom’sstrategies can be adapted to polynomials on ternary fields. In particular wedescribe the Toom-3 algorithm for F3[x] some other unbalanced algorithms.Algorithms are described with full details, not only the asymptotic complexityis given, but the exact sequence of operations for possibly optimal implemen-tations.Algorithms given here for F3[x] perfectly works, as well, for F3n [x], and maybe useful for computations inside F3n for large enough n.Keywords: Polynomial multiplication, finite fields, Toom-Cook, Karatsuba,optimal, convolution, squaring.AMS Subject Classication: 11A05, 12E30, 11T99, 12Y05

A solution for viscous flow on a vertical plane

Emilia-Rodica Borsa, Diana Luiza Borsa

Department of Mathematics and Computer ScienceUniversity of OradeaUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: eborsa@uoradea.ro

Abstract: In this paper we use a thin-film approximation to study the steadyflow of a thin trickle of viscous fluid down a near-vertical plane, gravity maybe considered the main driving force, but surface tension cannot be neglected.Keywords: viscous fluid, thin film approximation, surface tension gradient.2000 Mathematical Subject Classification: 76D08, 76D05, 76D27,76D45.

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Univalence criteria for some general integral operators

Daniel Breaz, Virgil Pescar, Nicoleta Breaz

Daniel Breaz, Nicoleta Breaz”1 Decembrie 1918” University of Alba IuliaDepartment of Mathematics510009 Alba Iulia, RomaniaE-mail: dbreaz@uab.ro, nbreaz@uab.ro

Virgil Pescar”Transilvania” University of BrasovDepartment of Mathematics500091 Brasov, Romania E-mail: virgilpescar@unitbv.ro

Abstract: In view of some integral operators Tα,β,Hγ1,γ2,...,γn,β,n for analyticfunctions f in the open unit disk U , sufficient conditions for univalence of theseintegral operators are discussed.

Computing the Hilbert polynomial with NORMALIZ

Winfried Bruns, Bogdan Ichim

Winfried BrunsUniversitat Osnabruck, FB Mathematik/Informatik49069 Osnabruck, GermanyE-mail: winfried@math.uos.de

Bogdan IchimInstitute of Mathematics, C.P. 1-76470700 Bucharest, RomaniaE-mail: bogdan.ichim@imar.ro

Abstract: Normaliz is a program for solving linear systems of inequali-ties. We present the ideas used in the implementation of the program for thecomputation of the Hilbert polynomial of an affine monoid.2000 Mathematical Subject Classification: Primary 05E99, 15A39; Sec-ondary 90C10

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Some inclusion relations for a certain family of multivalentfunctions involving nonhomogeneous Cauchy-Euler differential

equation

Adriana Catas

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: acatas@uoradea.ro

Abstract: By making use of multiplier transformations, a new subclass ofp-valent functions in the open unit disc is introduced. The main results of thepresent paper provide various interesting properties of functions belonging tothe new class. Some of these properties include, for example, several inclu-sion relationships, integral properties and modified Hadamard product for thefunction class which is considered here. Relevant connections of some of theresults obtained in this paper with those in earlier works are also provided.Keywords: analytic function, multiplier transformations, inclusion relation-ships, integral operator, modified Hadamard product.AMS Subject Classification: 30C45.

Convergence of the proximal point algorithm for variationalinequalities with regular mappings

Corina L. Chiriac

BIOTERRA University, BucharestRomaniaE-mail: corinalchiriac@yahoo.com

Abstract: In this paper we consider a general version of the proximal pointalgorithm for solving the variational inequality: find c ∈ C such that thereexists y ∈ T (x) with

〈x− u, y〉 ≤ 0,∀u ∈ C (1)

where T : X → 2X∗is a set-valued mapping from a Banach space X with its

dual X∗, and C ⊂ X a closed, convex subset. First, choose any sequence offunctions fn : X → X∗ are Lipschitz continuous. Then take an initial elementx0 ∈ C ∩D(T ); given x , define xn+1 by the inclusion

0 ∈ (T + NC + fn)(xn+1)− fn(xn), (2)

where NC(•) is the normality operator associated to C.We prove that if the Lipschitz constants of fn are bounded by half the recip-rocal of the modulus of regularity of T , then there exits a neighborhood V ofx (x being a solution to (1)) such that for each initial point x0 ∈ V one canfind a sequence xn generated by the algorithm (2) which is linearly convergentto x. Convergence results are studied for the cases when the mapping T isstrongly subregular and strongly regular.

