The Eighth Congress of Romanian Mathematicians

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I. Algebra and Number Theory

II. Algebraic, Complex and Differential Geometry and Topology

III. Real and Complex Analysis, Potential Theory

IV. Ordinary and Partial Differential Equations, Variational Methods, Optimal Control

V. Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics

VI. Probability, Stochastic Analysis, and Mathematical Statistics

VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences

VIII. Theoretical Computer Science, Operations Research and Mathematical Programming

IX. History and Philosophy of Mathematics

Mechanics, Numerical Analysis, Mathematical Models in Sciences 

(this list is in updating process)

BUCUR Andreea - Valentina
"Alexandru Ioan Cuza" University of Iasi, Romania
Title: Some non-standard problems related with the mathematical model of thermoviscoelasticity with voids (details)
In this presentation, we consider the constrained motion of a prismatic cylinder made of a thermoviscoelastic material with voids and subjected to final given data that are proportional, but not identical, to their initial values. We show how certain cross-sectional integrals of the solution spatially evolve with respect to the axial variable. Some conditions are derived upon the proportionality coefficients in order to show that the integrals exhibit alternative behavior.
Title: The Black Hole Effect and theGravitational Redshift Computation in the Frame of Post – Newtonian Type Garavitational Fields (details)
We analyze the gravitational redshift in the two-body problem associated to some post-Newtonian type gravitational fields. We start from the general relativistic metric and we discuss the “black hole effect” associated to each of the gravitational potentials. Also, the mathematical expression of the gravitational redshift is written down for all the considered potentials. Comparing with the Newtonian potential case, we are able to offer a deeper insight about the gravitational redshift problem in the relativistic (both general and special) theory. Our results may contribute to a better understanding of mechanisms involved in gravitationally lensed galaxies at high redshift.
Odessa National Academy of Telecommunications (ONAT), Ukraine
Title: Investigation of Specific Electromagnetic Field Problems Using Systems of Partial Differential Equations (details)
begin{document} Specific case of the differential Maxwell system is studied as original mathematical model of electromagnetic wave propagation in heterogeneous lines under expofunctional excitations. It is shown, that this system is equivalent to the general wave PDE (partial differential equation) with respect to all electromagnetic field intensities. Solvability criterion of this system in the class of non generalized functions is proved, and all main types of corresponding boundary problems are proposed and solved explicitly in the unified manner. end{document}
IVAN Secrieru
State University of Moldova, Republic of Moldova
Title: The stable approximate schemes for the evolution equation of the plane fractional diffusion process (details)
\begin{document} \titleart{The stable approximate schemes for the evolution equation of the plane fractional diffusion process } \autorart{ Ivan Secrieru } \medskip \coord{State University of Moldova, Republic of Moldova} \medskip \mail{ } % \addc{Initials. Last name of the first author, Initials. Last name of the second author}{ Title of article} % \stopcr \medskip The mathematical modeling of the problems that appear in physique, ecologies, hydrogeology, finance and other depend of the domain where this process is studied. For example, in the problem to transport any substance in atmosphere the main factors are the diffusion process, absorbtion of substance and advection- convection process. The classical model of this evolution problem with one space variable use the usual partial derivatives of first and second order (cf.[1]). In recent years many authors use the fractional space derivative to modeling such process. The class of approximate schemes for such models has been constructed in [2] for the case of one space variable. In this article is considered the same problem with two space variables of the form $$\qquad\frac{\partial{\varphi}}{\partial{t}}-d_{+}(x)\frac{\partial^{\alpha}{\varphi}} {\partial_{+}{x^{\alpha}}}-d_{-}(x)\frac{\partial^{\alpha}{\varphi}}{\partial_{-}{x^{\alpha}}}- d_{+}(y)\frac{\partial^{\alpha}{\varphi}}{\partial_{+}{y^{\alpha}}}-d_{-}(y)\frac{\partial^{\alpha}{\varphi}} {\partial_{-}{y^{\alpha}}}=f(x,y,t), $$ $$\qquad \qquad\qquad\varphi(x,y,0)=s(x,y),\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad (1)$$ $$ \varphi(x,y,t)=0 \qquad on \qquad the \qquad {\partial D},$$ in the domain $D=[0,a]\times[0,b]$ with the boundary $\partial {D}$ and the time interval $ [0,T]$. \medskip Using the decomposition principle it is proved the stability of the class of approximate schemes, constructed in [3] for the problem (1). \medskip \centerline{\bf References:} \medskip \noindent 1.G.I. Marchuk, {\it Mathematical modeling in problem to protection the environment}, Nauka, Moscow, 1982 (in Russian). \noindent 2.I.Secrieru, V.Ticau, Weighted approximate scheme for fractional order diffusion equation, Buletinul Institutul Politehnic din Iasi, tomul LVII(LXI), fasc.1, sectia MATEMATICA, MECANICA TEORETICA,FIZICA, Ed. POLITEHNIUM, Iasi, Romania, 2011 \noindent 3.I.Secrieru,Application of the decomposition principle for plane fractional diffusion equation, Proceedings of the Conf."Modelare mathematica, Optimizare si Tehnologii Informationale", ATIC, Chisinau * Evrica * 2014, Republica Moldova, 201-205. \end{document}
