BULETINUL ŞTIINŢIFIC
al Universităţii “Politehnica” din Timişoara, Romania
SCIENTIFIC BULLETIN OF
“Politehnica” University of Timişoara, Romania
Contents and abstracts
Seria MATEMATICǍ - FIZICǍ
Transactions on MATHEMATICS & PHYSICS
Tom 50 (64) , Fascicola 1, 2005, ISSN 1224-6069
Mathematics
SOME PROPERTIES OF UPPER AND LOWER CLOPEN CONTINUOUS MULTIFUNCTIONS
Erdal EKICI and Valeriu POPA
Abstract. In this paper, we introduce and study the notion of clopen continuous multifunctions. Characterizations and properties of upper (lower) clopen continuous multifunctions are obtained. The relationship between upper (lower) clopen continuous multifunctions and upper (lower) continuous multifunctions are also discussed.
Keywords: multifunction, clopen continuity, 0-dimensional space.
Address: Erdal EKICI, Department of Mathematics, CanakkaleOnsekizMartUniversity, Terzioglu Campus, 17020Canakkale, TURKEY, E-mail .
Valeriu POPA, Department of Mathematics, University of Bacău, 5500 Bacău, ROMANIA., E-mail .
L’EQUATION DIOPHANTIENNE (IV)
Gheorghe M. TUDOR
Résumé. Pour l’équation signalée plus haut, nous envisagerons quelques problémes relatifs aux solutions concernant des nombres entieres positifs. Plus précis, on étudie cette équation en procedant de la même maniè qu’on a fait dans le cas des équations considerées dans les ouvrages [5], [6], [7]. C’est ceci le but de ce travail.
Keywords:Équation Diophantienne
Address: Gheorghe M. TUDOR, “Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 3000004 Timişoara, ROMANIA.
A MINIMAX PROPERTY FOR A CLASS OF PERFECT INFORMATION GAMES
Gabriela CRISTESCU and Codruţa STOICA
Abstract.A minimax theorem, accompanied by purification result, is proven for perfect information games, other cases than those satisfying the conditions, which Kalmar stated in [5] for chess. We shall refer to the so-called “tube condition”. The concept of equilibrium point with respect to a given set is used in order to forward looking prove the main theorems.
Keywords:Extended form perfect information game, saddle – point of a function with respect to a set, tube shaped game, weakly dominated row.
Address: Gabriela CRISTESCU, “Aurel Vlaicu”University of Arad,Department of Mathematics,, Bd.Revoluţiei, No.81, 310130 Arad, ROMANIA, Email .
Codruţa STOICA, “Aurel Vlaicu” University of Arad, Department of Mathematics,, Bd.Revoluţiei, No.81, 310130 Arad, ROMANIA, Email .
THE VORONOVSKAJA THEOREM FOR THE SCHURER-STANCU OPERATORS
Dan BǍRBOSU
Abstract.The Schurer-Stancu operators are defined at (1.1). We establish a Voronovskaja type theorem for these operators. Also, we prove a similar result for the bivariate Schurer-Stancu operators.
Keywords:Schurer-Stancu operator; divided difference; Voronovskaja theorem; bivariate operator.
Address: Dan BĂRBOSU, North University of Baia Mare, Department of Mathematics and Computer Science, Victoriei 76, 430122 Baia Mare, ROMANIA, E-mail .
REPRODUCING KERNEL LOYNES SPACES
Loredana CIURDARIU
Abstract. In this note we generalize some results regarding reproducing kernel spaces obtained in [3] for Z = (X, X*) and Z = (X, X*) to an arbitrary pre-Loynes Z-space. For a given Z-valued positive definite kernel we construct a Loynes Z-space which admits as a reproducing kernel, using the functional completion as in [3], Theorem 2.2.10. As an application another construction of completion of a pre-Loynes space is given.
Keywords:Reproducing Kernel, Loynes Z-space, positive definite kernel
Address: Loredana CIURDARIU, “Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA.
