bulmate fiz abstract cuprins 2001 2006 - upt.robuletinul ŞtiinŢific al universităţii...

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 46 (60) , Fascicola 1, 2001, ISSN 1224-6069

CONTENTS MATHEMATICS

1. Malvina BAICA – The elliptical Fermat’s Last Theorem (elflt) and the Original Euclidean Fermat’s Last Theorem (EFLT)...............................…….

5

2. Mihail B. BANARU and Galina A. BANARU – About Six-Dimensional Planar Hermitian Submanifolds of Cayley Algebra .....................................

13

3. Constantin MILICI – Sur le Calcule Automatique de Quelques Integrales Trigonometriques ……………………………………………………………

18

4. Octavian LIPOVAN – On Set Valued Functions Probabilistic Submeasurability ............................................................................................

22

5. Cristian LĂZUREANU – Some Remarks about the Rigid Body with Two Quadratic Controls .........................................................................................

31

6. Camelia ARIEŞANU – Control and Stability on the Heisenberg Lie Group H(3) .................................................................................................................

35

7. Nicolae N. NEAMŢU – A Fuctional Definition of Exponential Function .... 41

8. Paşc GĂVRUŢĂ and Liviu CĂDARIU – Stability of the Eigenvectors of an Operator Coming From Cuntz Algebras and Wavelets ...........................

47

9. Doru PĂUNESCU – A Moment Problem for Operators ............................... 55

PHYSICS

10 Ioan LUMINOSU and Cristian MARCU – On the Heat Loos of Flat-Plate Solar Collector ................................................................................................

64

11. Dusan POPOV – Position and Momentum Information Entropies of The Rotating Morse Oscillator ..............................................................................

70

12. J.P.ŠETRAJIČIĆ, B.B. TOŠIĆ, S.M.STOJKOVIĆ, D.L.J.MIRJANIĆ – Charge Carrieres Energy Spectra and States in Anisotropic and Bounded Structures ........................................................................................................

80

Mathematics

THE ELLIPTICAL FERMAT’S LAST THEOREM (ELFLT) AND THE ORIGINAL EUCLIDEAN FERMAT’S LAST THEOREM (EFLT)

Malvina BAICA

Abstract. In this paper the author will show that the Elliptical Fermat’s Last Theorem (ELFLT) proved by Faltings in the geometry of the elliptic curves is equivalent to (not the same as) the original Fermat’s Last Theorem stated by Fermat in Euclidean Geometry and proced by the author.

Keywords: Euclidean algorithm, Baica’s General Euclidean Algorithm, Euclidean Fermat’s Last Theorem, Elliptic Fermat’s Last Theorem.

Address: Malvina BAICA; Department of Mathematical and Comp.Sciences; The University of Wisconsin, Whitewater, WI 53190, U.S.A.

ABOUT SIX-DIMENSIONAL PLANAR HERMITIAN SUBMANIFOLDS OF CAYLEY ALGEBRA

Mihail B. BANARU and Galina A. BANARU

Abstract. It is proved that six-dimensional planar Hermitian submanifolds of the octave algebra are ruled manifolds.

Keywords: planar submanifold, Hermitian manifold, ruled manifols, Cayley algebra. Address: Mihail Boris BANARU; Smolensk University of Humanities, Gertsen str., 2,

Smolensk, 214014; RUSSIA Galina Anatol BANARU; Smolensk State Pedagogical University Prjevalsky

str., 4 Smolensk, 214000; RUSSIA

SUR LE CALCULE AUTOMATIQUE DE QUELQUES INTEGRALES TRIGONOMETRIQUES

Constantin MILICI

Résumé. Dans ce présent travail nous proposons de préciser le calcule automatique de quelques coefficients α des sommes trigonométriques plus générales Ap,q exprimées par l’integrale: x x x .

Keywords: calcule automatique de quelques coefficients α Address: Constantin MILICI, “Politehnica” University of Timisoara, Department of

Mathematics, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA

ON SET VALUED FUNCTIONS PROBABILISTIC SUBMEASURABILITY

Octavian LIPOVAN

Abstract. Using probabilistic generalizations of submeasure notion, in [4] the author defined the probabilistic submeasurability of set valued functions and studied some properties of this. The purpose of this paper is to obtain a criterion of probabilistic submeasurability by using the notion of “control submeasure”.

Keywords: submeasure notion, probabilistic submeasurability. Address: Octavian LIPOVAN, “Politehnica” University of Timişoara, Department of

Mathematics, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

SOME REMARKS ABOUT THE RIGID BODY WITH TWO QUADRATIC CONTROLS

Cristian LĂZUREANU

Abstract – We prove the integrability via Jacobi’s elliptic functions of the rigid body equations with two particular quadratic controls and we study the stability of the equilibrium states of this equations.

Keywords: elliptic functions of the rigid body equation. Address: Cristian LĂZUREANU, “Politehnica” University of Timişoara, Department of


CONTROL AND STABILITY ON THE HEISENBERG LIE GROUP H(3)

Camelia ARIEŞANU

Abstract. In the last time there was a great deal of interest in the study of control system on matrix Lie groups in connection with their deep applications in robotics, classical mechanics and engineering. The goal of our paper is to study such control system on the Heisenberg Lie group H(3).

Keywords: control and stability, Lie groups. Address: Camelia ARIEŞANU, “Politehnica” University of Timişoara, Department of


A FUCTIONAL DEFINITION OF EXPONENTIAL FUNCTION

Nicolae N. NEAMŢU

Abstract. The purpose of this paper is to give a functional definition of the exponential function and the basic properties of the function.

Keywords: exponential function, basic properties of the function. Address: Nicolae N. NEAMŢU, “Politehnica” University of Timişoara, Department of


STABILITY OF THE EIGENVECTORS OF AN OPERATOR COMING FROM CUNTZ ALGEBRAS AND WAVELETS

Paşc GĂVRUŢĂ and Liviu CĂDARIU

Abstract. Are given two results concerning the stability of the eigenvector of an operator studied by O.Brately and P.E.T.Jorgensen in connexion with representations of the Cuntz algebras and wavelets.

Keywords: eigenvector, functional equation. Address: Paşc GĂVRUŢĂ and Liviu CĂDARIU “Politehnica” University of Timisoara,

Department of Mathematics, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

A MOMENT PROBLEM FOR OPERATORS

Doru PĂUNESCU

Abstract – We study a family of bounded linear operators double indexed by a subsemigroup, operators which satisfies both a positivity condition introduced by Zoltan Sebestyen in [5] and a regularity one introduced by P.Găvruţă and the author in [1]; we prove the these operators can be expressed in terms of communiting semigroups of operators acting on an appropriate Hilbert space.

Keywords: family of bounded linear operators. Address: Doru PĂUNESCU “Politehnica” University of Timişoara, Department of


Physics

ON THE HEAT LOOS OF FLAT-PLATE SOLAR COLLECTOR

Ioan LUMINOSU and Cristian MARCU

Abstract – The paper sets itself to illustrate, based on relations presented in literature, the way in which the global heat loss coefficient was predetermined by numerical method, as well to present its values, as a result of measurements performed by means of a set of collectors used in the western part of Romania.

Keywords: solar collector Address: Ioan LUMINOSU and Cristian MARCU “Politehnica” University of Timişoara,

Physics Department, P-ţa Regina Maria, Nr.1, ROMANIA.

POSITION AND MOMENTUM INFORMATION ENTROPIES OF THE ROTATING MORSE OSCILLATOR

Dušan POPOV

Abstract. In the paper we have examined the position – and moment – space information entropies of the rotating Morse potential, which plays a dominant role in model calculations in molecular spectroscopy. These entropies are related to new appearing kind of entropy, called “entropy of the hypergeometrical function” and which is calculated in the parabolic logarithm approximation. Keywords: Morse potential, molecular spectroscopy

Address: Dušan POPOV, “Politehnica” University of Timişoara, Physics Department, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

CHARGE CARRIERES ENERGY SPECTRA AND STATES IN ANISOTROPIC AND BOUNDED STRUCTURES

J. P. ŠETRAJIČIĆ, B. B. TOŠIĆ, S. M. STOJKOVIĆ, D. L. J. MIRJANIĆ

Abstract. In this paper we shll study crystaline structures where translational symmetry of the atom (ion) distribution of the electron (or hole) system in broken by the sputtering and due to existence of two boundary surfaces. This is a model of high-temperature superconductors in which the observed symmetry breaking orthogonal to CuO planes was treated as a perturbation. The single-particle fermion wave functions and the possible energies of charge carriers were determined. The competitive existence of the superconductive and normal regions in such sample was shown in agreement with experimental data. The conditions for the formation of superconductive states and the limitations on current density values in the planes parallel to boundary surfaces (in CuO planes) were obtained and discussed. Keywords: states in anisotropic structures

Address: J. P. ŠETRAJIČIĆ, Institute of Physics, Faculty of Sciences, University of Novi Sad, Trg D.Obradovića 4, 21 000 Novi Sad, Yugoslavia. B. B. TOŠIĆ ŠETRAJIČIĆ, Institute of Physics, Faculty of Sciences, University of Novi Sad, Trg D.Obradovića 4, 21000 Novi Sad, Yugoslavia.

S. M. STOJKOVIĆ, Technical Faculty “M.Pupin”, Zrenjanin, University of Novi Sad, Dj.Djaković bb, 23 000, Zrenjanin, Yugoslavia.

D. L. J. MIRJANIĆ, Faculty of Medicine, University of Banja Luka, Save Mrkalja 14, 78 000, Banja Luka, Bosnia and Hercegovina.



1. Valeriu POPA and Takashi NOIRI – On m-Continuous Multifuntions .................................. 1

2. Mihail BANARU – Two Theorems on Cosymplectic Hypersurfaces of Six-Dimensional Kahlerian Submanifold of Cayley Algebra ............................................................................

13

3. Titu BÂNZARU – Multifunctions with Values in Generalized Uniform Spaces …………….. 18

4. Octavian LIPOVAN - The Submeasurability of Functions with Values in Product of Probabilistic Metric Structure ................................................................................................

24

5. Dan DĂIANU - Structure of Additive a-Categories ............................................................. 32

6. Constantin MILICI - Sur le Calcule Automatique de Quelques Integrales Trigonometriques (II) ……………………………………………………………………………………………………….

44

7. Mihai NEAGU and Dan POPESCU - About the Pseudohomogeneous Distribution ................................................................................................................................................

48

8. Gabriela CRISTESCU and Liana LUPŞA - General Convexity for Functions Associated to General Convexity for Sets ..................................................................................................

47

9. Emil POPESCU - An Integral Representation of the Operators which Form a Feller Semigroup ...............................................................................................................................

62

PHYSICS

10. Bernhard ROTHENSTEIN, Albert ROTHENSTEIN, Floricica BARVINSCHI - Shadow Motion with Surprises ...........................................

66

11. Ioan ZAHARIE and Marin LIŢĂ - The Crystallization Kinetics of Fe65 Gd10 Cr5 BB20 Amorphous Alloys ..............................................................................

74

12. Adriana Sida MANEA - Theoretical and Experimental Study on the Flows in the Presence of an Airfoil ............................................................................

80

13. Dusan POPOV - Uncertainty Through the Coherent States for the BDS-Hamiltonian ............................................................................................

86

14. L.HRIANCA, M.CRISTEA, A.ZAMFIR, M.GANGĂL, M.ŞTEFĂNESCU - Radio frequency magnetic properties of Ni-Ferrite .....................................

94

Mathematics

ON M-CONTINUOUS MULTIFUNTIONS Valeriu POPA and Takashi NOIRI

Abstract. The authors define a multifunction F : X→Y to be m-continuous if for each point

x∈ X and any open sets G1, G2 of Y such that F(x) ⊂ G1 and F(x) ∩ G2≠ ∅, there exists and m-open set U of X containing x such that F(U) ⊂ C1(G1) and F(u)∩ C1(G2) ≠ ∅ for every u ∈ U. The functions enable us to unify continuity, α-continuity, quasi-continuity, precontinuity, and β-continuity for multifunctions. They obtain some characterizations and several properties concerning m-continuous multifunctions.

Keywords: minimal structure, m-open, m-continuous, multifunction. Address: Valeriu POPA, Department of Mathematics, University of Bacău, 5500 Bacău,

ROMANIA. Takashi NOIRI. Department of Mathematics, Yatsushiro College of

Technology, Yatshiro, Kumamoto, 866-8501, JAPAN.

TWO THEOREMS ON COSYMPLECTIC HYPERSURFACES OF SIX-DIMENSIONAL

KAHLERIAN SUBMANIFOLD OF CAYLEY ALGEBRA

Mihail BANARU

Abstract – It is proved that the type number of an arbitrary cosymplectic hypersurface of a six-dimensional Kahlerian submanifold of Cayley algebra is at most one.

Keywords: cosymplectic manifold, Khlerian manifold, type number. Address: Mihail Boris BANARU; Smolensk University of Humanities, Gertsen str., 2,

Smolensk, 214014; RUSSIA

MULTIFUNCTIONS WITH VALUES IN GENERALIZED UNIFORM SPACES

Titu BÂNZARU

Abstract – We consider multifunctions with values in generalized uniform spaces, where generalized uniform structure is expressed in terms of converings.

For nets of such multifunctions, relatioships between the almost uniform convergence and uniform one are established. Also, some characterizations of the continuity are given.

Keywords: uniform spaces, uniform structures, nets of multifunctions. Address: Titu BÂNZARU, “Politehnica” University of Timisoara, Department of

Mathematics, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA THE SUBMEASURABILITY OF FUNCTIONS WITH VALUES IN PRODUCT OF

PROBABILISTIC METRIC STRUCTURE

Octavian LIPOVAN

Abstract – In the [7] the author defines the submeasurability for the probabilistic metric structures-valued functions and studied some properties of this concept in the case of mappings valued in product of probabilistic metric structures.

Keywords: submeasurability of probabilistic metric structures Address: Octavian LIPOVAN Politehnica” University of Timişoara, Department of


STRUCTURE OF ADDITIVE A-CATEGORIES

Dan DĂIANU

Abstract. In this paper we present some classes of additive a-categories and we prove the constructivity of an a-category of modules over an a-category. Also we commence the study of concretizable a-categories (a-c-categories); we show that any a-c-category (C,C’) one insomorphically immerses in the canonical a-category over C’; we give also some results on the structure of simple and artinian a-c-categories.

Keywords: Address: Dan DĂIANU “Politehnica” University of Timişoara, Department of


SUR LE CALCULE AUTOMATIQUE DE QUELQUES INTEGRALES TRIGONOMETRIQUES (II)

Constantin MILICI

Résumé. Dans ce présent travail nous proposons de préciser le calcule automatique de quelques coefficients α des sommes trigonométriques plus générales Ap,q exprimées par l’integrale: x x x .

Keywords: Address: Constantin MILICI, “Politehnica” University of Timişoara, Department of


ABOUT THE PSEUDOHOMOGENEOUS DISTRIBUTION

Mihai NEAGU and Dan POPESCU

Abstract –.In the present paper we have introduced the notion of pseudohomogeneous distribution.

Keywords: pseudohomogeneous distribution. Address: Mihai NEAGU, and Dan POPESCU, “Politehnica” University of Timişoara,

Department of Mathematics, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

GENERAL CONVEXITY FOR FUNCTIONS ASSOCIATED TO GENERAL CONVEXITY FOR SETS

Gabriela CRISTESCU and Liana LUPŞA

Abstract. The purpose of this paper is to define a general notion of convexity for functions associated to a given notion of convexity for stes, without involving the notion of cone. Various couples of convexities for sets and for functions are presented in more frameworks.

Keywords: Address: Gabriela CRISTESCU, Aurel Vlaicu University of Arad, Department of

Mathematics and Computer Science, Bd.Revoluţiei, No.81, 2900 Arad, ROMANIA. Liana LUPŞA, Babeş-Bolyai University of Cluj-Napoca, Faculty of

Mathematics and Computer Science, Str.Kogălniceanu, No.1, 3400 Cluj-Napoca, ROMANIA.