Institute of Solid Mechanics of the Romanian Academy, Romania
Title: On the separation property between stable and unstable zones of the dynamical systems and it implications. (details)
Any definitely dynamical system with numerically specification of its parameters can be substituted by the corresponding dynamical system that depends on parameters, without parameters numerical particularization. We mention, as possible parameters of the dynamical systems, geometrical, physical (in particular mechanical), economical, chemical, biological parameters and other. We notice firstly the property of separation between stable and unstable zones, in the dynamical system free parameters domain, as important property of all definitely dynamical systems that depend on parameters met in the specialized literature so that we can emphasize this property as property that can contribute to environment mathematical modelling. The stability analysis of each dynamical system that depend on parameters is realized using the stable zones of the selected free parameters domain and some theorems concerning the linear dynamical system stable evolution through the matrix associated to the dynamical system definition or the dependence of the nonlinearly dynamical system stable evolution by the “first approximation” linear dynamical system stable evolution. The mathematical conditions that assure the continuity property transmissibility from the functions that define the dynamical system on parameters to the corresponding matrix eigenvalues functions of the linear dynamical system are analysed in the literature first time. These conditions assure and the separation between stable and unstable zones in the domain of dynamical system free parameters justified by us. The possibilities of stable evolution optimisation in the stable zones, assured by separation, on the specified dynamical system that depends on parameters are described.
"Al. I. Cuza" University, Iasi
Title: Well-posedness for a phase-field transition system endowed with a polynomial nonlinearity and a general class of nonlinear dynamic boundary conditions (details)
The convergence and error estimate results for an iterative scheme of fractional steps type, associated to the reaction-diffusion equation supplied with regular potential and a general class of nonlinear and non-homogeneous dynamic boundary conditions, are established.
Retired, Romania
Title: On the raindrop motion (details)
On the raindrop motion Dr. Angela Muntean, retired from Naval Academy “Mircea cel Batran” Constanta, Romania Abstract The paper deals with the way in which it has been studied the motion of raindrops in the case of collecting mass. Some aspects of raindrop motion has been studied, the velocity of the raindrop has been calculated. Provided in relation to the size of the raindrop to keep a spherical shape, it tries to estimate the height from which you must take in order for it to be spherical. Keywords: theorem of momentum, differential equations, equations of motion.
Astronomical Institute of the Romanian Academy, Romania
Title: The J5:2 mean motion resonance as a new source of H-chondrites (details)
The dynamical evolution of (214869) 2007 PA8, one of the largest Potentially Hazardous Asteroids was analyzed using a population of 1275 clones that was integrated backward in time for 200000 years using a realistic model of the Solar System modified to use an 80-bit extended precision data type. The numerical integration results shows that 2007 PA8 evolved rapidly on a time scale of $10^5$ years toward higher eccentricities, via the 5:2 mean motion resonance with Jupiter by eccentricity pumping.
University of Pitesti, Romania
Title: Some considerations on Reynolds' equation for the lubricant thin films (details)
The aim of our paper is to present some addictions of Reynolds' equation form depending on the flow domain geometry of lubricated fluid film. This aspect is very important especially in the case of the bio-tribological systems (human joints), because their geometries are very complex and so difficult to analytically approximated. Moreover, in these cases the simplifying assumptions of the Reynolds’ model must be applied according to each this geometry. One of our obtained results is related to a new form of the Reynolds equation for such a particular geometry.
POP Nicolae
Technical University of Cluj-Napoca and Institute of Solid Mechanics of the Romanian Academy, Romania
Title: Quasistatic contact problems for viscoelastic bodies (details)
We describe some of our recent results concerning the modeling and analysis quasistatic contact problems with Coulomb friction. The frictional contact, when slip takes place, must takes thermal effects into account and the wear of the contacting surfaces. For this we need to study thermoviscoelastic contact.
Astronomical Institute of the Romanian Academy, Romania