CONSTRUCTION OF A MULTIRESOLUTION ANALYSIS IN
A LATTICE FRAMEWORK
Radu-Lucian LUPŞA
Abstract.A generalization of multirezolution analysis of the wavelets theory is defined in this paper, followed by the construction of such an object in complete lattices. It is shown that the classical morphological opening and closure operators are fitted in this framework as particular cases. This construction introduces a property called pseudosublattice for a subset of a complete lattice. This type of structure leads to an intermediate between a subset that is complete lattice and a sublattice.
Keywords:Wavelets, multiresolution.
Address: Radu-Lucian LUPŞA, “Babeş-Bolyai” University of Cluj-Napoca, Faculty of Mathematics and Computer Science, Str.M.Kogălniceanu, Nr.1, 400084 Cluj Napoca, ROMANIA, E-mail .
ON A PARTICULAR STABILITY CRITERION IN A BINARY MIXTURE PROBLEM
Ioana DRAGOMIRESCU
Abstract.A new method to obtain the stability bound for a binary mixture problem in the case of competing effects when the Rayleigh number is equal to the Schmidt number is presented. The stability criterion was deduced explicitly in terms of the physical parameters involved in the problem.
Keywords: Stability criterion, Prandtl number, binary mixture.
Address: Ioana DRAGOMIRESCU,Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA.
ANALYSIS OF A DYNAMICAL SYSTEM DERIVED FROM THE LORENZ SYSTEM
Gheorghe ŢIGAN
...... Abstract.In this paper we study the stability and bifurcation of equilibria of a time-continuous dynamical system exhibits a Hopf bifurcation which for particular parameter values is subcritical.
Keywords: Hopf bifurcation
Address: Gheorghe Ţigan,Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA.
Physics
SOME THERMODYNAMIC PROPERTIES OF THE RELATIVISTIC
FERMIONS OSCILLATORS
Nicolina POP
Abstract. The behaviour of the chemical potential and specific heat, using the evaluation of the thermodynamic grand-canonical potential characterizing relativistic fermionic oscillators as the basic starting point, is analyze and are obtained approximative analytical and numerical results.
Keywords: relativistic fermionic oscillators, Fermi-Dirac statistics, thermodynamic properties.
Address: Nicolina POP, WestUniversity of Timişoara, V.Parvan Ave, 300223 Timisoara, ROMANIA
FROM THE SPACE DIMENSION TO TWO SPACE DIMENSIONIN SPECIAL RELATIVITY
Bernhard ROTHENSTEIN
...... Abstract. Authors derive the Lorentz-Einstein transformations for the space-time coordinates from a one-space dimension approach. They add to them the invariance of distances measured perpendicular to the direction of relative motion. We prove that the transition from the one-space dimension approach to the two-space dimension approach does not affect the transformation equation for the time coordinate.
Keywords:Lorentz-Einstein transformations.
Address: Bernhard ROTHENSTEIN, Ioan ZAHARIE, “Politehnica” University of Timişoara, Department Physics, P-ţa Regina Maria, Nr.1, ROMANIA.
THE REDUCTION OF CHARGE PROPAGATION IN NANOROAD
V. SAJFERT and B. TOŠIĆ
Abstract. The space distributions of electron concentrations in metallic quantum rod are analyzed in the work. The Green’s functions method, adapted for broken symmetry structure analyses, was applied. The main conclusion of this analysis is non-isomorphism of configuration-momentum space transition. Since the configuration space is wider than momentum one, auto-reduction of structure of structure takes place. In 3x3 quantum rod the charge carriers propagate along four lines, only. There are nine structures, which are conductive. In these substructures specific skin effect takes place. The results represent qualitative difference between nano and corresponding bulk structure and could have technological applications.
Keywords: spatial indices, the new Green function methodology, chemical potential, specific skin effect, electron concentrations.
Address:V. SAJFERTTechnical Faculty “M.Pupin” Zrenjanin, University of Novi Sad, Serbia and Montenegro,YUGOSLAVIA.
B. TOŠIĆ, VojvodinaAcademy of Sciences and Arts,Novi Sad,Serbia and Montenegro, YUGOSLAVIA.
TEACHING SPECIAL RELATIVITY AFTER 100 YEAR FROM ITS FOUNDATION
George J.SPIX and Bernhard ROTHENSTEIN
Abstract. The authors are aware of the fact that during 100 years of teaching special relativity some of our derivations could be found in modern textbooks or journals but consider that the way in wich they introduce the subject has some degree of originality.