AN INTEGRAL REPRESENTATION OF THE OPERATORS WHICH FORM A FELLER SEMIGROUP

Emil POPESCU Abstract. Keywords: Address: Emil POPESCU, Military Technical Academy of Bucharest, Department of

Mathematics, B-dul G.Coşbuc, 81-83, Bucharest, ROMANIA. Physics

SHADOW MOTION WITH SURPRISES

Bernhard ROTHENSTEIN, Albert ROTHENSTEIN, Floricica BARVINSCHI

Abstract. . A source of light moving parallel to the ground, with constant velocity u=βc and at a height H, approaches a vertical opaque wall of height h<H: (m=H/h). The wall casts a

shadow on the ground limited by a point Q(x,0) and the wall m

1m −<βit-self Qw(0,0), if . If

m1m −

>β , all the points between the wall and a point Q (x1 1,0) are in shadow, all the points

between Q (x1 1,0) and Q (x2 2, 0); (x >x2 1) are illuminated, whereas all the points characterized by x>x2 are in shadow too. Point Q moves in accordance with intuition to the left approaching the wall. Point Q moves to the left, whereas point Q moves to the right. Points Q and Q1 2 1 2 could move with velocities exceeding the velocity of light, as not carrying energy or information in the direction of their motion. The light is switched off at the instant the source is directly over the wall.

Keywords: light moving, shadow

Address: Bernhard ROTHENSTEIN and Floricica BARVINSCHI, “Politehnica” University of Timişoara, Physics Department, P-ţa Regina Maria 1, 1900 Timişoara, ROMANIA

Albert ROTHENSTEIN, Center of Vision Research, York University, 105 Farquaharson, Toronto, Ontario, Canada M3J1P3

THE CRYSTALLIZATION KINETICS OF Fe65Gd10Cr5BB20 AMORPHOUS ALLOYS

Ioan ZAHARIE and Marin LIŢĂ

Abstract. In the present paper the non-isothermal crystallization kinetics of Fe65Gd10Cr5BB20 amorphous alloys is investigated by differential thermal analysis (DTA). The crystallization of Fe65Gd10Cr5B20 B amorphous alloys has been realized through three processes characterized by the activation energies ε1=2.7±0.1eV, ε2=3.7±0.3eV, ε3=3.0eV. By X-ray diffraction (XRD) we established the crystalline phases which appeared in the non-isothermal crystallization proces: FeB, Fe2B, Fe3B, CrB4, Cr5BB3, Gd2B5B .

Keywords: non-isothermal, crystallization, activation energy Address: Ioan ZAHARIE, “Politehnica” University of Timişoara, Physics Department,

P-ţa Regina Maria 1, 1900 Timişoara, ROMANIA Marin LIŢĂ, Faculty of Mechanical Engineering, Department for Materials

Science and Heat Treatments, University “Politehnica”, Bd.Mihai Viteazu, nr.1, 1900 Timişoara, ROMANIA.

THEORETICAL AND EXPERIMENTAL STUDY ON THE FLOWS IN THE PRESENCE OF AN AIRFOIL

Adriana Sida MANEA

Abstract. This paper presents theoretical and experimental results obtained in the flow over an S airfoil in the directing apparatus of turbine – pump reversible hydraulic machines.

Keywords: airfoil, turbine, Reynold number Address: Adriana Sida MANEA,“Politehnica” University of Timişoara, Faculty of

Mechanical Engineering, Department for Materials Science and Heat Treatments, University “Politehnica”, Bd.Mihai Viteazu, nr.1, 1900 Timişoara, ROMANIA.

UNCERTAINTY THROUGH THE COHERENT STATES FOR THE BDS-HAMILTONIAN

Dušan POPOV

Abstract. In the paper we have examined the uncertainty relations both in the traditional formulation (THE Heisenberg relations) and in a new point of view (the entropic uncertainty relation) related to the BDS-Hamiltonian. This is a X-deformed non-Hermitian Hamiltonian for the harmonic oscilator, which was introduced by Beckeres Debergh and Szafraniec. With the BDS-coherent states we calculate the uncertainty relations and we obtain the lower bound in accordance with the general theorem formulated by Bialynicki-Birula and Mycielski. Keywords: X-deformed, harmonic oscillator, BDS-coherent states

Address: Dusan POPOV, “Politehnica” University of Timişoara, Physics Department, P-ţa Regina Maria Nr.1, O.P.5, ROMANIA

RADIO FREQUENCY MAGNETIC PROPERTIES OF Ni-FERRITE

L.HRIANCA, M.CRISTEA, A.ZAMFIR, M.GANGĂL, M.ŞTEFĂNESCU

Abstract. The dependence of complex magnetic susceptibility on frequency in the range of (10-50) MHz was perfromed for pulverous Ni-ferrite (NiFe2O4) with the grain sizes of 60-350μm,

of high purity, using a short-circuite transmission line and the Q-meter, ar room temperature. It can be noticed that its than δm versus frequence does not show a maximum in the accessible range of frequency but it shows the tendency to a maximum at a frequency value over 50 MHz. The real component χ of magnetic susceptibility presents a maximum value at about 42 MHz. Keywords: Ni-ferrite, Q-meter

Address: L.HRIANCA, A.ZAMFIR, Faculty of Physics, West University of Timişoara, B-dul V. Pârvan, No.4, 1900 Timişoara, ROMANIA.

M.ŞTEFĂNESCU, Faculty of Engineering Chemistry “Politehnica” University of Timişoara, ROMANIA

M.CRISTEA, M., M.GANGĂL, “Politehnica” University of Timişoara, Physics Department, P-ţa Regina Maria Nr.1, O.P.5, ROMANIA.




Seria MATEMATICǍ - FIZICǍ Transactions on MATHEMATICS & PHYSICS Tom 47(61) , Fascicola 1, 2002, ISSN 1224-6069


1. H.SASAYAMA - On the theory of hypercomplex n-tuple spaces, I supra nilfactors and supra-Fréchet differentiation in E(σ) ………………

1

2. L.S.VELIMIROVIC – On variation of the volume bounded by rotational surface under infinitesimal bending of meridian .......................................

6

3. L.S.VELIMIROVIC – On bending of hyperbolic paraboloid ................... 14

4. M.BAICA – Clarification of the author’s previous paper on Goldbach’s conjecture .………......................................................................................

20

5. N.BOJA – On the volume formula of an ε-absolutely thin tube ………... 35

6. G.CRISTESCU, L.LUPŞA – Generalized graph – related convex functions …………....................................................................................

39

7. C.STOICA, L.SIDA – Osculating convexity of first order for plane curves …………………………………………….....................................

45

8. F.MUNTEANU – Conservation laws for dynamical Hamiltonian systems on Hamilton space of order k ≥ 1 …………………………….....

53

9. P.GĂVRUTA, L.CĂDARIU – General stability of the cubic functional equation ......................................................................................................

59

PHYSICS

10. M.BOLDAN, M.GANGĂL – Researches regarding the Co-Be thin films 71

11. M.GANGĂL, M.BOLDAN – Researches upon the achievement of some new vitroceramic materials ........................................................................

75

12. B.ROTHENSTEIN, A.De SABATA, F.BARVINSCHI – Black-body radiation: The Lorentz transformation of Planck’s law ............................

78

13. I.HRIANCA, M.CRISTEA, A.RATUSZNA, N.STEFU – Complex magnetic permeability of some Li and Li-Zn ferrites ................................

85

14. M.CRISTEA, I.DAMIAN – EPR spectra of some ternary oxidic solid solutions .............. 90

15. H.E.PORTEIANU, T.DITTRICH, F.KOCH – Microwave transient photoconductivity studies in porous semiconductors ................................

97

16. C.MARCU, I.LUMINOSU, F.LUPEA – About the efficiency of solar energy storage in the pebble beds ..............................................................

104

Mathematics

ON THE THEORY OF HYPERCOMPLEX N-TUPLE SPACES I - SUPRA NILFACTORS AND SUPRA-FRÉCHET DIFFERENTIATION IN E(σ) -

Hiroyoshi SASAYAMA

Abstract. In the present paper, we shall show that the notion of the supra-nilfactors (i.e. supra zero divisor) can be considered also in the hypercomplex n-tuple space and that there is a sufficient condition for non-appearance of both nilfactors and supra-nilfactors in E(σ), together with the definition of supra-Fréchet differentiability equivalent to the one given in the previous paper [I.11] which gives the generalized C.R. equations.. Keywords: hypercomplex n-tuple, nilfactors.

Address: Hiroyoshi SASAYAMA, The Sasayama Institute, JAPAN

ON VARIATION OF THE VOLUME BOUNDED BY ROTATION SURFACE UNDER INFINITESIMAL BENDING OF MERIDIAN

Ljubica S. VELIMIROVIĆ

Abstract. In this paper we investigate infinitesimal bending of a curve. Specially, the infinitesimal bending field that plane curve includes in a family of plane curves is given. Change of the volume bounded by rotational surface, under infinitesimal bending of the meridian, remaining closed plane curve, is given. The variation of the volume in this case does not have to be zero. Two examples are considered. In a case of a circle the volume is stationary, but in a case of cardioid variation of volume is non-zero.

Keywords: Infinitesimal bending, curve, infinitesimal bending of meridian, variation, volume

Address: Ljubica S. VELIMIROVIĆ, University of Nis, Department of Mathematics; Cirila I Metodija 2, 18000 Niš, REPUBLIC OF SERBIA.

ON BENDING OF HYPERBOLIC PARABOLOID

Ljubica S. VELIMIROVIĆ

Abstract. In this paper we consider geometric characteristic of a surface of hyperbolic paraboloid. Bending and infinitesimal bending of such a surface is considered. Infinitesimal bending field of hyperbolic paraboloid is given. In building constructional sense it is a surface of a great bearing capacity by which a space based on any desired from can be covered.

Keywords: Hyperbolic paraboloid, infinitesimal bending, bending. Address: Ljubica S. VELIMIROVIĆ, University of Nis, Department of Mathematics;

Cirila I Metodija 2, 18000 Niš, REPUBLIC OF SERBIA.

CLARIFICATIONS OF THE AUTHOR’S PREVIOUS PAPER ON GOLDBACH’S CONJECTURE Malvina BAICA

Abstract. In a previous paper [1] the author gave a tentative proof of Goldbach’s

Conjecture. The purpose of this paper is to provide additional explanations and to give a definitive version of the above mentioned work.

Keywords: Goldbach’s Conjecture Address: Malvina BAICA, The University of Wisconsin, Department of Mathematical and

Comp. Science, Whitewater, WI 53190, U.S.A.

ON THE VOLUME FORMULA OF AN ε-ABSOLUTELY THIN TUBE

Nicolae BOJA

Abstract. It is established a formula of the volume of an ε-absolutely thin tube in the ambient Euclidean 3-space depending only on the tube tickness and on the total absolute curvature of its middle surface.

Keywords: ε-absolutely thin tube, shape operator, total absolute curvature, tube tickness and volume.

Address: Nicolae BOJA, “Politehnica” University of Timisoara, Department of Mathematics; P-ta. Victoriei, No. 2, 300006 – Timisoara, ROMANIA.

OSCULATING CONVEXITY OF FIRST ORDER FOR PLANE CURVES

Codruţa STOICA and Lavinia SIDA

Abstract. In this paper we intend to study the relationship between a convexity for curves defined by means of the position of the osculating circle’s center and various types of convexity for sets and functions. We take into account the classical convexity for functions, the generalized (H, C)-convexity for functions and the ((S, s), r) convexity for sets.

Keywords: convexity for curves , (H, C)-convexity for functions, ((S, s), r) convexity for sets. Address: Codruta STOICA, Lavinia SIDA, “Aurel Vlaicu” University of Arad,

Department of Mathematics and Computer Science; Bd. Revoluţiei, No. 81; 2900 Arad, Romania; E-mail: [email protected].

CONSERVATION LAWS FOR DYNAMICAL HAMILTONIAN SYSTEMS ON HAMILTON SPACES OF ORDER k ≥ 1

Florian MUNTEANU

Abstract. In this paper we study dynamical Hamiltonian systems on some submanifold of the dual bundle of a k tangent bundle. Using the notions of symmetry and pseudosymmetry we obtain a kind of conservation laws for the higher order Hamiltonian, like in the case of classical Hamiltonian on T*M.

Keywords: conservation law, symmetry, dynamical system, Hamiltonian system, Hamilton space of order k ≥ 1, Hamilton-Jacobi equations.

Address: Florian MUNTEANU, University of Craiova, Department of Applied Mathematics; 1100 Craiova, Romania, E-mail: [email protected]

GENERAL STABILITY OF THE CUBIC FUNCTIONAL EQUATION

Paşc GĂVRUTA and Liviu CĂDARIU

Abstract. In this paper, we give some general results on the stability of the cubic functional equation considered recently by J.M. Rassias [4].

Keywords: group homomorphism, cubic functional equation, Banach space, cubic mapping. Address: Pasc GAVRUTA, Liviu CADARIU, “Politehnica” University of Timisoara,

Department of Mathematics; P-ta. Victoriei, No. 2, 300006 Timisoara, ROMANIA; E-mail: [email protected]; [email protected].

mailto:[email protected]




Physics

RESEARCHES REGARDING THE CO-BE THIN FILMS M. BOLDAN, M.GANGĂL

Abstract. In order to achieve Co-Be ferromagnetic thin films using the electrodeposition

method. The conditions to be respected are: the adherence and the continuity of the obtained sample, the maximum of deposition efficiency and the chemical, mechanical and magnetic properties to be reproducible, answering to the purpose.

The experience shows that little changes in deposition conditions have a consequence major variations in the quality of the investigated samples.

Keywords: ferromagnetic thin films Address: M.BOLDAN, M.GANGĂL, “Politehnica” University of Timişoara, Physics

Department, P-ţa Regina Maria, Nr.1, ROMANIA.

RESEARCES UPON THE ACHIEVEMENT OF SOME NEW VITROCERAMIC MATERIALS

M.GANGĂL, M.BOLDAN

Abstract. Progress of modern techniques cannot be imagined without magnetic materials, thus, for this reason, in the last few years in order to obtain new materials, many studies were leaded on the achievement of vitroceramic materials containing metalic oxides.

Keywords: magnetic materials Address: M.BOLDAN, M.GANGĂL, “Politehnica” University of Timişoara, Physics

Department, P-ţa Regina Maria, Nr.1, ROMANIA.

BLACK-BODY RADIATION:THE LORENTZ TRANSFORMATION OF PLANCK’S LAW

Bernhard ROTHENSTEIN, Aldo De SABATA, Floricica BARVINSCHI

Abstract. A simple and transparent derivation of the Lorentz transformation of Planck’s law is presented. It requires the knowledge of the laws governing black-body radiation in the rest frame of the source, the Lorentz-Einstein transformations for the space-time coordinates of events, and the Doppler effect. A diagram is proposed that displays, in true values, the physical quantities associated to black-body radiation in the rest frame of the source, and in a reference frame relative to which the source moves with constant velocity.

Keywords: black-body radiation Address: B. ROTHENSTEIN, F. BARVINSCHI, “Politehnica” University of Timişoara,

Physics Department, P-ţa Regina Maria, Nr.1, ROMANIA; Aldo De SABATA, “Politehnica” University of Timişoara, Department of

Electrical Measures and Optoelectronics, Bv.V.Parvan, 2, 1900 Timişoara, ROMANIA,

COMPLEX MAGNETIC PERMEABILITY OF SOME LI AND LI-ZN FERRITES

I.Hrianca, M. Cristea, A. Ratuszna, N. Stefu

Abstract. The dependence of complex magnetic permeability on frequency in the range 4 ÷35 MHz was determined, for two types of powder Li ferrite and LiZn ferrite samples. The X - spectra of samples before and after calcination are discussed. The results of magnetic measurements

show very small magnetic losses, independent on frequency, but increase significantly after sintering process.

Keywords: Li ferrite, LiZn ferrite Address: M. CRISTEA, “Politehnica” University of Timişoara, Physics Department, P-ţa

Regina Maria, Nr.1, ROMANIA; I.HRIANCA, N.STEFU, West University of Timisoara, Faculty of Physics, Bd. V. Pârvan no.4, 1900, Timisoara, ROMANIA

A. RATUSZNA: Institute of Physics, University of Silesia, Katowice, Poland

MICROWAVE TRANSIENT PHOTOCONDUCTIVITY STUDIES IN POROUS SEMICONDUCTORS

Horia-Eugen PORŢEANU, Elisaveta KONSTANTINOVA, Vladimir KYTIN, Oleg LOGINENKO,Victor TIMOSHENKO,

Thomas DITTRICH, Frederick KOCH

Abstract: The dynamics of the photogenerated carriers in porous silicon and TiO2 anatase was studied at 35 GHz by measuring the change in time of the conductivity σ and dielectric constant εr. Localization of carriers leads to a positive change of εr, while quasifree carriers to a negative change. Size reduction in Si shortens the recombination time as long as the surface traps are not significant. Magnetic field investigations show opposite variation of conductivity in porous silicon compared with TiO2.