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On the approximation by Jakimovski-Leviatan operators

Alexandra Ciupa

Technical University, Cluj-NapocaCluj-Napoca, RomaniaE-mail: Ciupa.Alexandra@math.utcluj.ro

Abstract: We consider a modified Jakimovski-Leviatan operator in expo-nential weighted space of functions of one variable. We give a theorem onpoint-convergence of the considered sequence of operators and we prove thatthe operator has convexity preserving properties.Keywords: Modified Szasz-Mirakjan operators, exponential weight.AMS Subject Classification (2000) 41A36

Existence of solutions to quasilinear elliptic problems withboundary blow up

Dragos-Patru Covei

University Constantin Brancusi of Tg-JiuFaculty of EngeneeringBld. Republicii 1, 210152, Tg-Jiu, RomaniaE-mail: dragoscovei77@yahoo.com

Abstract: This paper studies existence of solutions to quasilinear ellipticproblems on bounded domains which blow up at the boundary. The differentialoperator is the p-Laplacian and the source is assumed to be positive andincreasing.Keywords: Existence of solution.2000 Mathematics Subject Classification: Primary: 35J60;

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Solving a Cauchy problem with MATHEMATICA

Mircea Dragan, Simona Dragan, Sorin Muresan

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: smuresan@uoradea.ro

Abstract: In this paper we want to give a refinement of some classical resulton numerical approximation for the solution of a Cauchy problem. So, weconsider the problem

x′ (t) = f (t, x (t)) , t ∈ [t0, T ]

x (t0) = x0.(1)

It’s known that x (t) is solution of (1) iff x (t) is fixed point of the Volterraintegral operator

V : C [t0, T ] → C [t0, T ] , V (x (t)) = x0 +

t∫

t0

f (s, x (s)) ds

and, from this, we obtain that x (t) is also the zero for the operator

S : C [t0, T ] → C [t0, T ] , S (x (t)) = x (t)− x0 −t∫

t0

f (s, x (s)) ds. (2)

Just like in the classical numerical results we consider the knots:

t0 < t1 < ... < tN = T

not necesarily having the same distance between them. Hence we will approx-imate x (t) by the function x (t) which have

x (ti) = x (ti) ≡ xi, for all i = 0, N.

Using (2) we find the implicit recurrence relation

xi+1 = xi +

ti+1∫

ti

f (s, x (s)) ds.

We want to give an explicit recurrence relation which contains the partialderivative of f and which can be implemented with MATHEMATICA.Keywords: Cauchy problem, Volterra integral operator, differentiability2000AMS Classification: 65L05

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Hillam algorithm to locate fixed points

Raluca Efrem

University of CraiovaDepartment of Mathematics, Faculty of Mathematics and InformaticsStr. A.I. Cuza, No.13, 400575, Craiova, RomaniaE-mail: ra efrem@yahoo.com

Abstract: Dynamical systems allow to model various phenomena or pro-cesses by only describing their way of evolution. It is an important matter tostudy the global and the limit behavior of such systems. A possible descriptionof this limit behavior is via the limit sets.The first step in analyzing a dynamical system is to determine the location andthe stability type of the limit sets. The most common method is the manualsearch for limit sets. When a researcher looks for new behavior in a system,he typically use a simulation program that display trajectories or orbits. Hechange the parameters or the initial condition, and he lets the system run un-til it reach the steady state. When the approximate location of an interestinglimit set has been found, he applies more sophisticated methods to calculateits precise position.The most practical and simplest method in locating a limit set is to applynumerical algorithms. The main advantages of this approach are the rapidrate of convergence and the ability to locate stable, nonstable and unstablelimit sets.In this paper we will present an algorithm that help us to locate fixed points,we build his Maple code, and implement him on an example.Keywords: dynamical system, fixed point, numerical algorithmAMS Subject Classification: 37N30, 37M05

The thermal dilatation of a silicon porous plate

Remus D. Ene, Florica Ioana Dragomirescu

“Politehnica” University of TimisoaraDepartment of MathematicsRomaniaE-mail: eneremus@gmail.com

Abstract: A mathematical model describing the thermal oxidation of aporous silicon is presented. The thermal stresses that appear during thegrowth of the oxide (due to the dilatation in volume), as well as those generatedduring the decreasing of the plate’s temperature (due to the thermal dilatationdifferences between the oxide and the plate) are numerically modelled.Keywords: silicon porous plates, thermal stresses.2000 AMS Mathematics Subject Classification: 74K20, 74N15.