Keywords: Lorentz-Einstein transformations, relativistic dynamics, relativistic electrodynamics.
Address:George J. SPIX, BSSE, 1951 Illinois Institute of Technology.
Bernhard ROTHENSTEIN, “Politehnica” University of Timişoara, Department Physics, P-ţa Regina Maria, Nr.1, ROMANIA.
Seria MATEMATICǍ - FIZICǍ
Transactions on MATHEMATICS & PHYSICS
Tom 50 (64), Fascicola 2, 2005, ISSN 1224-6069
Mathematics
THE FUNDAMENTAL SOLUTION OF THE EQUATION X2 – DY2 = 1
Malvina BAICA and Aldo PERETTI
Abstract: In this paper the authors use Analytic Number Theory tools to find the fundamental solution of the equation X2 – DY2 = 1. Algebraicaly this equation is related with units in algebraic number quadratic fields.
Keywords: Analytic Number Theory, quadratic fields
Address: Malvina BAICA; The University of Wisnsconsin, Department of Mathematical and Comp.Sciences; 53190Whitewater, Wisconsin, U.S.A.
Aldo PERETTI, J.F.KennedyUniversity, Buenos Aires, ARGENTINA
PSEUDOSUBMEASURABLE AND INTEGRABLE FUNCTIONS
Octavian LIPOVAN
Abstract: We define the notion of pseudosubmeasurable as a generalized of the submeasure notion. Using families of pseudosubmeasures and the associated topological rings, the pseudosubmeasurable function concept is defined. The convergence in measure, almost everywhere convergence and almost uniform convergence are generalized to the sequence of functions with values pseudometric spaces. Finally, we develop an integration theory for these functions, with respect to semigroup valued measure.
Keywords: Pseudosubmeasures, pseudometric spaces, convergence in measure, almost everyehere convergence, almost uniform convergence
Address:Octavian LIPOVAN, “Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA.
L’EQUATION DIOPHANTIENNE (V)
Gheorghe M. TUDOR
Résumé. En ce qui concerne l’équation signalée plus haute, nous envisagerons quelques questions relatives aux solutions (x, y, z), où x, y, z sont des nombres naturels. Au sujet de ce problème, nous avons en vue l’équation xx · yy = zz , pour laquelle le mathématicien chinois CHAO-KO a trouvé un nombre infini de telles solutions (x, y, z), dont x, y, z sont des nombres naturels (voir, par exemple, [6]).
Keywords: Équation Diophantienne.
Address: Gheorghe M. TUDOR, “Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA.
FIXED POINTS IN GENERALIZED METRIC SPACE AND THE STABILITY OF A QUADRATIC FUNCTIONAL EQUATION
Liviu CǍDARIU
Abstract: A fixed point method is applied to prove a Hyers-Ulam-Bourgin type stability theorem for the functional equation f(x + 2y) + f(x – 2y) – 4f(x+y) – 4f(x-y)+ 6f(x) – 24f(y)=0.
Keywords: quartic functional equation, fixed points, Hyers-Ulam-Rassias stability.
Address: Liviu Cadariu, “Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA, E-mail .
PARTICULAR SOLUTION OF VEKUA DIFFERENTIAL EQUATION BY USINGMITRINOVIĆ METHOD
Miloš ČANAK, Ljubomir PROTIĆ and Liljana STEFANOVSKA
Abstract:In many cases of solving Vekua complex differential equation it is possible to find a particular solution by using Mitrinovic method. The particular solution can be used for obtaining a general solution of a wider class of Vekua equations in final and closed form, that wasn’t done in literature.
Keywords: Vekua equations.
Address: Miloš ČANAK, Faculty of Agriculture, University of Belgrade, Serbia and Montenegro.
Ljubomir PROTIĆ, Faculty of Mathematics, University of Belgrade, Serbia and Montenegro.
Liljana STEFANOVSKA, Faculty of Technology and Metallurgy, “Ss Cyril and Methodius” University, Skopje, Republic of Macedonia.