Keywords: porouse silicon Address: E. KONSTANTINOVA , V. KYTIN, O. LOGINENKO,

V. TIMOSHENKO, Lomonosov Moscow State University, Moscow, RUSSIA. T. DITTRICH, F. KOCH, Technische Universität München,

Physik-Department E16, 85747 Garching, GERMANY

ABOUT THE EFFICIENCY OF SOLAR ENERGY STORAGE IN THE PEBBLE BEDS

Cristian MARCU, Ioan LUMINOSU, Filip LUPEA

Abstract. It is well known, that the solar energy utilization in the processes of heating has required, in the most instances, the presence of a storage segment [1]. The method of the pebble bad storage is very suitable into all of the cases in which the air is circulated as the thermal agent (the working fluid).

The paper provides a review of the behavior of the pebble bed storage systems in correlation with the shape and the sizes of storage tancks and storage materials, the rate flow of air and some considerations on the thermal balance.

Keywords: solar energy Address: Cristian MARCU, Ioan LUMINOSU “Politehnica” University of Timişoara,

Physics Department, P-ţa Regina Maria, Nr.1, ROMANIA Filip LUPEA, “Politehnica” University of Timişoara, Electroenergetics Department, Str. V.Pârvan Nr.2, 1900, Timişoara, ROMÂNIA

Seria MATEMATICǍ - FIZICǍ Transactions on MATHEMATICS & PHYSICS Tom 47(61), Fascicola 2, 2002, ISSN 1224-6069


1. H.SASAYAMA - On the Theory of Hypercomplex n-tuple Spaces, II - Generalized R.Fueter’s Polynomials - ……………………………………………………………………….

1

2. M.CÂRDU, M.BAICA – Elements of Poligonal Trigonometry .…………………………. 7

3. L.CĂDARIU – A General Theorem of Stability for the Cauchy’s Equation ………… 14

4. L.CRISTEA – A Metric Property of Special Simplexes ………………............................. 29

5. O.LIPOVAN – The √-Uniformities on Probabilistic Metric Structures- -Valued Function Spaces ………………………………………………............................................... 33

6. Gh.M.TUDOR – Inégalites Intégrales (II) ……………………………………………………. 42

7. M.NEAGU, D.POPESCU – Distributional Functional Identities Characterizing Quadratic Polynomials ………………………………………………………………………..

46

PHYSICS

8. A. RATUSZNA, J. RYBCZYNSKI, Ph. DANIEL – Studies of structural distortion of NaZnF

3 perovskite ................................................................ 52

9. Abraham A. UNGAR – The Relativistic Doppler Effect Without Clock Synchronization .........................................................................................

60

10. B. ROTHENSTEIN, I. ZAHARIE – Zero, Infinite and Negative Reception Periods of Acoustic Signals? What Does That Mean? .............

69

11. B. ROTHENSTEIN, D. PĂUNESCU, F. BARVINSCHI – A relativistic space-time diagram for photographers in relative motion .........................

75

12. D. POPOV – Photon-Added Coherent States of the Harmonic Oscillator – Revisited .................................................................................................

83

13. I. HRIANCA, M. CRISTEA, M.BOLDAN, A. ZAMFIR, C. CAIZER – Some aspects of the maagnetic behaviour of LiZn ferrite .........................

91 14. L. LIGHEZAN – The application of the symmetry groups theory on the study of the F

color center energy levels in alkali halides .........................

99 Mathematics

ON THE THEORY OF HYPERCOMPLEX N-TUPLE SPACES II - GENERALIZED R.FUETER’S POLYNOMIALS -

Hiroyoshi SASAYAMA

Abstract. R. Fueter introduced left and right regular polynomials and showed any function f(z), which is regular at the origin, can be expanded in the uniformly convergent series:

)(321 zp nnn

)()( 321321321 )(0

zpczfw nnnnnnmnnnm

∑∑=++

∞

=== . In his paper [II.1] (1963) on the theory of

quaternion functions of a quaternion variable z = kkk

ix∑=

3

0, were considered the polynomials

( )( ) ( ) )(,!

1321

)(002201 mnnnxixxixxix

m mmr

m kkk

kkkk =++−−−≡ ∑ K )(321 zp nnn

Keywords: Multilinear function extended to the left, to the right from the ordinary symmetric multilinear functions, Right-Left generalized R.Fueter’s polynomials.. Address: Hiroyosi SASAYAMA, The Sasayama Institute, JAPAN

A GENERAL THEOREM OF STABILITY FOR THE CAUCHY’S EQUATION

Liviu CĂDARIU

Abstract. In this paper, we obtain a slight generalization to β-normed spaces of the Theorems of Rassias, Gajda and Kim & Jun concerning the stability of Cauchy’s functional equation.

Keywords: β-normed spaces Address: Liviu CADARIU, “Politehnica” University of Timişoara, Department of

Mathematics, P-ta Victoriei, No. 2, 300006-Timişoara, ROMANIA, [email protected].

A METRIC PROPERTY OF SPECIAL SIMPLEX

Ligia-Loreta CRISTEA

Abstract. In this paper we generalise a welknown metric property of rectangular triangles with congruent catheti for special s-simplices, s ≥ 3.

Keywords: special s-simplices Address: Ligia Loreta CRISTEA, “Politehnica” University of Timişoara, Department of

Mathematics, P-ta. Victoriei, No. 2, 300006-Timişoara, ROMANIA.

The √-UNIFORMITIES ON PROBABILISTIC METRIC STRUCTURES-VALUED FUNCTION SPACES

Octavian LIPOVAN

Abstract. In [9] the author defines a general form of submeasure with probabilistic structure in such way that the topological ring of sets introduced is a uniform space. As particular cases some probabilistic generalizations of the submeasure concept from [8] are obtained. The probabilistic submeasure are introduced for modeling those situation in which we have only probabilistic information about the measure of the set.

In this paper, using probabilistic generalizations of submeasure notion, there are introduced some uniformities on probabilistic metric structures-valued function spaces.

Keywords: probabilistic generalizations of submeasure notion; metric structures Address: “Politehnica” University of Timişoara, Department of Mathematics, P-ta.

Victoriei, No. 2, 300006-Timişoara, ROMANIA.

INÉGALITÉS INTÉGRALES (II)

Gheorghe M. TUDOR

Abstract. Dans cet articles, nous avons en vue quelques résultats relatifs aux inégalités concernant des polynômes trigonométriques, obtenus certaines ouvrages (voir par exemple [2], [3], [4]). Ces inégalités nous donneront la possibilité d’obtenir quelques inégalités intégrales, a notre avis, intéressantes..

Keywords: polynômes trigonométriques, Address: Gheorghe M. TUDOR, “Politehnica” University of Timişoara, Department of

Mathematics, P-ta Victoriei, No. 2, 300006-Timişoara, ROMANIA.


DISTRIBUTIONAL FUNCTIONAL IDENTITIES CHARACTERIZING QUADRATIC POLYNOMIALS

Mihai NEAGU and Dan POPESCU

Abstract: Author studies three distributional functional identities which characterize quadratic polynomials utilizing notion of direct extensions and direct sections of distributions. In the next papers, this results will be generalized.

Keywords: distributional functional identity; quadratic polynomials Address: Mihai NEAGU, Dan POPESCU, “Politehnica” University of Timişoara,

Department of Mathematics, P-ta. Victoriei, No. 2, 300006 Timişoara, ROMANIA.. Physics

STUDIES OF STRUCTURAL DISTORTION OF NAZNF3 PEROVSKITE

A.RATUSZNA , J. RYBCZYŃSKI, Ph. DANIEL Abstract. Perovskite – like crystal, NaZnF3 has been studied by the powder X-ray

diffraction technique at the room temperature because the measurements of the lattice parameters versus temperature have not shown any changes of the symmetry.

The monoclinic distortion caused by the tilting of ZnF6 octahedra, type of a-b+a-, distortion of these octahedra and displacement of the sodium cations from their special positions has been described in the higher symmetry, orthorhombic with the lattice parameters: a=5.581(3)Å, b=7.766(2)Å, c=5.407(2)Å.

Keywords: powder X-ray diffraction, Rietveld profile refinement, perovskite structures, NaZnF3, Address: A. RATUSZNA, J. RYBCZYŃSKI, Institute of Physics, University of Silesia,

Katowice, Poland Ph. DANIEL, Laboratoire de Physique de l’Etat Condensè URA CNRS No807

Université du Maine, Avenue Olivier Messiaen, 72017 Le Mans-France

THE RELATIVISTIC DOPPLER EFFECT WITHOUT CLOCK SYNCHRONIZATION

Abraham UNGAR

Abstract. The synchronization of distant inertial clocks and the measurement of the one-way speed of light (or any signal) presuppose one another. According to Reichenbach, clock synchronization is a matter of convention and, hence, the one-way speed of light is immeasurable. A recently developed formalism for dealing with special relativity theory without clocl synchronization, as viewed by Reichenbach, is applied here to the study of the Doppler effect without clock synchronization. In accordance with the immeasurability of one-way velocities, it is shown here that Doppler effect is synchrony free.

Keywords: Doppler effect Address: Abraham UNGAR, Department of Mathematics, North Dakota State University,

Fargo, ND 58105, USA, E-mail: [email protected]

ZERO, INFINITE AND NEGATIVE RECEPTION PERIODS OF ACOUSTIC SIGNALS? WHAT DOES THAT MEAN?

Bernhard ROTHENSTEIN, Ioan ZAHARIE

Abstract. The behaviour of the formulas describing the Doppler shift in the case of source

and observer moving with sonic and supersonic velocities is investigated. The occurrence of zero, infinite and even negative reception period is explained.

Keywords: Doppler shift, observer Address: B. ROTHENSTEIN, I. ZAHARIE, “Politehnica” University of Timişoara,

Physics Department, P-ţa Regina Maria, Nr.1, ROMANIA, e-mail: [email protected] , e-mail: [email protected]

A RELATIVISTIC SPACE-TIME DIAGRAM FOR PHOTOGRPHERS IN RELATIVE MOTION

Bernhard ROTHENSTEIN, Doru PĂUNESCU, Floricica BARVINSCHI

Abstract. A relativistic space-time diagram is proposed, displaying in true values the space-time coordinates (in Cartesian and in polar coordinates as well) of “photographed” events, as detected from the reference frame where the point is at rest and from inertial reference frames relative to which it moves with constant speed parallel to the common OX(O’X’) axes. The diagram is used in order to find out the photographed shape of lines parallel to the OY (O’Y’) axes and of circles the center of which are located somewhere in the (X’O’Y’) plane.

Keywords: space-time Address: B. ROTHENSTEIN, F. BARVINSCHI, “Politehnica” University of Timişoara,

Physics Department, P-ţa Regina Maria, Nr.1, ROMANIA Doru PĂUNESCU, “Politehnica” University of Timişoara, Mathematics Department,

P-ţa Regina Maria, Nr.1, ROMANIA

PHOTON-ADDED COHERENT STATES OF THE HARMONIC OSCILLATOR-REVISITED

Dušan POPOV

Abstract. We examine some characteristics of photon-aded coherent states (PACSs), i.e. normalization, non-orthogonality, resolution of the unity, as well as the photon-added thermal states (PATSs). We find a more compact expression of the integration measure in the resolution of the unity, by using the Meijer’s G-function. Also, we find the diagonal representation of the density operator and, implicitly, the Q-and P-distribution functions.

Keywords: photon-added, Address: Dušan POPOV, “Politehnica” University of Timişoara, Physics Department, P-

ţa Regina Maria, Nr.1, Timişoara, ROMANIA, e-mail: [email protected]

SOME ASPECTS OF THE MAGNETIC BEHAVIOUR OF LiZn FERRITE

I. HRIANCA, M. CRISTEA, M. BOLDAN, A. ZAMFIR, C. CAIZER

Abstract. The paper presents some experimental aspects concerning the rotational hysteresis of LiZn ferritewith Bu2O3 admixture synthesized by ceramic method. It was followed the effect curves of rotational hysteresis for ferrite samples (disc-shaped) that are rotated (3-50 rot/s) in a static magnetic field (2-100 kA/m) as well as the influence of samples’ peliculiarities on effect curves. Also the magnetic hysteresis loops of ferrite samples by magnetoinductive method, at 50 Hz were registrated.

Keywords: rotational hysteresis, LiZn ferrite, magnetic hysteresis loop Address: M. CRISTEA, M. BOLDAN, “Politehnica” University of Timişoara, Physics

Department, P-ţa Regina Maria, Nr.1, ROMANIA, I. HRIANCA, A. ZAMFIR, C. CAIZER, West University of Timişoara,

Faculty of Physics, Bd. V.Pârvan 4, Timişoara, ROMANIA



THE APPLICATION OF THE SYMMETRY GROUPS THEORY ON THE STUDY OF THE F COLOR CENTER

ENERGY LEVELS IN ALKALI HALIDES

Liliana LIGHEZAN

Abstract. In this paper, using the symmetry groups theory, a scheme of the F color center electronic energy levels in alkali halides has been represented, specifying the degeneracy, the symmetry properties of those levels and the symmetry of the wave functions of the states associated with these levels. The influence of the crystal lattice vibrations on the electronic energy levels has also been analyzed.

Keywords: alkali halides, Address: L. LIGHEZAN, “Politehnica” University of Timişoara, Physics Department, P-

ţa Regina Maria, Nr.1, ROMANIA






1. M.BAICA, M.CÂRDU – Regarding the General Character of the Poliganal Trigonometry Elements of Polygonal Trigonometry .………………………………………….

1

2. N.N.NEAMŢU – Existence and Uniqueness of the Solution for the Cubic Functional Equation ……………………………………………………………………………………………

7

3. H.DEMIRBÜKER, L.Z.AKGÜN – Conharmonic Transformations in Generalized Weyl Spaces ……………………………………………………………………………………………..

12

4. Gh.M.TUDOR – Sur les zéros des Séries de puissance (V)………………………………… 20

PHYSICS

5. S.B.LAZAREV, O.I.BODROŽA-PANTIĆ*, M.R.PANTIĆ** - Surface electron states of thin metallic films ………………………………………………………………………………….

24

6. V. SAJFERT, R. ĐAJIĆ, M. PANTIĆ, B. TOŠIĆ -Nano Tubes Model for DNA Transcription ……………………………………………………………………………………….

31

7. B. ROTHENSTEIN, R.P.GRUBER and F. BARVINSCHI - Differently Accelerated Twins Without Differential Aging………………………………………………………………………..

38

8. M. CRISTEA, I. DAMIAN, M. BOLDAN, M. GANGĂL -Rotational hysteresis of shiny electrolitical nickel layers…………………………………………………………………….. …

43

9. B. ROTHENSTEIN, I. ZAHARIE - With the relativistic velocity addition law through special relativity …………………………………………………………………………………….

51

10. B. ROTHENSTEIN, I. DAMIAN - The nature of the Coulombian field: Why two formulas for the electric field created by a uniformly moving point charge? ……………………….

59

11. V. DOROBANTU, G. GRÜN - X – ray inspection of pipelines having large diameters … 69

Mathematics

REGARDING THE GENERAL CHARACTER OF THE POLIGONAL TRIGONOMETRY

Malvina BAICA and Mircea CÂRDU

Abstract. In this paper, we will demonstrate the general character of the polygonal trigonometry (PT) whose fundamental elements are valid for both the case of quadratic trigonometry (QT) and the case of classical trigonometry (CT).

QT is the particular case of the PT and the lower limit of the number of sides n of trigonometric polygon (n=4), and CT is the particular case of PT situated at the upper limit of the value n, thus n= ∞.

Keywords: quadratic trigonometry (QT), the polygonal trigonometry, classical trigonometry (CT).

Address: Malvina BAICA; Department of Mathematical and Comp.Sciences; The University of Wisconsin, Whitewater, WI 53190, U.S.A.