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Norm extensions on the generalized semidirect product

Dorina Fechete, Ioan Fechete

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: iifechete@yahoo.com

Abstract: If G is a left R - module and α, β are an antiendomorphism,respectively an endomorphism of the unitary ring R which satisfies the identityα (a) · β (b) = β (b) · α (a) , we can construct on the direct product R ×G (ofthe additive groups R and G) a ring structure by setting the multiplication(a, x) · (b, y) = (ab, α (b) · x + β (a) · y) . This ring is denoted by Rnβ

α G and iscalled the generalized semidirect product (with respect to α and β) of R andG. In this paper, we give a family of pseudo-norms of the ring R nβ

α G, (inthe case that R and G are a pseudo-normed ring, respectively group) whichextends the pseudo-norms of R and G.

On the geometrization of the Rheonomic Lagrangianmechanical systems

Camelia Frigioiu, Katica (Stevanovic) Hedrih

Camelia FrigioiuDunarea de Jos University of Galati, RomaniaFaculty of SciencesStr. Domneasca nr 47, Galati - 800008, RomaniaE-mail: cfrigioiu@ugal.ro

Katica (Stevanovic) HedrihUniversity of Nis, SerbiaFaculty of Mechanical EngineeringMathematical Institute SANU BelgradeUl. Vojvode Tankosica 3/22, 18 000 - Nis, SerbiaE-mail: katica@masfak.ni.ac.yu

Abstract: In this paper using the Lagrangian rheonomic geometries onestudies the dynamical system of a rheonomic nonconservative mechanical sys-tem, whose evolution curves are given, on the phase space TM × R, by La-grange equations.Keywords: rheonomic Lagrange space, nonlinear connection, mechanical sys-tem, Lagrange’s equations.AMS Classification: 70H03, 70F20, 53C44, 58B20

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New properties for the p variables Stancu operators

Loredana-Florentina Galea

Agora University of OradeaPiata Tineretului no.8, 410526, Oradea, RomaniaE-mail: galea.loredana@gmail.com

Abstract: In this paper we are concerned with a general class of linearpositive operators. Based on the results of the weakly Picard operators theoryour aim is to study the good and special weakly Picard operators convergenceand some properties of the iterates of p variables Stancu operators.Keywords: weakly Picard operators, good weakly Picard operators, specialweakly Picard operators.2000 AMS Mathematics Subject Classification: 47H10, 41A10, 39H12.

The variational method of Schiffer-Goluzin in an extremalproblem from the class of the univalent functions

Miodrag Iovanov

”Constantin Brancusi University of Targu-JiuE-mail: miovanov@utgjiu.ro, iovanovm@yahoo.com

Abstract: Let S be the class of functions f(z) = z + a2z2 + · · · , f (0) =

0 , f′(0) = 1 which are regular and univalent in the unit disk |z| < 1.

For 0 ≤ x ≤ a < 1 we consider the equation Re[(x− a)f(x)] = 0 f ∈ S.Denote ϕ(x) = Re[(x − a)f(x)]. Because ϕ(0) = 0 and ϕ(a) = 0 it followsthat there is x0 ∈ (0, a) so that: ϕ

′(x0) = 0.

The aim of this paper is to find maxx|ϕ′(x) = 0.If x is maxx|ϕ′(x) = 0 , then for x > x the equation ϕ

′(x) = 0 does not have

real roots. Since S is a compact class, there exists.This problem was first proposed by Petru T. Mocanu in [2]. We will determineby using the variational method of Schiffer-Goluzin [1].Keywords: regular function, variational method, extremal function.

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Remarks on some metrical fixed point theorems

Tania A. Lazar

Commercial Academy Satu Mare, RomaniaSt. Mihai Eminescu 5, Satu-Mare, RomaniaE-mail: tanialazar@yahoo.com

Abstract: The purpose of this paper is to give another proof for somewell-known fixed point theorems in the literature. Our result extend a recentapproach of R.S. Palais.Keywords: fixed point, Reich‘s theorem, ϕ-contraction.Mathematics Subject Classification 2000: 47H10,54H25.

Mk-type Estimates for maximal multilinear commutator ofBochner-Riesz operator

Huang Mingliang, Liu Lanzhe

Changsha University of Science and TechnologyDepartment of MathematicsChangsha, 410077, P.R.of ChinaE-mail: ming62109@sina.com, lanzheliu@163.com

Abstract: In this paper, we prove the Mk-type inequality for maximalmultilinear commutator related to Bochner-Riesz operator. By using the Mk-type inequality, we obtain the weighted Lp-norm inequality and the weightedestimates on the generalized Morrey spaces for the maximal multilinear com-mutator.Keywords: Maximal multilinear commutator; Bochner-Riesz operator; BMO;Mk-type estimates; Morrey spaces; A1-weight.