ON SOME EXPONENTIAL DIOPHANTINE EQUATIONS
Gheorghe M. TUDOR and Tudor BÎNZAR
Abstract:In this paper, two types of exponential Diophantine equations are studied. It is shown that these equations have infinitely many solutions of positive integers described by families depending on two parameters.
Keywords: Exponential Diophantine Equations
Address: Gheorghe M.TUDOR, Tudor BÎNZAR,“Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA.
ON THE CHANDRASEKHAR – GALERKIN METHOD IN A CONVECTION PROBLEM FOR A MICROPOLAR FLUID
Ioana DRAGOMIRESCU
Abstract.The direct Chandrasekhar-Galerkin method is applied to solve a problem of convection for a micropolar fluid. For various unknown functions different expansion functions were chosen such that all boundary conditions be automatically satisfied. Aproximate numerical evalutions of the Rayleigh number are obtained in the even and the odd case. These results agree very well with those obtained by us in [3], by Budianski-DiPrima method.
Keywords:stability, micropolar fluid, Rayleigh number.
Address: Ioana DRAGOMIRESCU,“Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, No.1, 300004 Timişoara, ROMANIA.
Physics
ILLUSTRATING EINSTEIN’S SPECIAL RELATIVITY: A RELATIVISTIC DIAGRAM THAT DISPLAYS IN TRUE VALUES THE COMPONENTS OF A FOUR VECTOR
Bernhard ROTHENSTEIN, Ştefan POPESCU and George J. SPIX
Abstract:After having shown that the corresponding components of a four vector transform via the same transformation factors as the space-time coordinates of the same event do, we design a relativistic diagram that displays in true values theirs components. One diagram worksfor events generated by tardyons whereas a second diagram works for events generated by light signals or photons. We consider both approaching and receding tardyons respectively photons in each case. We also show how the relativistic diagram for radar and photographic detections of moving profiles.
Keywords: Relativistic diagram, Photographic detections
Address: Bernhard ROTHENSTEIN, “Politehnica” University of Timişoara, Physics Department, P-ţa Regina Maria, Nr.1, ROMANIA.
Ştefan POPESCU, Siemens Munchen Germany
J. SPIX,BSSE, 1951 Illinois Institute of Technology
DESIGN OF A KEPLER TELESCOPE PROVIDING
AN ERRECTED IMAGE
Corina GRUESCU, Marius Costache
Abstract: The paper describes the methods for the design and analysis of the traditional and erected image Kepler telescope. The authors seek for diffraction limited systems, having a very good image quality. The design uses original software, conceived for synthesis. The analysis is performed automatically using the soft OSLO LT. The image quality is evaluated for each component as well as for the system objective-erector. The paper contains original elements concerning the design and the approach in image quality analysis.
Address: Corina GRUESCU, University Politehnica of Timisoara, Mechanical Faculty, Mechatronics Department, Bd. Mihai Viteazu nr.1, e-mail: .
Marius Costache, University Politehnica of Timisoara, Physics Department, P-ţa Regina Maria, Nr.1, 300004 Timisoara, ROMANIA, e-mail .
IR ABSORBTION OF SOME ME2O3 OXIDES AND THEIR SOLID SOLUTIONS
Minerva CRISTEA
Abstract:The experimental results concerning the infrared absorption spectra (400-4000 cm-1) of the isomorphous oxides -Al2O3, -Fe2O3, -Cr2O3, that crystallize into the trigonal system with the space group D3d, as well as of their ternary solid solutions with 10% -Fe2O3 having the same type of structure, are presented and discussed.
The IR spectra were obtained by using powdered samples tablet – formed with KBr, at room temperature and the recordings for the whole field were performed with two spectrometers, Karl Zeiss type UR-10 and Specord 75 IR.
The spectra of the oxides and those of the ternary solid solutions exhibit two absorbtion bands below 700 cm-1. Taking into account the crystalline structure and the degree of covalence of the M-O bonds, an attribution model of these two IR absorption bands is suggested.
Keywords: infrared absorption spectra.
Address: Minerva CRISTEA, “Politehnica” University of Timişoara, Physics Department, P-ţa Regina Maria, Nr.1, 300004 Timisoara, ROMANIA.