Mircea CÂRDU, Socet S.A., 168-184 Calea 13 Septembrie, Sector 5, 76302, Bucharest, ROMANIA.

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR THE CUBIC FUNCTIONAL EQUATION

Nicolae N. NEAMŢU Abstract. The inspiration for this paper was caught by the cubic functional equation, which

was discussed by J.M.Rassias [3] and P.Găvruţă and L.Cădariu [2]. The goal of this paper is to prove the existence and uniqueness of the solution to the cubic functional equation and to actually determine it.

Keywords: cubic functional equation Address: Nicolae N. NEAMŢU, “Politehnica” University of Timişoara, Department of


CONHARMONIC TRANSFORMATIONS IN GENERALIZED WEYL SPACES

Hakan DEMIRBÜKER and Leyla Zeren ARGÜN

Abstract. In this paper, we have studied conformal transformations preserving harmonic functions (Conharmonic transformations) in generalized Weyl spaces.

Keywords: harmonic functions. Address: Hakan DEMIRBÜKER , Istanbul Technical University, Faculty of Science and

letters, 80626 Maslak, Istanbul, TURKEY. Leyla Zeren ARGÜN, Mimar Sinan University, Faculty of science and letters

Cirağan caddesi zah sok. No 2, TURKEY.

SUR LES ZEROS DES SERIES DE PUISSANCE (V) Gheorghe Marin TUDOR

Résumé. Dans cet ouvrage, nous allons continuer l’étude sur la localisation des zéros des

séries de puissances. Dans les ouvrages [1], [2], le problème essentiel réside, en essence, dans le fait qu’on détermine effectivement, une limite infériuere pour les modules des zéros de séries de puissances.

Dans cette note, il est question de donner une amelioration des résultats signalés ci-dessus. Keywords: zéros des séries. Address: Gh.Marin TUDOR, “Politehnica” University of Timişoara, Department of

Mathematics, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA. Physics

SURFACE ELECTRON STATES OF THIN METALLIC FILMS S.B. LAZAREV, O.I.BODROŽA-PANTIĆ, M.R. PANTIĆ

Abstract. Surface electron states of thin metallic films was analyzed using Green's function

method. We have calculated diagonal components of free-electron Green's functions which enabled the complete insight into the electron spectra and thermodynamical properties of electron system. The comparison with crystal bulk has shown that electron spectra of thin films is strongly influenced both by the film thickness and boundary conditions. The numerical calculations

performed for thin metallic films demonstrate that surface states can be in the form of P-states or N-states. In the case of thick films some analytical considerations of surface states are also possible.

Keywords: Surface states, Thin films, Green's function Address: S.B.Lazarev, O.I.Bodroža-Pantić, Higher School of Technology, Šabac, Serbia

and Montenegro,Department of Mathematics, Novi Sad, Serbia and Montenegro M.R.PANTIĆ, Higher School of Technology, Šabac, Serbia and Montenegro,

Department of Physics, Novi Sad, Serbia and Montenegro

NANO TUBES MODEL FOR DNA TRANSCRIPTION Vjekoslav SAJFERT, Rajka DAJIĆ, Milan PANTIĆ, Bratislav TOŠIĆ

Abstract. Using the energy asymmetries in the hydrogen-binded structures the model is

formulated explaining further decay of CAN double chain and also explaining further decay of only one of obtained single chains. The model is similar to the Scott’s model of α-helix where the spiral is substituted with interacting discs. Explanation of mentioned DNA transformation is based on the estimate of free energy of discs with even number of hydrogen bonds.

Keywords: asymmetric energy, α-helix, DNA transformation Address: V. SAJFERT, Technical Faculty “Mihajlo Pupin” 23000 Zrenjanin, Djure

Djakovica bb, Serbia and Montenegro, [email protected] R. ÐAJIĆ, M. PANTIĆ, B. TOŠIĆ, Institute of Physics, Faculty of science,

21000 Novi Sad, Dositeja Obradovica 4, Serbia and Montenegro

ROTATIONAL HYSTERESIS OF SHINY ELECTROLITICAL NICKEL LAYERS Minerva CRISTEA, Ioan DAMIAN, Maria BOLDAN, Mariana GANGĂL

Abstract. Rotational hysteresis is the discontinuous remagnetization phenomenon of a

ferromagnetic substance which rotates uniformly in a magnetic field or which exists in a rotating magnetic field. The following goals are presented in the paper: a) the experimental effect curves - induced voltage (U) depending on the intensity of the magnetic field H(O-60 kA/m), at a constant rotating frequency; b) dependence of the induced voltage (U) on the rotating frequency (ν), of the samples (10-35 rot/s) in a constant magnetic field. Shiny nickel layers of different thickness (8.7 - 112 μm), deposited electrolytically from a concentrated bath on copper support, have been investigated. The characteristics of the effect curves depend on thickness and differ from those obtained for deposited electrolytically thin layers of nickel or laminated strips (0.1 mm; 0,4 mm) studies by other authors.

Keywords: hysteresis, ferromagnetic substance Address: Minerva CRISTEA, Ioan DAMIAN, Maria BOLDAN, Mariana GANGĂL,

“Politehnica” University of Timişoara, Physics Department, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

WITH THE RELATIVISTIC VELOCITY ADDITION LAW THROUGH SPECIAL RELATIVITY


Abstract. It is shown that if we can define a physical quantity with proper character in a given inertial reference frame (kinematic, dynamic, electromagnetic in its nature) which transforms when detected from a reference frame relative to which it moves with velocity ux as

2

20 1

cu

FF x−= then we can derive for it transformation equations following one and the same

procedure, which involves the addition law of relativistic velocities which can be derived without


using the Lorentz transformations. The transformation equation derived that way, generates the physical quantities uxF and u'xF', for which physicists invent names reflecting theirs physical meaning.

Keywords: physical quantity, inertial reference Address: Bernhard ROTHENSTEIN, Ioan ZAHARIE, “Politehnica” University of

Timişoara, Physics Department, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

THE NATURE OF THE COULOMBIAN FIELD: WHY TWO FORMULAS FOR THE ELECTRIC FIELD CREATED BY A UNIFORMLY MOVING POINT CHARGE?

Bernhard ROTHENSTEIN, Ioan DAMIAN

Abstract. A derivation of the electric field created by a uniformly moving charge from its retarded position is presented. The derived formula has a general character showing how the electric field depends on the position of the point where the field is measured, on the time when the information about the creation of the field leaves the charge and on its velocity. The field described by the derived formula is mapped, showing the time variation of its components, of its magnitude and direction as measured at a given point in space and the magnitude and the direction of the field at different points in space but at the same instant of the time. Arguments are presented for the fact that a detachment of the electric field from its source takes place.

Keywords: coulombian field, time variation Address: “Bernhard ROTHENSTEIN, Ioan DAMIAN, Politehnica” University of


X-RAY INSPECTION OF PIPELINES HAVING LARGE DIAMETERS

Vasile DOROBANŢU, G.GRÜN

Abstract. Some of the basic ideas and procedures of the X – ray technique in checking the pipelines with large diameters are presented.

Keywords: X-ray technique Address: Vasile DOROBANŢU, “Politehnica” University of Timişoara, Physics

Department, P-ţa Regina Maria Nr.1, O.P.5, ROMANIA. Seria MATEMATICǍ - FIZICǍ Transactions on MATHEMATICS & PHYSICS Tom 48 (62) , Fascicola 2, 2003, ISSN 1224-6069


1. M.BAICA – Today’s Status of the Fermat’s last theorem .…………………………………… 1

2. Gh.M.TUDOR – L’Équation diophantienne (I) ……………………….………………………. 13

3. R.NEGREA – On the convergence of successive approximations for McShane stochastic integral equations and financial applications ………………………………………………….

19

4. G.CRISTESCU – Duality and the Galois connection between two convexity spaces …… 27 5. T.NOIRI, V.POPA – Properties of upper and lower θ - continuous multifunctions ……… 35

6. C.POPA – Some properties and applications of a modified Kovarik algorithm ………… 49

7. J.UŠAN, M.ŽIŽOVIC – One remark on (k(m – 1)+1) – groups …………………………… 57

8. R.L.LUPŞA – Quad-tree construction for ordered Dithering mask ………………………. 63

9. D.I.DUCA, L.LUPŞA - Bi-(ϕ, ψ) convex-concave functions ……………. ………………… 67

10. P.GǍVRUŢA – Some properties of frames in Hilbert spaces ……………………………… 73

11. M.TUBA – Controlled maximum entropy method optimization of the initial network topology and routing ………………………………………………………………………………

81

PHYSICS

12. B. ROTHENSTEIN, I. ZAHARIE – The physycs behind the phase invariance derivation of Doppler shift formulas ………………………………………………………………………….

88

13. I. LUMINOSU – Determination of controllable variables of flat-plate solar collector by digital simulation considering the efficiency criterion ……………………………………….

93

14. B. ROTHENSTEIN, I. DAMIAN – An analysis of the classical acoustic Doppler effect revisited…………………………………………………………………………………………….

103

15. N. POP – Shift operators of the (d+1) – dimenional relativistic rotating oscillators …….. 112

16. I.HRIANCA, M.CRISTEA, V.VILCEANU, M.FEDER, M.BOLDAN, A.ZAMFIR – Some aspects of the magnetic behaviour of MnZn ferrite ……………………………………………

120

Mathematics

TODAY’S STATUS OF THE FERMAT’S LAST THEOREM Malvina BAICA

Abstract. In this paper the author will show that G.Faltings finished the proof of (ELFLT)

using deformations instead of higher levels of the Euler Systems on March 1995. Also, the author used the Baica’s Generalized Euclidean Algorithm (BGA) as the only Euler System of the Algebraic Number Theory and proved (EFLT) on April 1994. We will show that (ELFLT and (EFLT) are equivalent but the functor to show that they are the same can not be produced.

Keywords: Fermat’s Last Theorem, Euclidean Fermat’s Last Theorem Address: Address: Malvina BAICA; Department of Mathematical and Computer

Sciences; The University of Wisconsin, Whitewater, WI 53190, U.S.A.

L’ÉQUATION DIOPHANTIENNE (I) Gheorghe M. TUDOR

Résumé. Dans ce travail, sur l’équation signalée plus haute, nous envisagerons quelques

questions relatives aux solutions contenant des nombres entiers positifs. En ce qui concerne cette équation, on peut la considérer comme une extension (à gauche) de l’équation xx yy = zz (voir, par exemple [1]). Nous nous proposons de généraliser certaines résultats obtenus dans ce qui concerne la résolution de l’équation x x ⋅ y y = z z

Keywords: Équation Diophantienne Address: Gheorghe TUDOR, “Politehnica” University of Timişoara, Department of


ON THE CONVERGENCE OF SUCCESSIVE APPROXIMATIONS FOR McSHANE STOCHASTIC INTEGRAL EQUATIONS AND FINANCIAL APPLICATION

Romeo NEGREA

Abstract. The existence and pathwise uniqueness results for solutions of McShane’s stochastic integral equations without assuming a Lipschitz condition on the coefficients are presented. An application to financial modelling in the general conditions is given.

Keywords: Stochastic integral equation of McShane type, belated McScane’s integrals financial modelling.

Address: Romeo NEGREA, “Politehnica” University of Timişoara, Department of Mathematics, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

DUALITY AND THE GALOIS CONNECTION BETWEEN TWO CONVEXITY SPACES

Gabriela CRISTESCU

Abstract. The dualities between two convexity spaces, according to the definition of Kay and Womble, are studied. Representation theorem are derived, using the corresponding terms coming from the lattice generators. An approach to the Galois connection between two convexity spaces has as the main results its equivalence with the duality theory.

Keywords: Convexity space, duality between two convexities, Galois connection. Address: Gabriela CRISTESCU, Aurel Vlaicu University of Arad, Department of

Mathematics and Computer Science, Bd.Revoluţiei, No.81, 2900 Arad, ROMANIA.

PROPERTIES OF UPPER AND LOWER θ - CONTINUOUS MULTIFUNCTIONS

Takashi NOIRI, Valeriu POPA

Abstract. In this paper we obtain new characterization of upper an lower θ - continuous multifunctions and investigate several properties of such multifunctions.

Keywords: θ - continuous Multifunctions Address: Valeriu POPA, Department of Mathematics, University of Bacău, 5500 Bacău,

ROMANIA. Takashi NOIRI. Department of Mathematics, Yatsushiro College of

Technology, Yatshiro, Kumamoto, 866-8501, JAPAN.

SOME PROPERTIES AND APPLICATIONS OF A MODIFIED KOVARIK ALGORITHM

Constantin POPA

Abstract. In a previous paper we presented a modified version of Kavarlik’s approximate orthogonalization algorithm for arbitrary symmetric matrices. In the present one, we analyse some of its properties. The first part of the paper deals with a result concerning the linear convergence of the algorithm, while in the second one we apply it for numerical solution of consistent linear least-squares problems of which matrix is symmetric. The basic idea is to modify also the right hand side of the problem during the transformation of the matrix. We prove that sequence of vectors generated in this way converges to the minimal norm solution of the problem. Some applications are also pressented for a collocation discretization of a “model problem” first kind integral equation.

Keywords: symmetric Kovarik algorithm, linear convergence, symmetric least-squares problems, first kind integral equations.

Address: Constantin POPA,

ONE REMARK ON (K(M-1)+1) – GROUPS

Janez UŜAN, Mališa ŽIŽOVIC

Abstract. In this article (k(m-1)+1) – groups for m > 2 and k ≥ 2 are described using one (k+1) – group, one k – ary operation and one (k-1)-ary operation.

Keywords: n-group, nHG-algebra Address: Janez UŜAN, Institute of Mathematics, University of Novi Sad, Trg

D.Obradovića 4, 21000 Novi Sad, Serbia and Montenegro, YUGOSLAVIA

Mališa ŽIŽOVIC, Faculty of Technical Science, University of Kragujevac, Svetog Save 65, 32000 Čačak, Serbia and Montenegro, Yugoslavia.

QUAD-TREE CONSTRUCTION FOR ORDERED DITHERING MASK

Radu Lucian LUPŞA

Abstract. Rendering greyscale images on printers transforming images form greyscale to bi-level black and white. Ordered dithering is the fastest algorithm for this transformation. It has been made popular with the blue noise mask algorithm. We propose here a novel algorithm for producting the mask for ordered dithering.

Keywords: greyscale images, mask algorithm. 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.

BI-(ϕ, ψ) CONVEX-CONCAVE FUNCTIONS

Dorel I.DUCA, Liana LUPŞA

Abstract. An extension of the concept of convex function is given in a very general framework provided by a set in which a general convexity for its subsets is defined.

Keywords: generalized convex functions, generalized partial convex functions. Address: Dorel I. DUCA, Babeş-Bolyai University of Cluj-Napoca, Faculty of

Mathematics and Computer Science, Str.Kogălniceanu, No.1, 3400 Cluj-Napoca, ROMANIA Liana LUPŞA, Babeş-Bolyai University of Cluj-Napoca, Faculty of Mathematics

and Computer Science, Str.Kogălniceanu, No.1, 3400 Cluj-Napoca, ROMANIA.

SOME PROPERTIES OF FRAMES IN HILBERT SPACES

Paşc GĂVRUŢĂ

Abstract. We give some characterizations in the frame theory in connection with the operator ∑

∈

=In

nnXY yxxxL , . We prove also a Welch – type inequality for Besel sequences in finite

– dimensional Hilbert spaces. It is proved that a Bessel sequence is a Welch sequence if and only if the sequence is a tight frame.

Keywords: frame theory, Hilbert spaces. Address: Paşc GĂVRUŢĂ, “Politehnica” University of Timisoara, Department of


CONTROLLED MAXIMUM ENTROPY METHOD OPTIMIZATION OF THE INITIAL NETWORK TOPOLOGY AND ROUTING

Milan TUBA

Abstract. Suitability of the MEM (Maximum Entropy Method) to the network design problem has been investigated [5] and mathematical model for its application has been developed [7]. Further improvements are developed in [8]. That model determined variable and constraints that satisfy MEM formalism and give feasible initial routing. Improvements that allow control of the optimization process are introduced in this paper. Limitation of the MEM that no variable can become equal tp zero is eliminated

Keywords: Network Design Problem, Network Topology, Routing, MEM. Address: Milan TUBA, Matematicki Fakultet Studentski trg 16 11000 Belgrade,

Yugoslavia.