A problem of approximation of the system reliability

Bogdan Gheorghe Munteanu

Henri Coanda Air Forces AcademyDepartment of Fundamental Sciences160 Mihai Viteazu St., Brasov, RomaniaE-mail: munteanu77@yahoo.com

Abstract: The reliability of a system with two reparable components is in-vestigated. In order to study the probabilistic behaviour, we assume that theevolution of the system is of a Markov type (for example: birth and deathprocess).Keywords: reliability, limit theorems.AMS Subject Classification: 62K10, 60F05.

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Numerical remarks on the Cauchy problem

Sorin Muresan, Octavia Nica

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: smuresan@uoradea.ro

Abstract: In this paper we compare, from numerical analysis point of view,two methods which solve the Cauchy problem

x′ (t) = f (t, x (t)) , t ∈ [t0, t1]x (t0) = x0.

(1)

Firstly, it’s known that the function x (t) ∈ C [t0, t1] is a solution of (1) iff x (t)is a fixed point of Volterra integral operator

V : C [t0, t1] → C [t0, t1] , V (x) (t) = x0 +

t∫

t0

f (s, x (s)) ds.

Secondly, in [3], T. Burton suggest to find the solution x (t) of (1) using thefixed points of the operator

B : C [t0, t1] → C [t0, t1] , B (v) (t) = f

t, x0 +

t∫

t0

v (s) ds

.

Keywords: Cauchy problem, Picard iterations, Volterra integral operator2000 AMS Classification: 47H10, 54H25

References

[1] I.A. Rus, Principii si aplicatii ale teoriei punctului fix, Ed. DACIA, 1979.

[2] , Generalized contractions and applications, Cluj University Press, 2001.

[3] T. Burton, Fixed points, differrential equations, and proper mappings, Seminar on fixedpoint theory Cluj-Napoca, Ed. Casa Cartii de Stiinta, Volume 3, 2002

[4] T.A. Burton, Bo. Zhang, Periodicity in delay equations by direct fixed point mappung,Differential Equations and Dynamical Systems 6 (1998), 413-424.

[5] J.K.Hale, Theory of Functional Differential Equations, Springer, New York, 1977.

[6] C.E. Langenhop, Periodic and almost periodic solutions of Volterra integral differentila equa-tions with infinite memory, J.Differential Equations 14 (1973), 424-430.

[7] V. Volterra, Lecons sur la Theory Mathematique de la Lutte pour la Vie, Gauthier-Villars,Paris, 1931.

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Study of nonlinear perturbation of the Laplacian viageneralization contraction

Ion Marian Olaru

University of Sibiu, RomaniaE-mail: olaruim@yahoo.com

Abstract: In this paper we shall use the technique of generalization contrac-tion in the study of boundary value problem for a semilinear equation of theform −∆u + λu + f(u) = gKeywords: maximal monotone operator, stongly positive operator, Picardoperators, fixed points, data dependence.2000 Mathematical Subject Classification: 35J65, 47H05

Strong differential subordinations and superordinations

Georgia Irina Oros, Gheorghe Oros

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: goros@uoradea.ro, gh oros@yahoo.com

Abstract: The concept of differential subordination was introduced in [2]by S.S. MILLER and P.T. MOCANU and studied in [3]. The concept ofstrong differential subordination was introduced in [1] by J.A. ANTONINOand S. ROMAGUERA. They have applied this concept in the special case ofBriot-Bouquet strong differential subordination. In [5] we have studied thestrong differential subordinations in the general case, following the generaltheory of differential subordinations presented in [3].The notion of differentialsuperordination was introduced in [4] by S.S. MILLER and P.T. MOCANUas a dual concept of differential subordination. In [6], G. I. OROS introducedand studied the concept of strong differential superordination following thegeneral theory of differential superordinations presented in [3]. A series ofarticles followed, in which the authors have studied different cases of strongdifferential subordinations and strong differential superordinations.Keywords: univalent function, differential subordination, strong differentialsubordination, differential superordination, strong differential superordination2000 Mathematical Subject Classification: 30C45, 34A30

References

[1] Jos A. Antonino And Salvador Romaguerra, Strong differential subordination to Briot-Bouquet differential equations, Journal of Differential Equations, 114(1994), 101-105.

[2] S.S. Miller And P.T. Mocanu, Differential subordinations and univalent functions, MichiganMath. J., 28(1981), 157-172.