SOLUTIONS IN DILATON GAUGE OF GRAVITATION
Simona BABETI and G. ZET
Abstract: A deSitter gauge theory of gravitational field is developed using a spherical symmetric Minkowski space-time as base manifold. The gravitational field is described by gauge potentials and the field equations are derived from dilaton gravity, in the presence of a special combination of higher derivative terms in the integral of action associated to the gravitational gauge fields. Solutions without singularities are obtained and an example of such solution is given with its dependence on the cosmological constant. The calculations are performed using an analytical program conceived in GRTensor II for Maple 8.
Keywords: Minkowski space-time, gravitational field, gauge potentials.
Address: Simona BABETI, “Politehnica” University of Timişoara, Department of Physics, P-ţa Regina Maria, Nr.1, 300004 Timisoara, ROMANIA.
G. ZET, Department of Physics, “g.Asachi” Technical University Iasi, ROMANIA, E-mail .
A CENTURY OF QUANTUM PHYSICS
Bratislav S.Tošić
Abstract: In this paper we refer to the main aspects of the development of quantum mechanics during one century of the year foundamentation. We follow the main facts and experiments which have been constitute the foundations of quantum mechanics, as: the Planck’s hypotesis of quanta, the Einstein’s explanation of photoelectrical effect, the De Broglie’s theory reffering to the wave-corpuscular dualism and so one.
All these and many other phenomene, theory have been made the quantum mechanics as the some fuitfull theory of the XX century physics.
Keywords: Planck’s hypotesis of quanta, Einstein’s photoelectrical effect, De Broglie’s wave-corpuscular dualism.
Address: Bratislav S.Tošić, Academy of Sciences and Arts of Vojvodina, Serbia and Montenegro, University of Novi Sad, Faculty of Natural Sciences, Trg D.Obradovica 4 Novi Sad, Serbia and Montenegro.
EXERGETIC ANALYSIS OF A FLAT-PLATE SOLAR COLLECTOR
Ioan LUMINOSU, Laurenţiu FARA
Abstract: The solar-thermal energy efficiency increases without extremum points with the flow rate. The fluid outlet temperature increases with the collecting area. The absence of maximum points for the functions and has created difficulties in the design of flat-plate solar collectors. The exergy efficiency of a flat-plate solar collector, presents points of local maxima and a point of global maximum. The paper proposes an exergy analysis of a flat-plate solar collector. The method has proven valuable in the design of solar collectors for the specific climatic and insolation conditions of a certain region.
Keywords: Flat-plate solar collector.
Address: Ioan LUMINOSU, “Politehnica” University of Timişoara, Department of Physics, P-ţa Regina Maria, Nr.1, 300004 Timisoara, ROMANIA.
L.FARA, Department of Physics, Faculty of Applied Science, Bucharest “Politehnica” University, 313 Splaiul Independenţei, Bucharest , 060032, ROMANIA.
THE QUANTUM STATISTICS OF THE CHEMICAL REACTIVITY. PART III: ELECTRONIC DENSITY REACTIVITY
Mihai V. PUTZ
Abstract:The main directions of the modern quantum physical chemistry are: the study of atoms in molecules, the defining of global reactivity indices of the multi-electronic systems within poly-nuclear fields, and the describing of the electronic distributions and bonds by the so called electronic localization functions. These researches lines are all on the electronic density based as the primer quantum variable. Therefore, the structural ensemble of the substances is represented through the hierarchy of the density functionals and electronic localization functions at various levels of matter organization. Still, the difficulties, sometimes astonished and the inherent errors, in computing electronic densities for the increased systems in poly -electronic and -nuclear complexity open the need for finding of the alternative schemes, based on the electronic density as well, but having an iterative character respecting the atomic basis. The present work show how the implementation and application on the nanosystems can be treated upon an unified quantum model of the chemical bonding nature based on the couple density functional electronegativity - Markovian electronic localization functions, due to the iterative character of the quantum electronegativity.
Keywords: Electronic localization, Markovian electronic localization.
Address: Mihai V. PUTZ, Chemistry Department, WestUniversity of Timisoara, Str.Pestalozzi, No.16, 300115 Timisoara, ROMANIA.