Physics

THE PHYSICS BEHIND THE PHASE INVARIANCE DERIVATION OF DOPPLER SHIFT FORMULAS


Abstract. It is shown that the derivation of Doppler shift formulas using the invariance of the phase, obscures the fact that the calculation of the circular frequency ω=2π/T requires the same time interval as the measurement of the velocities present in such formulas. If the velocities of source and receiver are constant, the time intervals are finite. If not, we work with instantaneous velocities and so the involved time intervals are “very small” the periods being of the same order. Under such conditions, we make the “very small” period approximation.

Keywords: Doppler shift, Address: Bernhard ROTHENSTEIN, Ioan ZAHARIE, “Politehnica” University of


DETERMINATION OF CONTROLLABLE VARIABLES OF FLAT-PLATE SOLAR COLLECTOR BZ DIGITAL SIMULATION CONSIDERING

THE EFICIENCY CRITERION

Ioan LUMINOSU

Abstract. The efficiency equation of conventional solar collector of the type plate-tube, established on some simplifying hypotheses is expressed by the dependence η = f (α, β, (τα)ef), where α = Ac⋅UL , β = ⋅Cm& p

The graph of the dependence η = f (α, β, (τα)ef) on the axes η, α, β with (τα)ef , as parameters, leads to the three-dimension picture of the efficiency. The computer designs the surface point by point and displays the values of variables. From the values list, the user chooses the values α and β depending on the desired efficiency. Then by relation of definition he establishes the operational, geometrical and the material parameters of the collector.

The results of the digital model are compared to the experimental data obtained on a collector with air, for witch Tf,I = Ta, W = 0, F’= 1, u = 1.

Keywords: solar collector, Address: Ioan LUMINOSU, “Politehnica” University of Timişoara, Physics Department,

P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA.

AN ANALYSIS OF THE CLASSICAL DOPPLER EFFECT REVISITED


Abstract. Acoustic Doppler shift formulas, free of assumptions concerning how large is the distance between source and receiver or how large the frequency is, are derived. Subsonic, sonic and supersonic velocities are considered. It is shown that the Doppler factor is non-linear.

Keywords: Doppler shift, Doppler factor Address: Bernhard ROTHENSTEIN, Ioan DAMIAN, “Politehnica” University of

Timişoara, Physics Department, P-ţa Regina Maria, Nr.1, O.P.5, ROMANIA

SHIFT OPERATORS OF THE (d+1) – DIMENSIONAL RELATIVISTIC ROTATING OSCILLATORS

Nicolina POP

Abstract. The super symmetry of the models of quantum relativistic rotating oscillators in arbitrary dimensions, defined as Klein-Gordon fields in backgrounds with deformed anti-de Sitter metrics, is presented pointing out the supersymmetric operators. We calculate the shift operators: the raising and lowering operators for these models using the action of the supersymmetry operators and the form of the normalized radial fundation of the (d+1)-dimensional rotating oscillators. The shift operators are different from those of the supersymmetry, they are not pure differential operators and they are not adjoint to each other.

Keywords: differential operators Address: Nicolina POP, West University of Timişoara, V.Pârvan Ave, 4, 1900 Timişoara,

ROMANIA.

SOME ASPECTS OF THE MAGNETIC BEHAVIOUR OF MnZn FERRITE

I. HRIANCA, M.CRISTEA, V.VILCEANU, M.FEDER, M.BOLDAN, A.ZAMFIR

Abstract. Rotational hysteresis is the discontinuous remagnetization phenomena of a ferromagnetic substance which rotates uniformly in a magnetic field or which exists in a rotating magnetic field. The following goals are presented in the paper : a) the experimental effect curves-induced voltage U Depending on the intensity of magnetic field H(O-90KA/m), at a constant rotating frequency ; b) Dependence of the induced voltage U on the rotating frequency f of the samples (10-35rot/s) in a constant magnetic field. We elaborated Mn0,54Zn0,37Fe2,06O4 ferrite with the addition of Bi2O3 in different proportion, by the conventional ceramic technique. It was followed the influence of samples ‘peculiarities on effects curves with samples into disk shape .It can be noticed that the rotational effect intensity increases with Bi2O3 content. The new information on the behaviour of the rotates ferrite in magnetic field can be used in the optimisation of ferrite technology and their applications.

Keywords: rotational hysteresis, MnZn ferrite Address: M.CRISTEA “Politehnica” University of Timişoara, Physics Department, P-ţa

Regina Maria, Nr.1, O.P.5, ROMANIA.




Seria MATEMATICǍ - FIZICǍ Transactions on MATHEMATICS & PHYSICS Tom 49(63) , Fascicola 1, 2004, ISSN 1224-6069


1. M.CIOBANU – Geometric structures associated to some dynamic systems ……………… 1

2. B.CRSTICI, D.DǍIANU – New generalizations of Cauchy’s functional equation ……… 7

Gh. TUDOR – L’équation Diophantienne ( ) ( ) ( ) kkk yk

mxk

mxmx yx...xx =⋅ 221121

13 3. (II) ……

4. A.VERNESCU - Some aspects related to the discrete analogue of differential and integral equations ……………………………………….........................................................

20

5. J.UŠAN, M.ŽIŽOVIC – nHG–Algebras as algebras of the types < 2, 1, 1, 1, 0, 0 > with laws ………………………………………………………………………………………………….

26

6. M.BAICA, A.PERETTI – The binary Goldbach Problem …………………………………… 30

7. O.LIPOVAN – A criterion for pseudosubmeasurable functions ……………………………. 45

8. M.NEAGU – Distributional Functional Identities characterizing polynomials ………… 52

9. C.BOTA – On a property of minimal sets of a homeomorphism ……………………………. 59

10. A.GÎRBAN – Some remarks on the Lyapunov-Malkin Theorem (I) .……………………….. 62

PHYSICS

11. I.ZAHARIE – On the crystallization kinetics of Fe60Gd10Cr10BB20 amorphous alloys……………………………………………………………………………………………….

74

12. B. ROTHENSTEIN, I.DAMIAN – Relativistic doppler effect free of “plane wave” and “very high” frequency assumptions……………………………………………………………

80

13. M. PUTZ – The quantum statistics of the chemical reactivity. Part II. Fokker – Planck path integral density functional rate equation formulation………………………………….

90

14. V. SAJFERT, M. GARIĆ, J. P. ŠETRAJČIĆ, B. S. TOŠIĆ - Mechanical oscillations in Cylindrical Quantum Nano Dots ……………………………………………………………….

96

15. N. POP – Thermodynamic properties of relativistic fermion oscillators … 102 Mathematics

GEOMETRIC STRUCTURES ASSOCIATED TO SOME DYNAMIC SYSTEMS

Monica CIOBANU

Abstract. Having been given an implicit second order differential system on a smooth manifold M, suitable geometric structures are considered on the configuration space. The coefficients of the variational forms and of the adjoint forms, associated to the system, define these structures.

Keywords: dynamical systems, nonlinear connexions. Address: Monica CIOBANU, Universitatea de Vest “Vasile Goldiş” Arad, Facultatea de

Informatică, Bul.Revoluţiei, Nr.85-87, Arad, ROMANIA, e-mail: [email protected].

NEW GENERALIZATIONS OF CAUCHY’S FUNCTIONAL EQUATION

Borislav CRSTICI, Dan DAIANU

Abstract – In this paper we solve the functional equations: ⎪α f(x + y)⎪ = ⎪β f(x) + γ f(y)⎪, and ⎪α f(x + iy)⎪ = ⎪β f(x) + γ f(iy)⎪, where α, β, γ are arbitrary complex constants x, y are real variables, and f is an unknown entire function of a complex variable.

Keywords: complex variable. Address: Borislav CRSTICI, Dan DAIANU, “Politehnica” University of Timişoara,

Department of Mathematics, P-ţa Regina Maria, Nr.1, 300004 Timisoara, ROMANIA.

( ) ( ) ( ) kkk yk

mxk

mxmx yx...xx =⋅ 221121

L’EQUATION DIOPHANTIENNE II

Gheorghe M. TUDOR

Résumé - Sur l’équation signalée plus haut, nous avons en vue quelques questions relatives aux solutions contenant des nombres entiers positifs. Au sujet de ce problème nous envisagerons les résultats obtenus dans le travail [1]. Pour être plus clair, nous pouvons préciser que l’équation considérée plus haut est plus générale que l’équation laquelle a été cherchée dans [1]. Dans cet ouvrage, on va continuer l’étude effectuée sur l'équation rappelée plus haut. Le problème essentiel réside au fond, dans le fait qu’on détermine effectivement des solutions exprimées par des nombres entiers positifs pour l’équation plus générale,

.

kk yk

xk

xx yxxx =⋅ ...2121

( ) ( ) ( ) kkk yk

mxk

mxmx yx...xx =⋅ 221121

Keywords: L’équation Diophantienne. Address: Gheorghe M. TUDOR, “Politehnica” University of Timişoara, Department of

Mathematics, P-ţa Regina Maria, Nr.1, 300004 Timisoara, ROMANIA.

SOME ASPECTS RELATED TO THE DISCRETE ANALOGUE OF DIFFERENTIAL AND INTEGRAL EQUATIONS

Andrei VERNESCU

Abstract. Some linear recurrence equations with variable coefficients, satisfied by certain particular sequences of real numbers, has the property to determine uniquely not only the sequence-solution but also the value of the first term. This situation was emphasized in four examples proposed by Professor A.Lupaş and me. In the present work we give a theoretical statement for this matter.

Keywords: linear recurrence equations. Address: Andrei VERNESCU, University “Valahia”, Department of Mathematics,

Boulevard Unirii, 18, Târgovişte, ROMANIA.

nHG-ALGEBRAS AS ALGEBRA OF THE TYPES <2, 1, 1, 1, 0, 0> WITH LAWS

Janez USAN, Malisa ZIZOVIC

Abstract. In this article nHG-algebras are described as algebras of the type <2, 1, 1, 1, 0, 0> with laws .

Keywords: n-group, nHG-algebra. Address Janez USAN, Institute of Mathematics, University of Novi Sad, Trg.D.Obradovica

4, 21000 Novi Sad, Serbia and Montenegro, YUGOSLAVIA Malisa ZIZOVIC, Faculty of Tehnical Science, University of Kragujevac, Svetog

Save, 65, 32000 Cacak, Serbia and Montenegro, YUGOSLAVIA.

THE BINARY GOLDBACH PROBLEM

Malvina BAICA, Aldo PERETTI

Abstract. In this paper authors will present the results of Baica’s paper “Clarifications of the Author’s Previous paper in the Goldbach Conjecture” in a slightly different form and correct some misprints in it.

Keywords: Goldbach Conjecture. Address: Malvina BAICA; The University of Wisconsin, Department of Mathematical and

Computer Sciences;, 53190, Whitewater, Wisconsin,, U.S.A. Aldo PERETTI, University of Buenos Aires, ARGENTINA.

A CRITERION FOR PSEUDOSUBMEASURABLE FUNCTION

Octavian LIPOVAN

Abstract. In [3] the pseudosubmeasurable function concept is defined and some properties of this concept are studied. In this paper, using the notion of control submeasures, there are introduced a criterion of functions pseudosubmeasurability .

Keywords: Pseudosubmeasurable function, submeasure. Address: Octavian LIPOVAN, Politehnica” University of Timişoara, Department of


DISTRIBUTIONAL FUNCTIONAL IDENTITIES CHARACTERIZING POLYNOMIALS

Mihai NEAGU

Abstract. In this paper it is studied certains distributional functional identities which characterize polynomials. In distributions, the fixation of variables is an irregular operation. In its place we will use the direct section of distributions which is a regular operation in distributions.

Keywords: Distributional functional identities Address: Mihai NEAGU, Politehnica” University of Timişoara, Department of


ON A PROPERTY OF MINIMAL SETS OF A HOMEOMORPHISM

Constantin BOTA

Abstract. S.Matsumoto and M.Shishikura ([4]) aborded the study of minimal sets of a homeomorphism f : S1 × R. We consider here a homeomorphism f:X → X, X an arbitrary topological space. We will show that if M⊂X is a minimal set for f and contains an interior point then all points of set M are interior points.

Keywords: Dynamical system, minimal set. Address: Constantin BOTA, Politehnica” University of Timişoara, Department of


SOME REMARKS ON THE LYAPUNOV-MALKIN THEOREM (I)

Anania GÎRBAN

Abstract. The Lyapunov-Malkin theorem is discussed and some of its applications are pointed out. Keywords: Lyapunov-Malkin theorem. Address: Anania, GIRBAN, “Politehnica” University of Timişoara, Department of

Mathematics, P-ţa Regina Maria, No.1, 300004, Timisoara, ROMANIA.

Physics

ON THE CRYSTALLIZATION KINETICS OF Fe60Gd10Cr10BB20 AMORPHOUS ALLOYS

Ioan ZAHARIE

Abstract: In the present paper the non-isothermal crystallization kinetics of fe60gd10cr10b20 amorphous alloys is investigated by differential thermal analysis (dta). The crystallization of fe60gd10cr10b20 amorphous alloys has been realized through four processes characterized by the activation energies ε1 = 1.25 ± 0.14 ev, ε2 = 2.23 ± 0.18 ev, ε3 = 4.83 ± 0.04 ev, ε4 = 4.29 ± 0.69 ev. By x-ray diffraction (xrd) we established the crystalline phases which appeared in the non-isothermal crystallization process: feb, fe2b, fe3b, fe2gd, gd2b5, crb.

Keywords: Amorphous alloys, Thermal analysis, Non-isothermal crystallization, X-ray diffraction

Address: Ioan ZAHARIE, Physics Department, University “Politehnica” Timişoara, Piaţa Regina Maria nr.1, 1900 ROMANIA, E-mail: [email protected].

RELATIVISTIC DOPPLER EFFECT FREE OF “PLANE WAVE” AND “VERY HIGH” FREQUENCY ASSUMPTIONS


Abstract. We show that a free of assumptions approach to the Doppler effect (plane wave and “very small” period assumptions) leads to a Doppler factor which depends on the involved frequencies. The result is that the Doppler effect shifts differently the different frequencies present in the studied electromagnetic radiation.

Keywords: Doppler effect Address: Bernhard ROTHENSTEIN, Ioan DAMIAN, “Politehnica” University of

Timisoara, Physics Department, Piata Regina Maria Nr.1, Timisoara, ROMANIA, E-mail: [email protected], [email protected]

THE QUANTUM STATISTICS OF THE CHEMICAL REACTIVITY. PART II: FOKKER-PLANCK PATH INTEGRAL DENSITY FUNCTIONAL

RATE EQUATION FORMULATION

Mihai V. PUTZ

Abstract. The envisaged study likes to apply and to extend the recent Fokker-Planck path

integral representation of markovian processes (H. Kleinert, A. Pelster, and M. V. Putz, Phys. Rev. E, 65, 066128/1-7, 2002) to rate equation calculation for electronic and biological systems providing an accurate theoretical prediction of their reactivity. The reliability of the present research scheme is further sustained by the recent success of the computation of new atomic radii and related periodic properties (M. V. Putz, N. Russo, and E. Sicilia, J. Phys. Chem. A, 107, 5461-5465, 2003) on the base of the same chemical potential formulation as is in this project involved.

Keywords: quantum statistics Address: Mihai V. PUTZ, Chemistry Department, West University of Timişoara, Str.

Pestalozzi, No. 16, Timisoara, Tel/Fax: +40-256-490377, RO-300115, ROMANIA.

MECHANICAL OSCILLATIONS IN CYLINDRICAL QUANTUM NANO DOTS

Vjekoslav SAJFERT, Maja GARIĆ, Jovan P. ŠETRAJČIĆ, Bratislav S. TOŠIĆ

Abstract. Green function technique, suitable for analyses of spatially deformed structures, is developed in this paper and applied to phonon system. Some thermodynamical and kinetical phonon properties of cylindrical quantum dots are analysed using developed method. By application of advanced

Green function method it was shown that physical characteristics of quantum dots are spatially dependent. It was illustrated using diffusion coefficient and crystal density as illustrative example.