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[3] S.S. Miller And P.T. Mocanu, Differential subordinations. Theory and applications, Pure andApplied Mathematics, Marcel Dekker, Inc., New York, 2000.

[4] S.S. Miller And P.T. Mocanu, Subordinants of differential superordinations, Complex Vari-ables, vol. 48, no. 10, 815-826.

[5] Georgia Irina Oros And Gh. Oros, Strong differential subordination, Turkish Journal ofMathematics, 33(2009), 249-257.

[6] Georgia Irina Oros, Strong differential superordination, Acta Universitatis Apulensis,19(2009), 101-106

Best subordinants of the strong differential superordination

Gheorghe Oros, Adela Olimpia Taut

University of OradeaFirst author: Department of MathematicsSecond author: Faculty of Environmental ProtectionStr. Universitatii, No.1, 410087 Oradea, RomaniaE-mail: gh oros@yahoo.com, adela taut@yahoo.com

Abstract: The notion of differential superordination was introduced in [3]by S.S. Miller and P.T. Mocanu as a dual concept of differential subordination[2]. The notion of strong differential subordination was introduced by J.A.Antonino, S. Romaguera in [1]. This notion was developed in [4]. In paper[5] the author introduced the dual concept of strong differential superordina-tions. The aim of this paper is to obtain the best subordinants of the strongdifferential superordinations.

1 Main results

Theorem 3. Let h be univalent in U and let ϕ : C3 × U × U → C. Suppose that thedifferential equation

ϕ(q(z), zq′(z), z2q′′(z); z) = h(z) (1)

has a solution q, with q(0) = a, and one of the following conditions is satisfied:(i) q ∈ Q and ϕ ∈ φ[h, q](ii) q is univalent in U and ϕ ∈ φ[h, qρ], for some ρ ∈ (0, 1) or(iii) q is univalent in U and there exist ρ0 ∈ (0, 1) such that

ϕ ∈ φ[hρ, qρ] for all ρ ∈ (ρ0, 1).

If p ∈ H[a, 1] and ϕ(p(z), zp′(z), z2p′′(z); z, ξ) is univalent in U , for all ξ ∈ U and if psatisfies

h(z) ≺≺ ϕ(p(z), zp′(z), z2p′′(z); z, ξ), z ∈ U, ξ ∈ U (2)

thenq(z) ≺ p(z), z ∈ U

and q is the best subordinant.

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References

[1] S.S. Miller and P.T. Mocanu, Differential subordinations. Theory and applications, Pureand Applied Mathematics, Marcel Dekker, Inc., New York, 2000.

[2] S.S. Miller and P.T. Mocanu, Subordinants of differential superordinations, Complex Vari-ables, vol. 48, no. 10, 815-826, october 2003.

[3] Georgia Irina Oros and Gheorghe Oros, Strong differential subordination, Turkish Journalof Mathematics, 32(2008).

[4] Georgia Irina Oros and Gheorghe Oros, Second order nonlinear strong differential subordi-nations, Bull. Belg. Math. Soc. Simon Stevin, 16(2009), 171-178.

Periodic solutions of second-order differential inclusions systemswith (q,p)-Laplacian

Daniel Pasca

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: dpasca@uoradea.ro

Abstract: Some existence results are obtained for periodic solutionsof nonautonomous second-order differential inclusions systems with (q,p)-Laplacian:

ddt

(|u1(t)|q−2u1(t)) ∈ ∂u1F (t, u1(t), u2(t)), a.e. t ∈ [0, T ],

ddt

(|u2(t)|p−2u2(t)) ∈ ∂u2F (t, u1(t), u2(t)), a.e. t ∈ [0, T ],

u1(0)− u1(T ) = u1(0)− u1(T ) = 0,

u2(0)− u2(T ) = u2(0)− u2(T ) = 0,

(1)

where 1 < p, q < ∞, T > 0, and F : [0, T ]×RN×RN → R, ∂ denotes the Clarkesubdifferential and F (t, x1, x2) is measurable in t for each (x1, x2) ∈ RN , andlocally Lipschitz and regular in (x1, x2) for each t ∈ [0, T ].Keywords: (q,p)-Laplacian, inclusions systems, periodic solutions2000 Mathematical Subject Classification: 34C25, 49J24

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Remarks on a mathematical approach of the vertical windturbine with identical blades

Sonia Petrila, Balazs Albert

Sonia PetrilaComputer Science High School ”Tiberiu Popoviciu”Calea Turzii 140, 400495, Cluj-Napoca, RomaniaE-mail: titussoniapetrila@yahoo.com