Title: Two-body problem associated to Buckingham potential (details)
We study the two-body problem associated to Buckingham potential. Regularized equations of motion are obtained using McGehee-type transformations. In this framework, we describe two limit situations of motion, collision and escape, and provide the symmetries and the equilibrium points that characterize the problem.
POPESCU Nedelia Antonia
Astronomical Institute of the Romanian Academy, Romania
Title: Fractional kinetic equations as a model of intermittent bursts in solar wind turbulence (details)
The statistics of several quantities in space plasma are in agreement with some models based on space-time fractional derivative equations. In this paper we underline that the fractional calculus is a good approach to modeling the typical “anomalous” features that are observed in solar wind turbulence, which has both solar and interplanetary sources. In the case of solar wind velocity and interplanetary magnetic field data obtained by Ulysses mission, solutions of space-time fractional equations are used to analyze the presence or absence of heavy tails typically associated with multiscale behaviour.
Moldova State University, Republic of Moldova
Title: Computational scheme for drift-diffusion equations in multiply connected domain. (details)
The computational scheme for solving partial differential equations of convection-diffusion type, i.e. for equations that can be parabolic or hyperbolic depending on the values of the coefficients, is elaborated. Using as a framework the idea of the finite volume method, we create the algorithm and corresponding software to solve the nonlinear problem for semiconductor diode based on drift-diffusion equations in multiply connected domain. We construct the nonuniform grid for domain discretization. The refinement of the grid is carried out in areas where the impurity profile function has large gradients and in the vicinity of the point where the type of boundary condition is changed. There are presented some results of numerical simulation.
South East European University, FYR of Macedonia
Title: Algorithms for Accelerating Convergence of Power Series by means of Euler Type Operators (details)
This paper examines the acceleration convergence of alternative and non-alternative power series by means of an Euler type operator that is defined earlier by G.A.Sorokin [1984] and I.Z.Milovanovic [1989]. Through this type of linear operator of generalized difference of sequence is achieved that alternative and non-alternative power series to be transformed into series with higher speed of convergence than the initial series. The main contribution of this paper is findings and implementation of algorithms on accelerating convergence of power series.
SEICIUC Vladislav
Trade Cooperative University of Moldova, Republic of Moldova
\documentclass[11pt]{article} \usepackage{amssymb} \begin{document} \begin{center} DIRECT-APPROXIMATE METHODS IN SOLVING SOME CLASSES OF SINGULAR INTEGRAL EQUATIONS DEFINED ON ARBITRARY SMOOTH CLOSED CONTOURS \end{center} \begin{center} Vladislav Seiciuc \\ Trade Cooperative University of Moldova, Moldova\\ \end{center} \medskip The work includes algorithms and substantiation theory, in some Banach space, of direct-approximate methods in solving the following class of singular integral equations (SIE) defined on arbitrary smooth closed contour $\Gamma$ in the complex plane: 1) nonlinear singular integral equations(NSIE); 2) systems of NSIE; 3) linear singular integral equations (LSIE) with Carleman moved argument; 4) LSIE containing conjugated of unknown function; 5) LSIE with Carleman moved argument and conjugated of unknown function; 6) NSIE with Carleman moved argument; 7) NSIE with conjugated of unknown function. The direct-approximate methods in solving of SIE defined on a contour $\Gamma$ begin to be studied and resolved in the 80s of last century due to the works of V.Zoltarevschi and his disciples. Further results on approximation for functions defined on a contour $\Gamma$ with Lagrange polynomials built on Fejer nodes were established in H\"ol\-der $H_{\beta}(\Gamma)$, $0<\beta<1$, generalized H\"ol\-der $ H_{\omega}(\Gamma)$ and Lebesgue $L_{p}(\Gamma)$, $1
VLAD Serban E.
Oradea City Hall, Romania
Title: Asynchronous flows: the technical condition of proper operation and its generalization (details)
The asynchronous flows are given by Boolean functions $\Phi :\{0,1\}^{n}\longrightarrow \{0,1\}^{n}$ that iterate their coordinates $% \Phi _{1},...,\Phi _{n}$ independently on each other. In the study of the asynchronous sequential circuits, the situation when multiple coordinates of the state can change at the same time in called a race. When the outcome of the race affects critically the run of the circuit, for example its final state, the race is called critical. To avoid the critical races that could occur, $\Phi $ is specified in general so that only one coordinate of the state can change; such a circuit is called race-free and we also say that $% \Phi $ fulfills the technical condition of proper operation. We formalize in this framework the technical condition of proper operation and give its generalization, consisting in the situation when races exist, but they are not critical.