Keywords: mechanical oscillations Address: Vjekoslav SAJFERT, Technical Faculty “M. Pupin”, University of Novi Sad,

Serbia and Montenegro, [email protected]. Maja GARIĆ, Jovan P. ŠETRAJČIĆ, Bratislav S. TOŠIĆ, Department of

Physics, Faculty of Sciences, University of Novi Sad, Serbia and Montenegro.

THERMODYNAMIC PROPERTIES OF RELATIVISTIC FERMION OSCILLATORS

Nicolina POP Abstract: The partition function and the grand-canonical potential characterizing relativistic fermionic oscillators are established by restoring to the conversion of sums into integrals and by numerical methods. Thermodynamic properties such as the specific heat, the pressure and the number of particles are presented in some more detail. Keywords: Relativistic fermionic oscillators, partition function, thermodynamic properties

Address: Nicolina POP, West University of Timişoara, V.Parvan Ave. 4, 300223 Timişoara, Romania, E-mail: [email protected].

Seria MATEMATICǍ - FIZICǍ Transactions on MATHEMATICS & PHYSICS Tom 49(63), Fascicola 2, 2004, ISSN 1224-6069


1. Gh.M. TUDOR – L’équation Diophantienne (III) ………….. mk ym

yyxk

xx yyyxxx ⋅⋅⋅=⋅⋅⋅ ...... 21212121

1

2. C. MILICI – Sur le calcule automatiques integrales trigonometriques (III) .…………………….. 9

3. A. GÎRBAN – Some remarks on the Lyapunov-Malkin Theorem (II) ……………………………… 14

4. C. BOTA – A property of a monotone global semi-flow on a vector bundle ….............................. 26

5. I. DRAGOMIRESCU – Critical Rayleigh number in a convection in thawing subsea permafrost problem ………………………………………………………………………………

30

6. M. NEAGU – Distributional functional identities characterizing λ-polynomials ……………….. 38

7. C. BOTA, D. POPESCU – About periodic trajectories of a dynamical system on a topological manifold ………………………………………………………………………………..

44

8. Gh.M. TUDOR, T.BÎNZAR – On a Diophantine equation ………………………………………….. 48

9. L. CIURDARIU – On the topology of Loynes spaces …………………………………………………. 52

PHYSICS

10. B. ROTHENSTEIN, C. NAFORNIŢĂ – Three levels of understanding physical relativity: Galileo’s relativity, up-to-date Galileo’s Relativity and Einstein’s Relativity: A historical survey…………………………………………………………………………………………………..

60 11. D. POPOV – Coherent states formalism for the pseudoharmonic oscilator…………………. 70 12. M. CRISTEA, M. BIRZESCU, M. ŞTEFĂNESCU – High purity Ni-ferrite obtained from a

new organometallic precursor……………………………………………………………………….

79 13. P. BARVINSCHI – Seismic modeling and imaging using the reverse-time migration

method.…………………………………………………………………………………………………

86


14. P. BARVINSCHI – Brilliance of an X-ray source for a foil type target……………………….. 94

15. I. DAMIAN – Malu’s law for a real polarizer…………………………………………………….. 98

16. L. LIGHEZAN – UV-VIS absorbtion of the color centers formed in electrolyticaly colored CaF

2 crystals ………………………………………………………………………………………….. 104

Mathematics

L’EQUATION DIOPHANTIENNE (III) mk ym

yyxk

xx yyyxxx ⋅⋅⋅=⋅⋅⋅ ...... 2121 2121

Gheorghe M. TUDOR

Résumé. Dans cet ouvrage, nous envisagerons quelques équations semblables à celle-là signalée plus haut, lesquelles ont été étudiées dans [6], [7]. Au sujet de cette problème, nous chercherons d’une façon semblable cette équation, en ce qui concerne l’existence et la détermination des solutions exprimées par des nombres entiers positifs. D’autre part, nous avons en vue et d’autres équations analogues à cette équation.

Keywords: Équation Diophantienne. Address: Gheorghe M. TUDOR, “Politehnica” University of Timişoara, Department of

Mathematics, P-ţa Regina Maria, Nr.1, 300004, Timisoara, ROMANIA.

SUR LE CALCULE AUTOMATIQUES DE QUELOUES INTEGRALS TRIGONOMETRIQUES (III)

Constantin MILICI

Résumé. Dans ce présent travail nous proposons de préciser le calcule automatique de quelques coefficients α des sommes trigonométriques plus générales Ap,q exprimées par l’integrale : x x x .

Keywords: calcule automatique de quelques coefficients α. Address: Constantin MIICI, “Politehnica” University of Timişoara, Department of


SOME REMARKS ON THE LYAPUNOV –MALKIN THEOREM (II)

Anania GÎRBAN

Abstract – The Lyapunov-Malkin theorem is discussed and some of its applications are pointed out.

Keywords: Lyapunov-Malkin theorem. Address: Gheorghe M. TUDOR, “Politehnica” University of Timişoara, Department of


A PROPERTY OF A MONOTONE GLOBAL SEMI-FLOW ON A VECTOR BUNDLE

Constantin BOTA

Abstract. Relative to a monotone dynamical system (X, ≤, Φ) on a Banach space X. H.S.Smith [6] proved the next result: if K , K are compact subsets of X satisfying K < K1 2 1 2, then there are open sets U and V, K ⊂ U, K ⊂ V, and t ≥ 0, ε > 0 such that Φ (U) ≤ Φ(V), t ≥ t1 2 1 t+s 1, 0 ≤ s < ε. We prove that the same result holds for a monotone global semi-flow on a vector bundle.

Keywords: Dynamical system, Banach space, Compact subspace. Address: Constantin BOTA, “Politehnica” University of Timişoara, Department of


CRITICAL RAYLEIGHT NUMBER IN A CONVECTION IN THAWING SUBSEA PERMAFROST PROBLEM

Ioana DRAGOMIRESCU Abstract. Permafrost implies frozen ground. Thawing permafrost is a problem that

concerns many scientist. Convection that takes place in the porous medium situated between the ocean bed and the thawing permafrost layer is a phenomenon that was studied extensively. In [6] the model of convection in thawing subsea permafrost is treated using the compound matrix method. Instead, we used the direct method to determine the secular equation which give us the critical Rayleigh numbers below which convection cannot occur for this convection model.

Keywords: Frozen ground, Thawing permafrost. Address: Ioana DRAGOMIRESCU, “Politehnica” University of Timişoara, Department

of Mathematics, P-ţa Regina Maria, Nr.1, 300004, Timisoara, ROMANIA.

DISTRIBUTIONAL FUNCTIONAL IDENTITIES CHARACTERIZING λ-POLYNOMIALS

Mihai NEAGU

Abstract. In this paper it is studied certains distributional functional identities which characterize λ-polynomials. In distributions, the fixation of variables is an irregular operation. In the place we will use the direct section of distributions which is a regular operation in distributions.

Keywords: λ-polynomials, λ-polynom of degree at nust k. Address: Mihai NEAGU, “Politehnica” University of Timişoara, Department of


ABOUT PERIODIC TRAJECTORIES OF DYNAMICAL SYSTEM ON A TOPOLOGICAL MANIFOLD

Constantin BOTA, Dan POPESCU

Abstract. We extend some properties of periodic trajectories of a dynamical system on a metric space to a dynamical system on a topological manifold.

Keywords: Dynamical system, Periodic trajectories. Address: Constantin BOTA, Dan POPESCU, “Politehnica” University of Timişoara,

Department of Mathematics, P-ţa Regina Maria, Nr.1, 300004, Timisoara, ROMANIA.

ON A DIOPHANTINE EQUATION Gheorghe M. TUDOR, Tudor BÎNZAR

Abstract. In this paper the problem of finding of some classes of positive rational, in particular

positive integer solutions for the equation 3,... 132121 ≥=⋅⋅⋅ − kxxxx x

kxk

xx k is tackled. Also it is shown that the equation in question has infinitely many solutions described by families depending on k-1 parameters.

Keywords: Positive integer solutions. Address: Gheorghe M. TUDOR, Tudor BÎNZAR, “Politehnica” University of Timişoara,

Department of Mathematics, P-ţa Regina Maria, Nr.1, 300004, Timisoara, ROMANIA.

ON THE TOPOLOGY OF LOYNES SPACES Loredana CIURDARIU

Abstract . Loynes introduced in [4] the notion of VE-space and respectively VH-space (or

LVH-space), as generalizations of prehilbertian, respectively Hilbert space. LVH-space have also been named pseudohilbertian space in [7] and later Loynes spaces in [1] and [8].Laoynes in [4], [5] studied (positive definite) functions and elements of spectral theory in such space, and in [6] he tried to

generalize stochastic processes by using such structures. In [1] and then in [7] and [8] these spaces are used in the abstract study of the stochastic processes. A more systematic utilization of them was done in [3]. In this note it is our aim to describe the topology in a Loynes space with the aid of seminorms.

Keywords: VE-space, VH-space, Hilbert space, Pseudohilbertian space. Address: Loredana CIURDARIU, “Politehnica” University of Timişoara, Department of


Physics

THREE LEVELS OF UNDERSTANDING PHYSICAL RELATIVITY: GALILEO’S RELATIVITY, UP-TO-DATE GALILEO’S RELATIVITY

AND EINSTEIN’S RELATIVITY: A HISTORICAL SURVEY. Bernhard ROTHENSTEIN, Corina NAFORNITA

Abstract: We present a way of teaching Einstein’s special relativity. It starts with Galileo’s

relativity, the learners know from previous lectures. The lecture underlines that we can have three transformation equations for the space-time coordinates of the same event, which lead to absolute clock readings, time intervals and lengths (Galileo’s relativity), to absolute clock readings but to relative time intervals and lengths (up-to-date Galileo transformations) and to relative clock readings time intervals and lengths.

Keywords:physical relativity, Einstein’s relativity Address: Bernhard ROTHENSTEIN, Politehnica University of Timişoara, Physics

Department, ROMANIA, E-mail: [email protected] NAFORNITA, Politehnica University of Timişoara, Communications

Department., Timişoara, ROMANIA

COHERENT STATES FORMALISM FOR THE PSEUDOHARMONIC OSCILLATOR

Dušan POPOV

Abstract: In the paper we have constructed the Barut-Girardello, Klauder-Perelomov and Gazeau-Klauder coherent states for the pseudoharmonic oscillator and we have examined some of their properties. In order to examine the behavior of a quantum canonical gas of pseudoharmonic oscillators, the Husimi’s Q-function and the diagonal P-representation of the density operator are constructed, which are useful to calculate the thermal expectation values.

Keywords: Pseudoharmonic oscillator, Coherent states, Density matrix. Address: Dušan POPOV, University "Politehnica" of Timisoara, Physics Department, Piaţa

Regina Maria No. 1, 300004 Timisoara, ROMANIA, e-mail: [email protected]

HIGH PURITY Ni-FERRITE OBTAINED FROM A NEW ORGANOMETALLIC PRECURSOR

Minerva CRISTEA, Mihail BÎRZESCU, Mircea ŞTEFĂNESCU

Abstract. The paper presents the results concerning the synthesis of heteropolynuclear glyoxylates [Fe2NiII(OH)4(C2H2O4)2(OH2)2⋅xH2O, their thermal conversion into nickel ferrite and their dynamic magnetic hysteresis cycles at 50 Hz.

Keywords: Ni-ferrite, hysteresis Address: Minerva CRISTEA, University "Politehnica" Timisoara, Physics Department,

ROMANIA. Mihail BÎRZESCU, Mircea ŞTEFĂNESCU, University "Politehnica"

Timişoara, Faculty of Chemical Engineering, Romania.



SEISMIC MODELING AND IMAGING USING THE REVERSE-TIME

MIGRATION METHOD

Paul BARVINSCHI Abstract: Reverse-time migration for post-stack seismic data is implemented using the finite-difference method for solving the seismic P-wave equation with non-reflecting boundary conditions. Synthetic data for two complex geological models are migrated and resulting seismic section images are presented. Some limits of the technique are also discussed.

Keywords: reverse-time Address: Paul BARVINSCHI, Universitatea de Vest din Timişoara, Facultatea de Fizică,

Bvd. V. Parvan, nr.4, 300223 Timişoara, Romania, E-mail: [email protected]

BRILLIANCE OF AN X-RAY SOURCE FOR A FOIL TYPE TARGET

Paul BARVINSCHI Abstract: A study of the temperature distribution in a stationary foil type target and the brilliance of the focus, defined as the maximum input power per unit area of the focus, has been carried out in the case of a constant thermal conductivity and neglecting radiation.

Keywords: X-ray Address: Paul BARVINSCHI, Universitatea de Vest din Timişoara, Facultatea de Fizică,

Bvd. V. Parvan, nr.4, 300223 Timişoara, Romania, E-mail: [email protected]

MALUS’ LAW FOR A REAL POLARIZER

Ioan DAMIAN Abstract. We present a possibility to measure the degree of polarization of a partially polarized light beam furnished by a real (imperfect) polarizer. A generalized formula for the Malus’law is derived, which holds when a partially polarized light beam passes through a real polarizer.

Keywords: polarized light, polarizer, degree of polarization Address: Ioan DAMIAN, Universitatea “Politehnica” Timişoara, Catedra de Fizică, P-ţa

Regina Maria nr.1, e-mail: [email protected].

UV – VIS ABSORPTION OF THE COLOR CENTERS FORMED IN ELECTROLYTICALY COLORED CaF2 CRYSTALS

Liliana LIGHEZAN, Irina NICOARA, Petru NEGREA

Abstract. The color centers in crystals are structural defects of the crystal lattice in which electrons or holes have been captured. In this paper, some considerations about the electrolytic creation of the color centers in CaF2 crystal have been made. The results obtained from the electronic spectra of these color centers have been presented. A correlation between our results and those obtained from the additive and irradiative colored CaF2 crystals has also been made.

Keywords: color centers, CaF2 crystals, laser materials, condensed matter. Address: Liliana LIGHEZAN, Irina NICOARA, West University of Timisoara, Faculty

of Physics, Bld. Vasile Parvan No 4, Timisoara, Romania, [email protected], [email protected]

Petru NEGREA, “Politehnica” University of Timisoara, Faculty of Industrial Chemistry and Environmental Engineering, P-ta Victoriei No 2, Timisoara, Romania, [email protected].












1. E. EKICI, V. POPA – Some Properties of Upper and Lower Clopen Continuous Multifunctions …………………………………………………. ………………………………………. 1

2. Gh.M. TUDOR – L’équation Diophantienne (IV) …… …………….

pk wx

kxx wxxx =⋅⋅⋅ ...2121 12

3. G. CRISTESCU, Codruţa STOICA – A Minimax Property for a Class of Perfect Information Games …………………………………………... ………………………………………………………

19

4. D. BǍRBOSU – The Voronovskaja Theorem for the Schurer-Stancu Operators ....................... 14

5. L. CIURDARIU – Reproducing Kernel Loynes Space ………………………. ………………….. 32

6. R.L.LUPSA – Construction of a Multiresolution Analysis in a Lattice Framework ………… .. 45

7. I. DRAGOMIRESCU – On a Particular Stability Criterion in a Binary Mixture Problem …… 53

8. Gh. ŢIGAN – Analysis of a Dynamical System Derived from the Lorenz System ……………… 61

PHYSICS

9. N. POP – Some thermodynamic properties of the relativistic fermions oscillators ………… 73

10. B. ROTHENSTEIN – From one space dimension to two space dimensions in special relativity .……………………………………………………………………………………………..

83

11. V. SAJFERT, B. TOŠIĆ – The reduction of charge propagation in nanorod………………… 87 12. G. J. SPIX, B.ROTHNESTEIN – Teaching special relativity after 100 years from its

foundation ……………………………………………………………………………………….…….

97 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, Canakkale Onsekiz Mart University,

Terzioglu Campus, 17020 Canakkale, TURKEY, E-mail [email protected]. Valeriu POPA, Department of Mathematics, University of Bacău, 5500 Bacău,

ROMANIA., E-mail [email protected].

L’EQUATION DIOPHANTIENNE (IV) p

kxk

xx xxx ωω=⋅ ...2121

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 [email protected].

Codruţa STOICA, “Aurel Vlaicu” University of Arad, Department of Mathematics,, Bd.Revoluţiei, No.81, 310130 Arad, ROMANIA, Email [email protected].

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 [email protected].