Balazs AlbertBabes-Bolyai UniversityStr. M. Kogalniceanu, nr. 1, 400084, Cluj-Napoca, RomaniaE-mail: balazsalb@gmail.com

Abstract: A wind turbine with vertical axis, whose identical shape bladesare radially arranged around a fixed rotation axis, is considered. Our pur-pose is to point out some remarks (together with practical work suggestions)about such turbines and on a mathematical approach of the fluid flow inducedby this turbine. An algorithm for assesement of the current rototranslationparameters in the case of the “double rotating” blades is envisaged.Keywords: wind turbine with identical blades, conformal mapping, B.V.P.of Volterra type2000 AMS Mathematics Subject Classification: 76G25, 76B10

Optimization consideration on a parachute problem

Titus Petrila, Balazs Albert

Titus PetrilaAcademy of Romanian ScientistsCluj-Napoca, Romania E-mail: aosrtransilvania@yahoo.com

Balazs AlbertBabes-Bolyai UniversityStr. M. Kogalniceanu, nr. 1, 400084, Cluj-Napoca, RomaniaE-mail: balazsalb@gmail.com

Abstract: The heavy non-permanent fluid flow facing a turbine bucket alongits symmetry axis (which is also the “parachute problem”), in the presence ofgravity is considered. Our purpose is to evaluate the drag on the concaveprofile in view of some optimization considerations.Keywords: vertical wind turbines with buckets, parachute type profile, math-ematical model of Helmholtz type, B.V.P. of mixed (Volterra) type, optimiza-tion considerations2000 AMS Mathematics Subject Classification: 76B25, 76G25

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The behavior of the positive solutions of a nonlinear differenceequation

Gheorghe Radu, Gheorghe Anton, Bogdan Gheorghe Munteanu

Gheorghe RaduHenri Coanda Air Force Academy160 Mihai Viteazul Street, 500183 Brasov, RomaniaE-mail: gh.radu@gmail.com

Gheorghe AntonTrades and Services High School14 bis,Bazalt street, Buzau, RomaniaE-mail: anton g10@yahoo.com

Bogdan Gh. MunteanuHenri Coanda Air Force Academy160 Mihai Viteazul Street, 500183 Brasov, RomaniaE-mail: munteanu77@yahoo.com

Abstract: The main objective of this paper is to study the behavior ofpositive solutions of the following important nonlinear difference equation:

un = 1 +

k∑i=1

αiun−pi

m∑j=1

βjun−qj

, n ∈ N0

where αi, i = 1, k and βj , j = 1,m are positive numbers such thatk∑

i=1αi =

m∑j=1

βj = 1 and pi, i = 1, k and qj , j = 1,m are natural numbers such that p1 <

p2 < ... < pk and q1 < q2 < ... < qm. The case when gcd(p1, ..., pk, q1, ..., qm) =1 is the most important. For this case we prove that if all pi, i = 1, k are evenand all qj , j = 1,m are odd, then every positive solution of this equationconverges to a periodic solution of period 2, otherwise, every positive solutionof the equation converges to a unique positive equilibrium.Keywords: difference equations, positive solutions, bounded character, peri-odic solutions.AMS Subject Classification: 39A10, 39A11.

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Topological classification for linear autonomous ODE

Liviu Horia Popescu

University of OradeaDepartment of Mathematics and Computer ScienceUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: lpopescu2002@yahoo.com

Abstract: Autonomous linear differential equations on Banach spaces arestudied via topological equivalence. Using analytical methods, we show thatexponential dichotomy implies structural stability.Keywords: autonomous equation, topological equivalence, structural stabil-ity;2000 Mathematical Subject Classification: 34D30

Hybrid models with time delay for the social diffusion.Numerical simulation

Andrea Sandru, Dumitru Opris

Andrea SandruAurel Vlaicu University of AradFaculty of Exact SciencesStr. E. Dragoi nr.2, 310330, Arad, RomaniaE-mail: sandruandrea@gmail.com

Dumitru OprisWest University of TimisoaraDepartment of Mathematics, Faculty of Mathematics and Computer ScienceBd. V. Parvan, nr. 4, 300223, Timisoara, RomaniaE-mail: opris@math.uvt.ro