REPRODUCING KERNEL LOYNES SPACES

Loredana CIURDARIU

Abstract. In this note we generalize some results regarding reproducing kernel spaces obtained in [3] for Z = Β(X, X*) and Z = Δ(X, X*) to an arbitrary pre-Loynes Z-space. For a given Z-valued positive definite kernel Γ we construct a Loynes Z-space ΗΓ which admits Γ 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


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 [email protected].

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


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


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, West University of Timişoara, V.Parvan Ave, 300223 Timisoara,

ROMANIA

FROM THE SPACE DIMENSION TO TWO SPACE DIMENSION IN 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. SAJFERT Technical Faculty “M.Pupin” Zrenjanin, University of Novi Sad, Serbia and Montenegro, YUGOSLAVIA.

B. TOŠIĆ, Vojvodina Academy 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


1. M. BAICA, A. PERETTI – The Fundamental Solution of the Equation X2-DY2 = 1 …………. 1 10 2. O. LIPOVAN –Pseudosubmeasurable and Integrable Functions ……… ….. ………………

3. Gh.M. TUDOR - L’équation Diophantienne (V) ………… …………….. pq zyx zyx =⋅ 18

4. L. CǍDARIU – Fixed Points in Generalized Metric Space and the Stability of a Quartic Functional Equation ………………………………………… …………………………………. 25 M.ČANAK, L.PROTIĆ, L.STEFANOVSKA – Particular Solution of Vekua Differential Equation by using Mitrinovic Method …………………. …………………………………………

5. 35

6. Gh.M. TUDOR, T.BÎNZAR – On Some Exponential Diophantiene Equations …. ……… …. 47

I. DRAGOMIRESCU – On the Chandrasekhar-Galerkin Method in a Convection Problem for a Micropolar Fluid ………………………………... …………………………………………..

7. 53

PHYSICS B. ROTHENSTEIN, St. POPESCU, G.J. SPIX – Illustrating Einstein’s Special Relativity: A relativistic Diagram that Displays in True Values the Components of a Four Vector ……

8. 62

C. GRUESCU, M. COSTACHE – Design of a Kepler Telescope Providing an Errected Image ………………………………………………………….. …………………………………….

9. 76

10. M. CRISTEA – IR Absorbtion of some M2O3 Oxides and Their Solid Solutions .................... 83

11. S.BABETI, G. ZET – Solutions in Dilaton Gauge Theory of Gravitation …….................. …. 92

12. B.S. TOŠIĆ - A Century of Quantum Physics …………………………… …………………….. 100

13. I. LUMINOSU, L. FARA – Exergetic Analysis of a Flat-Plate Solar Collector ...................... 108 14. M.V. PUTZ – The Quantum Statistics of the Chemical Reactivity. Part III: Electronic

Density Reactivity …………………………………………………………………………………… 115

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; 53190 Whitewater, Wisconsin, U.S.A. Aldo PERETTI, J.F.Kennedy University, 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) pq zyx zyx =⋅

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


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 [email protected].

PARTICULAR SOLUTION OF VEKUA DIFFERENTIAL EQUATION BY USING MITRINOVIĆ 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 works for 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: [email protected].

Marius COSTACHE, University Politehnica of Timisoara, Physics Department, P-ţa Regina Maria, Nr.1, 300004 Timisoara, ROMANIA, e-mail [email protected].

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 α-Al2O3, α-Fe2O3, α-Cr2O3, that crystallize into the trigonal system with the space group D3d, as well as of their ternary solid solutions with 10% α-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 [email protected].

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 )(, Cof AfT =)(mfen &=η and has created difficulties in the design of flat-plate solar collectors. The exergy efficiency of a flat-plate solar collector, ),( Cex Amf &=η 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, West University of Timisoara,

Str.Pestalozzi, No.16, 300115 Timisoara, ROMANIA.

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 51 (65), Fascicola 1, 2006, ISSN 1224-6069


1. Gh.M. TUDOR, M. NEAGU – About the Diophantine Equations ……… ... …………………. 3

2. O. LIPOVAN – An Elementary Integral for Set-Valued Functions ……… …………………… 9

3. M. BAICA, M. CÂRDU – The Infratrigonometry, an Inferior Order Neighbourhood Domain of Transtrigonometry ……………… ….……………………………………………….

16

4. O.T. POP, M. FǍRCAŞ – Some Approximation for Bernstein Polynomials of two Variables on a Triangle …………………………… ...…………………………………………………………..

22

5. M. BAICA, M. CÂRDU – The Ultratrigonometry, a Superior Order Adjacent Domain of the Transtrigonometry ………………………................................................................................

29

6. T. BÎNZAR, L. CIURDARIU – Noncomutative Finite Systems of Gramian Isometrics Isometries and Applications ………………………………… ……………………………………

36

7. Gh. ŢIGAN – Analysis of the Reconnection Process in Nontwist Cubic Maps ……………………………………………………………………………………………………………

45

8. L. CIURDARIU, T.BÎNZARU – A Characterization of Subnormality for Linear Bounded Operators on Loynes Spaces …………………………… ..........................................................

55

PHYSICS

M.V. PUTZ – The Quantum Statistics of the Chemical Reactivity. Part IV: Magnetic and Electric Atomic Properties Derived from Atomic Radii ………………………………………..

9. 62

I. LUMINOSU – The Absorption of the Unpolarized Mono-Chromatic Electromagnetic Radiation by a very Diluated Ferrofluid ………............………………………………………..

10. 71

11. J.D. JANJIĆ, B.S. TOŠIĆ – Polyethylene as Light Amplifier ………………………………….. 80

12. I. ZAHARIE – Analysis of the Classical Shift Doppler Formulas ………………………….… 88

13. M.PAULESCU, E. TULCAN-PAULESCU, P. GRAVILA – Modeling of Quantum Semiconductor Via the Transfer Matrix Method ………………………………………………..

95

14. M. CRISTEA, V. CHIRIŢOIU – Some aspects of IR Absorption in the Isomorphous Me2O3 Ternary System ............…………………………………………………………………………….

102

Mathematics

ABOUT THE DIOPHANTINE EQUATIONS (I) Gheorghe M. TUDOR, Mihai NEAGU

Abstract. In this paper it will be given some solutions (x, y, z) in natural numbers or in

positive rational numbers for the Diophantine equations (for α = 1 and for α = -1). ααα=⋅ zxy zyx

Keywords: Diophantine equation. Address: Gheorghe M. TUDOR, Mihai NEAGU, “Politehnica” University of Timişoara,

Departament of Mathematics, P-ţa. Victoriei, No. 2; 300006 – Timisoara, Romania; E-mail: [email protected] .

AN ELEMENTARY INTEGRAL FOR SET-VALUED FUNCTIONS

Octavian LIPOVAN

Abstract. This paper presents a study of some of the structure associated with one elementary integral of set valued functions and shows that under suitable assumptions, it possesses fairly good properties. In particular we indicate dominated convergence and completeness results in a general setting. This approach of the integral is made in terms of submeasures and associated topological rings.

Keywords: topological rings. Address: Octavian LIPOVAN, “Politehnica” University of Timişoara, Department of

Mathematics, P-ţa. Victoriei, No. 2; 300006 Timisoara, Romania; E-mail: [email protected]

THE INFRATRIGONOMETRY, AN INFERIOR ORDER NEIGHBORHOOD DOMAIN OF TRANSTRIGONOMETRY

Malvina BAICA, Mircea CARDU

Abstract. In this paper we apply the formulas for the basic functions of Transtrigonometry [3] for one of its adjacent domain of inferior order (0 ≤ k < 1). We will analyze the particularities of these basic functions characteristics in this domain which we named Infratrigonometry.

Keywords: Transtrigonometry, Special trigonometric functions. Address: Malvina BAICA, The University of Wisconsin, Department of Mathematical and

Comp. Science, Whitewater, WI 53190, U.S.A. E-mail: [email protected] ; Mircea CARDU, Herbing S.R.L., 9 Otelari Street, Sector 2, Bucharest, Romania;

E-mail: [email protected]

SOME APPROXIMATION THEOREMS FOR BERNSTEIN POLYNOMIALS OF TWO VARIABLES ON A TRIANGLE

Ovidiu T. POP, Mircea FARCAS

Abstract. In this paper we will give the approximation theorems for Bernstein polynomials of two variables on a triangle.

Keywords: Linear positive operators, Bernsteinbivariate polynomials, approximation formula. Address: Ovidiu T.POP,Mircea FARCAS, West University “Vasile Goldis” of Arad,

Branch of Satu Mare, 26 M.Viteazu Street, 440030 – Satu Mare, Romania; E-mail: [email protected] and [email protected]

THE ULTRATRIGONOMETRY, A SUPERIOR ORDER ADJACENT DOMAIN OF TRANSTRIGONOMETRY

Malvina BAICA, Mircea CARDU

Abstract. In a previous paper regarding the Infratrigonometry (IT) [3], we performed an analysis about some basic elements of the Transtrigonometry (TT) [2] extended to its inferior domain in function of the order values k. Thus, if for TT, k has values in the domain 1 < k < 2, for IT the order k has values in the domain 0 ≤ k < 1.

In this paper we perform the analysis of another adjacent to TT domain, this time of a superior order namely for 2 < k ≤ ∞. We call this domain „Ultratrigonometry” (UT). For this domain we will point out its particular characteristics for the basic functions in this Trigonometry.

Keywords: Ultratrigonometry, Transtrigonometry, Infratrigonometry, Special trigonometric







functions. Address: Malvina BAICA, The University of Wisconsin, Department of Mathematical and

Comp. Science, Whitewater, WI 53190, U.S.A. E-mail: [email protected] ; Mircea CARDU, Herbing S.R.L., 9 Otelari Street, Sector 2, Bucharest, Romania;

E-mail: [email protected]

NONCOMMUTATIVE FINITE SYSTEMS OF GRAMIAN ISOMETRIES AND APPLICATIONS

Tudor BINZAR, Loredana CIURDARIU

Abstract. Using a Wold-type decomposition for noncommutative finite systems of gramian isometries on Loynes spaces , a characterization of gramianconstant inner operators associated with such systems ins given.

Keywords: gramianconstant inner operators. Address: Tudor BINZAR, Loredana CIURDARIU, “Politehnica” University of

Timişoara, Departament of Mathematics, P-ţa. Victoriei, No. 2; 300006 – Timisoara, Romania; E-mail: [email protected] , [email protected]

ANALYSIS OF THE RECONNECTION PROCESS IN NONTWIST CUBIC MAPS

Gheorghe ŢIGAN

Abstract. The reconnection process in the dynamics of cubic nontwist maps, introduced in [7], is studied. The paper extends the results presented in [14]. Namely, we study the local and global bifurcations related to reconnection, following a one dimensional section in the parametric space associated to a nontwist cubic Hamiltonian system..

Keywords: Area preserving maps, nontwist maps, reconnection bifurcation. Address: Gheorghe TIGAN, “Politehnica” University of Timişoara, Departament of

Mathematics, P-ţa. Victoriei, No. 2; 300006 – Timisoara, Romania; E-mail: [email protected]

A CHARACTERIZATION OF SUBNORMALITY FOR LINEAR BOUNDED OPERATORS ON LOYNES SPACES

Loredana CIURDARIU, Tudor BINZAR

Abstract. In this paper a Halmos-Bram criterion for linear bounded operators on Loynes spaces that admit adjoint is proved.

Keywords: Gramian subnormal operators, Loynes spaces. Address: Loredana CIURDARIU, Ttudor BINZAR, “Politehnica” University of

Timişoara, Departament of Mathematics, P-ţa Victoriei, No. 2; 300006 – Timisoara, Romania; E-mail: [email protected] , [email protected] Physics

THE QUANTUM STATISTICS OF THE CHEMICAL REACTIVITY. PART IV: MAGNETIC AND ELECTRIC ATOMIC PROPERTIES DERIVED

FROM ATOMIC RADII

Mihai V. PUTZ

Abstract: Based of the atomic radii density functional scale the magnetic susceptibility and

static polarizability of isolated atoms are analytically developed in terms of outer shell atomic properties. It follows that the associate elemental scales display the suitable periodical shapes respecting the experimental first ionization potentials being therefore reliable when iterative molecular information are extracted from the atomic levels.








Keywords: chemical reactivity Address: Mihai V. PUTZ, PhD, Chemistry Department, West University of Timisoara,

Str. Pestalozzi, No. 16, Timisoara, 300115, ROMANIA, email: [email protected], [email protected]

THE ABSORPTION OF THE UNPOLARIZED MONO-CHROMATIC

ELECTROMAGNETIC RADIATION BY A VERY DILUTED FERROFLUID

Ioan LUMINOSU

Abstract: The FP10 ferrofluid is prepared using the chemical precipitation method. The dispersant is the oil and the stabilizer is the oleine. The average diameter of the magnetite particles is 11.354 nm. The absorption of the electromagnetic mono-chromatic radiation is determined using the SPECORD UV - VIS spectrophotometer.

This work proposes an optical method based on the statistical interpretation of the experimental data regarding the spectral absorption of the electromagnetic radiation by the FP10 ferrofluid in order to estimate the average diameter of the ferrofluid aggregates.

The optical method allowed the estimation that the average diameter of the aggregates from the very diluted solutions of the FP10 ferrofluid is of about 4 nm and the average number of particles in an aggregate is 4. The diluted solutions of the FP10 ferrofluid are stable and their use in technical applications is convenient.

Key words: absorption, biphasic, colloidal, extinction, mono-chromatic, spectrophotometer. Address: Ioan LUMINOSU, Physics Department, University "Politehnica", Piata Regina

Maria No. 1, Timisoara, 300004, ROMANIA, e-mail [email protected]

POLYETHYLENE AS LIGHT AMPLIFIER

Jevrem D.JANJIC, Bratislav S. TOSIC

Abstract: It was experimentally found thet the polyethylene foil noticeably amplifies intensity of light, and that amplification is proportional to the foil thickness. It was separated seven lines from mercury lamp and every of them was amplified. This relatively high number of lines can be explained, most probably, by the presence of impurities. Light amplifying is the consequence of simultaneous transition big groups of electrons from higher to some lower energy level. Monomers of olyethylene have not sufficient number of levels to explain seven amplified lines. It was reason to formulate a model of polyethylene as sistem of weakly interacting parallel linear chains with about fifty monomers per chain. The collective electron energy levels of the chain make a “stairway” for electron transitions from higher to lower levels. By means of this model experimental data were reprodeced with exactness up to one percent. Keywords: light amplification, polyethylene, inverse population, coherent photons

Address: J. D. JANJIC, Department of Physics, Faculty of Sciences, Trg D. Obradovica 4, 21000 Novi Sad, Serbia

B. S. TOSIC, Vojvodina Academy of Sciences and Arts, Dunavska 37, Novi Sad, Serbia

ANALYSIS OF THE CLASSICAL SHIFT DOPPLER FORMULAS Ioan ZAHARIE

Address: In this paper we establish the shift Doppler formulas for all cases of relative motion of the source and of the receiver . Both the source and the receiver can be at rest or in motion.

Keywords: shift Doppler Address: Ioan ZAHARIE, Physics Department, “Politehnica” University Timisoara, P-ţa

Regina Maria nr.1, 300004 Timişoara, ROMANIA, E-mail: [email protected]

MODELING OF QUANTUM SEMICONDUCTOR

VIA THE TRANSFER MATRIX METHOD Marius PAULESCU, Eugenia TULCAN-PAULESCU, Paul GRAVILA

Abstract. This paper reviews the transfer matrix method for computing the transmittance

coefficient for an arbitrarily sequence of rectangular potential barriers. The numerical model, implemented in our simulation system SQS, is appropriate to compute different semiconductor devices. The examples presented argue for the elegance, simplicity and feasibility of the method.

Keywords: quantum semiconductor Address: M. PAULESCU, E. TULCAN-PAULESCU, P. GRAVILA, West University of

Timisoara, Physics Department, E-mail: [email protected]

SOME ASPECTS OF IR ABSORPTION IN THE ISOMORPHOUS Me2O3 TERNARY SISTEM

Minerva CRISTEA, Viorel CHIRITOIU

Abstract. The experimental results concerning the infrared absorption spectra (400-4000 cm-1) of samples with 30% mol α-Fe2O3 from the isostructural oxides α-Fe2O3, α-Cr2O3, α-Al2O3 ternary system are presented and discussed. The IR spectra were obtained by using powdered samples tablet formed with KBr, at room temperature. Some investigated samples are solid solutions and the others contain two phases and these belong to gap miscibility from the ternary system. All spectra exhibit two absorption bands below 700 cm-1 that are larger for samples from gap miscibility.

Keywords: IR absorbtion, infrared spectra Address: MINERVA CRISTEA, VIOREL CHIRIŢOIU, Physics Department, “Politehnica”

University Timişoara, P-ţa Regina Maria Nr.1 Timişoara, Cod 300004, ROMANIA Seria MATEMATICǍ - FIZICǍ Transactions on MATHEMATICS & PHYSICS Tom 51 (65), Fascicola 2, 2006, ISSN 1224-6069


1. M. BAICA, M. CÂRDU – The Paratrigonometry and some of its Specific Symmetries …………………………………………………………………………………………..

1

2. P. GĂVRUTA, L. CIURDARIU, L. GĂVRUTA – On the Hyers-Ulam Stability of Parseval Frames ……… ……………………………………………………………………………………….

12

3. O. LIPOVAN – On the Lebesque Decomposition for Probabilistic Multivalued Measures … 18

4. M. MEGAN, C. STOICA – On exponential Trichotomy for Discrete Time Skew-Evollution Semiflows in Banach Spaces ……………………………………………………………………….

25

5. M. ČANAĐIJA, J. BRNIĆ – Solution Strategies for Nonlinear Coupled Thermomechanical Problems ......................................... .....................................................

33

6. G. TURKALJ, G. VIZENTIN, D. LANC – FE Stability Analysis of Elastic Frames Accounting for Connections Flexibility ....................................................................

41

7. O. BUNDĂU – Hopf Bifurcation Analysis of the Growth Model with Delay ……………… 50 8. A. ARON, C. POP, M. PUTA, P. SUSOI – Some Remarks on a Nonlinear

Control System on SO(4) ............................................... ..................................................... 57 9. L. CĂDARIU, V. RADU – A General Fixed Point Method for the Stability of Jensen

Functional Equation ........................................... ...................................................................

63 10. A. ARON, St. NICOARĂ, M. PUTA – A Counterexample to a Theorem of

Lyapunov ....................................................................... ........................................................

73 11. N. BOJA – Some Analytical Manifolds with Indefinite Metrics, III .................................. 78 12. L. MIHON – Modelling Elements for the Auxiliary Systems which Works on Road Vehicle . 85

PHYSICS

13. V. SAJFERT, V. MILIĆEVIĆ, V. JEVTIĆ- Medical Image Digitalization and and Archiving

Information Sistem in Serbia ……………………………………………………………………… 93

14. Z. TODOROVIC - Theory of the Origin of the Electron .................................................... 102 15. Z. B.TODOROVICH - Theory of the Electron as a Composite Particle ............................... 111 16. P. G. O. FREUND - Ideas of Space ……………………………………………………………… 125 17. C. GRUESCU, M. COSTACHE - Zoom Erectors in Measuring Apparatuses

Schemes ..................................................................................................................... 133

18. M. F. NICOLOV, C. F. WOENSDREGT - Different Force Fields Applications to Theoretical Growth Forms of Oxide Crystals ………………………………………………….

143

19. M. F. NICOLOV, C. F. WOENSDREGT - Analysis of Crystal Structure and Morphology… 149 Mathematics

THE PARATRIGONOMETRY AND SOME OF ITS SPECIFIC SYMMETRIES Malvina BAICA , Mircea CARDU

Abstract. In this paper the authors provide a systematisation of all nonconventional

trigonometries, other than the Classical Trigonometry (CT) [7], considering that these are: Quadratic Trigonometry (QT) [1], Polygonal Trigonometry (PT) [6], Transtrigonometry (TT) [3], Infratrigonometry (IT) [4] and Ultratrigonometry (UT) [5]. We adopt this generic denomination of Paratrigonometry (PRT) which includes these mentioned nonconventional trigonometries, as well as the Classical (conventional) Trigonometry (CT). Also, we will analyse some symmetric situations for the functions which represent mathematical modelling of the basic trigonometric figures of Paratrigonometry (as well as “Trigonometric circle” of CT, for example). Keywords: Nonconventional trigonometries, Paratrigonometry, Symmetric functions. Address: Malvina BAICA, The University of Wisconsin, Department of Mathematical and Comp. Science, Whitewater, WI 53190, U.S.A. E-mail: [email protected] ;

Mircea CARDU, Herbing S.R.L., 9 Otelari Street, Sector 2, Bucharest, Romania; E-mail: [email protected] .

ON THE HYERS-ULAM STABILITY OF PARSEVAL FRAMES

Pasc GĂVRUTA, Loredana CIURDARIU, Laura GĂVRUTA

Abstract. We give three results on the stability in the Hyers_Ulam sense of Parseval frames. Our results are strongly related to a recently result of P.G.Casazza [2].

Keywords: Parseval frames, Hyers-Ulam stability Address: Pasc GĂVRUTA, Loredana CIURDARIU, Laura GĂVRUTA, “Politehnica”

University of Timişoara, Departament of Mathematics, P-ţa. Victoriei, No. 2; 300006 Timisoara, Romania, E-mail: [email protected] .




ON THE LEBESQUE DECOMPOSITION FOR PROBABILISTIC

MULTIVALUED MEASURES

Octavian LIPOVAN

Abstract. The main aim of this paper is to study the notion of non-atomic and purely atomic probabilistic multivalued measures. We thus obtain the Lebesgue decomposition theorem for absolutely continuous probabilistic multivalued measures.

Keywords: non-atomic and purely atomic probabilistic. Address: Octavian LIPOVAN, “Politehnica” University of Timişoara, Departament of

Mathematics, P-ţa. Victoriei, No. 2; 300006 Timisoara, ROMANIA; E-mail: [email protected]

ON EXPONENTIAL TRICHOTOMY FOR DISCRETE TIME SKEW-EVOLLUTION SEMIFLOWS IN BANACH SPACES

Mihail MEGAN, Codruta STOICA

Abstract. In this paper we define the notion of discrete time skew-evolution semiflow in Banach spaces. A unified treatment for some uniform asymptotic behaviours, as exponential growth, exponential trichotomy for the property of trichotomy is provided. An equivalent definition and a characterization for the property of trichotomy by means of two projection families is also given.

Keywords: Discrete time skew-evolution semiflow, exponential growth, exponential decay, exponential stability, exponential instability, exponential trichotomy.

Address: Mihail MEGAN, West University of Timisoara, Faculty of Mathematics, Vasile Parvan Street, Timisoara, ROMANIA; Email: [email protected];

Codruta STOICA, “Aurel Vlaicu” University of Arad, Departament of Mathematics; Arad, ROMANIA; E-mail: [email protected].

SOLUTION STRATEGIES FOR NONLINEAR COUPLED THERMOMECHANICAL PROBLEMS

Marko CANADIJA, Josip BRNIC Abstract. The paper gives insight into procedures used to deal with nonlinear character of coupled thermomechanical problems. Decoupling technique, finite element model and consistent tangent operators are particularly analysed. Some details of finite strain thermoplasticity are presented. Proposed model is verified by means of a standard academic example.

Keywords: character of coupled thermomechanical problems, finite strain thermoplasticity Address: Marko CANADIJA, Josip BRNIC, University of Rijeka, Faculty of

Engineering, Department of Engineering Mechanics; Vukovarska 58, HR-51000 Rijeka, Croatia; E-mail: [email protected].

FE STABILITY ANALYSIS OF ELASTIC FRAMES ACCOUNTING FOR CONNECTIONS FLEXIBILITY

Goran TURKALJ, Goran VIZENTIN, Domagoj LANC

Abstract. Flexible connections and their influence on the elastic buckling load value of frame structures are considered. A numerical approach based upon FE method is presented. Equilibrium equations of a buckled beam member are derived applying linearized virtual work principle. Connection stiffness is taken into account by modifying conventional stiffness matrices, thus obtaining a hybrid beam element which enables the integration of flexible connections in stability analysis. Stability analysis is treated as an eigenvalue problem.





Keywords: frame structure, stiffness matrices, eigenvalue problem. Address: Goran TURKALJ, Goran VIZENTIN, Domagoj LANC, University of Rijeka,

Faculty of Engineering , Department of Engineering Mechanics, Vukovarska 58, HR-51000 Rijeka, Croatia; E-mail: [email protected]

HOPF BIFURCATION ANALYSIS OF THE GROWTH MODEL WITH DELAY

Olivia BUNDĂU

Abstract. In this paper, we study Hopf bifurcation of a growth of a model in which production occurs with delay while new capital is installed (time-to build), considering the case when the delay kernel for a capital is Dirac distribution. The time-to-build technology is shown to yield a system of differential functional equations with a unique steady state. We demonstrate that the steady state exhibits the Hopf bifurcation and we determine the direction and stability of the bifurcating periodic solutions by applying the normal form theory and the center manifold theorem. An example for justifying the theoretical results is also given.

Keywords: Growth model, Optimality, Hopf cycles. Address: Olivia BUNDAU, “Politehnica” University of Timişoara, Departament of

Mathematics, P-ţa. Victoriei, No. 2; 300006 Timisoara, ROMANIA; E-mail: [email protected]

SOME REMARKS ON A NONLINEAR CONTROL SYSTEM ON SO(4)

Anania ARON, Camelia POP, Mircea PUTA, Paul SUSOI

Abstract. An optimal control problem on the Lie group SO(4) is discussed and some of its properties are pointed out.

Keywords: Optimal control, spectral stability, nonlinear stability. Address: Anania ARON, Camelia POP, Politehnica” University of Timişoara,

Departament of Mathematics, P-ţa. Victoriei, No. 2; 300006 Timisoara, ROMANIA Mircea PUTA, Paul SUSOI, West University of Timisoara, B-dul V.Parvan, No

4, 300223-Timisoara, Romania; E-mail: [email protected] ; [email protected].

A GENERAL FIXED POINT METHOD FOR THE STABILITY OF JENSEN FUNCTIONAL EQUATION

Liviu CĂDARIU, Viorel RADU

Abstract. The aim of this paper is to obtain generalized stability results in the Ulam-Hyers sense for Jensen functional equation. To prove these results a fixed point theorem for generalized contractions is used.

Keywords: Jensen functional equation, fixed points, stability, generalized contractions. Address: Liviu CADARIU, “Politehnica” University of Timişoara, Department of

Mathematics, P-ţa. Victoriei, No. 2; 300006 Timisoara, Romania; E-mail: [email protected] Viorel RADU, West University of Timisoara, Faculty of Mathematics, B-dul.

V.Parvan no 4, 300223 Timisoara, Romania; E-mail: [email protected].

A COUNTEREXAMPLE TO A THEOREM OF LYAPUNOV

Anania ARON, Stefan NICOARĂ, Mircea PUTA Abstract. We give a new counterexample to a well known theorem of Lyapunov.

Keywords: Address: Anania ARON, Ştefan NICOARA, Politehnica” University of Timişoara,

Departament of Mathematics, P-ţa. Victoriei, No. 2; 300006 Timisoara, ROMANIA, [email protected]

Mircea PUTA, West University of Timisoara, B-dul V.Parvan, No 4, 300223-Timisoara, Romania; E-mail [email protected]









SOME ANALYTICAL MANIFOLDS WITH INDEFINITE METRICS, III Nicolae BOJA

Abstract. In this paper, the third part of the survey on analytical manifolds of constant

sectional curvature of pseudo-Riemannian type, a metric structure and also an analytical manifold structure on some non-Euclidean spaces are presented.

Keywords: Generalized system of trigonometric functional equations, selfpolar frame, pseudo-Riemannian manifolds of constant sectional curvature.

Address: Nicolae BOJA, “Politehnica” University of Timişoara, Departament of Mathematics, P-ţa Victoriei, No. 2; 300006 Timisoara, Romania; E-mail: [email protected] .

MODELLING ELEMENTS FOR THE AUXILIARY SYSTEMS WHICH WORKS ON ROAD VEHICLE

Liviu MIHON

Abstract. The paper presents some research and studies in the domain of ABS working conditions starting from the general balance equation of moving and taking in consideration different linearization methods of this equation. The mathematical model is verified with Simulink software and the exploitation curves in the driving cycle are taking in consideration. On example for an automatic regulator system is presented.

Keywords: ABS working condition, automatic regulator system. Address: Liviu MIHON, TMTAR Department, “Politehnica” University of Timisoara,

M.Viteazu Blvd. 1, 300222-Timisoara, Romania; E-mail: [email protected]. Physics

MEDICAL IMAGE DIGITALIZATION AND ARCHIVING INFORMATION SYSTEM IN SERBIA

Vjekoslav SAJFERT , Vladimir MILIĆEVIĆ, Vesna JEVTIĆ

Abstract: The paper gives a brief presentation of digital and archiving imaging system (PACS) with a survey of the main characteristics and development of the system worldwide as well as the possibilities and the area of its implementation in our conditions. We have given a proposition for digitalization and archiving of both the existing and future medical imaging in accordance with our possibilities for world standards implementation

Keywords: Medical imaging, PACS Serbia. Address: Vjekoslav SAJFERT, Vladimir MILIĆEVIĆ, Vesna JEVTIĆ, TF “Mihajlo

Pupin”, Đure Đakovića bb, 23000 Zrenjanin, Serbia, E-mail: [email protected]

THEORY OF THE ORIGIN OF THE ELECTRON Zoran TODOROVIC

Abstract: Quantum-mechanical theory of the possible origin of the electron has been derived

with reliable working formulae, which describe the concrete physical characteristics of the electron. Keywords: quantum theory Address: Zoran TODOROVIC, Faculty of Sciences, Prishtina University, Serbia

THEORY OF THE ELECTRON AS A COMPOSITE T PARTICLE

Zoran TODOROVIC

Abstract: On the basis of derived modified quantum commutation relations for sub-spins have been shown that electron could be a composite particle. Applying quantum commutators has been calculated fractal size of each sub-particle which build the internal structure of the electron.

Keywords: Address: Zoran TODOROVIC, Faculty of Sciences, Prishtina University, Serbia



IDEAS OF SPACE

Peter G. O. FREUND

Abstract. The evolution of our concept of space is traced from its beginnings when space was viewed as a given, unalterable three-dimensional “container” of physical phenomena, to the current view inspired by string theory, in which space of a predictable dimensionality emerges from the dynamics of the string. This modern concept does not share the fundamental nature of the old concept, and in fact is only meaningful as long as we do not probe extremely small distances. Moreover, it turns out that two spaces which do not even have the same dimension can nevertheless describe the same physics, even though the force of gravity is present in the higher-dimensional space, while it is surprisingly absent in the lower-dimensional space.

Keywords: concept of space Address: Peter G. O. FREUND, Department of Physics and Enrico Fermi Institute,

University of Chicago, Chicago, IL 60637, USA

ZOOM ERECTORS IN MEASURING APPARATUSES SCHEMES

Corina GRUESCU, Marius COSTACHE

Abstract: The paper describes the design and analytical methods of measuring apparatuses which work with finite object distance and contain image erectors. Aiming at a constant value microscope’s magnification, the authors suggest the use of a zoom aphocal erector. The calculus provides the displacement law of the first doublet in respect with the object abscissa of the microscope. The design of the microscope uses an original software, developed for the basic calculus. The specialized software OSLO LT was used for the analysis of image quality and proved a very high quality for the original components.

Keywords: analytical methods of measuring apparatuses Address: Corina GRUESCU, University Politehnica of Timişoara, Mechanical Faculty,

Mechatronics Department, Bd. Mihai Viteazu nr.1, e-mail: [email protected] COSTACHE, University Politehnica of Timisoara, Physics Department Piaţa Regina Maria nr.1, e-mail: [email protected]

ANALYSIS OF CRYSTAL STRUCTURE AND MORPHOLOGY

Mirela F. NICOLOV, Cornelis F. WOENSDREGT

Abstract : Physical analysis of the theoretical TiO2 structure was done. Keywords: Surface structure and topography Address: Mirela F. Nicolov, “Aurel Vlaicu” University of Arad, Research Department ,

Bd. Revolutiei Nr.77, 310130 Arad , Romania. Cornelis F. Woensdregt, Faculty of earth Sciences , Utrecht University, PO BOX

80021, NL 3508 TA Utrecht , The Netherlands



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