Abstract: The dissemination of newness or of information in a communityis called social diffusion. The social diffusion conducts to the stratification ofthe members collectivity in backings, opponents, undecided and unintereseted.The models hybrid is given by a systems of equations with delayed arguments,Wiener process and Liu processe. The simulation was realized for sample of1052 member of a social group, the diffusion curves allow prediction formularegarding the dynamical social diffusion process. MathematicsKeywords: social diffusion, bifurcation theory, dynamic model, Wiener pro-cesses, Liu processes.AMS Subject Classification:34K50, 35L65, 26A33, 37N99, 60H10

25

Concomitants of order statistics for bivariate pseudo-gaussiandistribution

Saman Shahbaz, Muhammad Qaiser, Arif Rafiq, Ana Maria Acu

Saman Shahbaz, Muhammad Qaiser, Arif RafiqCOMSATS Institute of Information TechnologyLahore, PakistanE-mail: samans@hotmail.com, qshahbaz@gmail.com, arafiq@comsats.edu.pk

Ana Maria Acu“Lucian Blaga” University, SibiuDepartment of MathematicsStr. Dr. I. Ratiu, No 5-7, 550012-Sibiu, RomaniaE-mail: acuana77@yahoo.com

Abstract: Distribution of the r-th and r-th and s-th concomitants of or-der statistics for bivariate Pseudo-Gaussian distribution has been obtained.Moments and joint moments have also been obtained for the resulting distri-butions.Keywords: Concomitants, Pseudo-Gaussian distribution.AMS Subject Classification: 60E05

The calculus of variations for processes with independentincrements

Nadia Mirela Stoian

Transilvania University of Brasov, RomaniaDepartment of Mathematical Analysis and ProbabilityE-mail: Nadia Stoian@yahoo.com; nadia.stoian@unitbv.ro

Abstract: The aim of this paper is to construct the stochastic calculus ofvariations for general zero mean processes with independent increments and,in particular for general Levy processes without drift. The calculus based onthe operators D and , is such that for the Gaussian processes they coincide withthe Malliavin derivative and Skorohod integral, respectively. We introduce thefamily of polynomials which contains the Sheffer set of polynomials. By usingthese polynomials it is proved the chaos decomposition theorem of L2(Ω). Thedefinition of Malliavin derivative and Skorohod integral for a certain class ofstochastic processes is given and it is shown that they are equal.Keywords: processes with independent increments, Levy processes, Malli-avins calculus, Wiener chaos decomposition, Skorohod integral, multiple inte-gral, orthogonal polynomials.

26

On nonuniform stability for stochastic cocycle on Banach spaces

Diana Stoica, Ludovic Dan Lemle

Politehnica University of TimisoaraEngineering Faculty of HunedoaraRevolutiei Street Nr. 5, Hunedoara 331128, RomaniaE-mail: diana.stoica@fih.upt.ro, dan.lemle@fih.upt.ro

Abstract: This paper presents the nonuniform exponential stability in meansquare for stochastic cocycles on Banach spaces, and there are defined bymeans of stochastic semiflow, which is generated by Wiener shift. There arepresented several general characterizations of this property out of which canbe deduced well known results of the stability theory.Keywords: Stochastic semiflow, stochastic cocycles, nonuniform exponentialstability in mean squareAMS Subject Classification: Primary 60H10, 60H15; Secondary 60H20

On a certain differential inequality

Roxana Sendrutiu

University of OradeaUniversitatii Street No.1, 410087 Oradea, RomaniaE-mail: roxana.sendrutiu@gmail.com

Abstract: This talk is intended to present certain conditions on the complex-valued functions A,B : U → C defined in the open unit disc U = z ∈ C :|z| < 1 such that the differential inequality

Re [A(z)p2(z) + B(z)p(z) + α(zp′(z)− 1)3 − 3β(zp′(z))2 + 3γ(zp′(z)) + 1] > 0

implies Re p(z) > 0, where p ∈ H[1, n],α, β, γ ∈ C.Keywords: differential inequality, functions with positive real part.AMS Classification Number: 30C80

27

On necessary optimality conditions for Pareto minima inset-valued optimization problems with geometric constraints

Radu Strugariu

“Gh. Asachi” Technical University, IasiDepartment of MathematicsBd. Carol I, nr. 11, 700506 – Iasi, RomaniaE-mail: rstrugariu@gmail.com

Abstract: The aim of this paper is to obtain necessary optimality conditionsfor Pareto minima in set-valued vector optimization problems with geometricconstraints. We use a new method to derive generalized Fermat rules, basedon openness results for multifunctions.Keywords: set-valued mappings, openness, Frechet coderivative, Mor-dukhovich coderivative, generalized Fermat rules;Mathematics Subject Classification (2000): 90C29, 90C26, 49J52

A note on a subclass of analytic functions defined byRuscheweyh derivative and generalized Salagean operator

Alina Alb Lupas, Daniel Breaz

Alina Alb LupasUniversity of OradeaDepartment of Mathematics and Computer ScienceStr. Universitatii nr. 1, 410087 Oradea, RomaniaE-mail: dalb@uoradea.roDaniel Breaz”1 Decembrie 1918” University of Alba Iulia, RomaniaE-mail: dbreaz@uab.ro

Abstract: By means of Ruscheweyh derivative and generalized Salageandifferential operator we define a new class RDγ(m, µ, α, λ) involving functionsf ∈ An. Parallel results, for some related classes including the class of starlikeand convex functions respectively, are also obtained.Keywords: Analytic function, starlike function, convex function,Ruscheweyh derivative, generalized Salagean operator.2000 Mathematical Subject Classification: 30C45

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Some applications of sums of random variables in non-lifeinsurance

Mihaela Covrig, Daniela Ioana Todose, Emilia Titan

The Academy of Economic Studies, BucharestDepartment of Statistics and EconometricsPiata Romana, No.6, Bucharest, Sector 1, Romania, cod 010374E-mail: mihaelacovrig@gmail.com, daniela.todose@gmail.com, emilia titan@yahoo.com

Abstract: In the non-life insurance business, an actuary faces the problem ofdetermining the distribution function of a sum of random variables which arenot necessarily independent, like aggregate claims of an insurance portfolio.The paper points out some applications of approximating such sums when theindividual distribution functions of the terms are known, but their dependenceunknown, for the computation of the stop-loss premiums and estimates of theruin probability.Keywords: comonotonicity, insurance premium principle, stop-loss premium,stochastic dominance, ruin probability.2000 Mathematics Subject Classification: 91B30, 62P05, 68W25.

On some computational methods in risk theory

Iulian Mircea, Mihaela Covrig

Iulian MirceaThe Academy of Economic Studies, BucharestDepartment of MathematicsPiata Romana, No.6, Bucharest, Sector 1, Romania, cod 010374E-mail: mirceaiulian91@yahoo.com

Mihaela CovrigThe Academy of Economic Studies, BucharestDepartment of Statistics and EconometricsPiata Romana, No.6, Bucharest, Sector 1, Romania, cod 010374E-mail: mihaelacovrig@gmail.com

Abstract: The ruin probability of an insurance company is one of the mainissues in actuarial mathematics. In the classical Poisson model of the risktheory there exist analytic expressions for the ruin probability, but in other riskmodels, there are not. For this, researchers try to find upper and lower bounds,and better approximations. In this paper, we discuss some risks models andmethods of estimating the ruin probability: Tijms, Willmot, Grandell, Renyi,and the diffusion approximation. The latter can be obtained approximatingthe risk process by a Brownian motion with drift. We present a model withsize fluctuations where the possibility of an increase of the business is takeninto account.Keywords: ruin probability, phase-type, risk process, diffusion approxima-tion, Brownian motion.2000 Mathematics Subject Classification: 91B30, 62P05, 68W25.

Author index

Acu A.M., 26Alb Lupas A., 7, 28Albert B., 23Alexandrescu A., 7Andrica D., 8Anton G., 24

Balaj M., 9Bica A.M., 9Bodrato M., 10Borsa D.L., 10Borsa E.R., 10Breaz D., 11, 28Breaz N., 11Bruns W., 11

Catas A., 7, 12Chiriac C.L., 12Ciupa A., 13Covei D.-P., 13Covrig M., 29

Dragan M., 14Dragan S., 14Dragomirescu F.I., 15

Efrem R., 15Ene R.D., 15

Fechete D., 16Fechete I., 16Frigioiu F., 16

Galea L.F., 16

Hedrih (Stevanovic) K., 16

Ichim B., 11Iovanov M., 17

Lanzhe L., 18Lazar I.C., 8Lazar T.A., 18Lemle L.D., 27

Mangra D., 8Mingliang H., 18Mircea I., 29Munteanu B.G., 18, 24Muresan S., 14, 19

Nica O., 19

Olaru I.M., 20Opris D., 25Oros G., 20, 21Oros G.I., 20

Pasca D., 22Pescar V., 11Petrila S., 23Petrila T., 23Popescu L.H., 25

Qaiser M., 26

Radu G., 24Rafiq A., 26

Sandru A., 25Sendrutiu R., 27Shahbaz S., 26Stoian N.M., 26Stoica D., 27Strugariu R., 28

Taut A.O., 21Titan E., 29Todose D.I., 29