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CAIM 2014 Bookofabstracts CAIM 2014 18th–21st SEPTEMBER, 2014 BACAU,˘ ROMANIA BookofAbstracts Organized by ROMAI “Gh. Mihoc- C. Iacob” Institute of ”Vasile Alecsandri” University of Mathematical Statistics and Applied Bac˘au, Faculty of Sciences AOS¸R Mathematics of Romanian Academy Sponsors: The Municipality of Bac˘au, AEROSTAR S.A. Bac˘au, ISSSCO Bac˘au, Softescu Bac˘au, GRAFIT INVEST S.R.L. Bac˘au, METALBAC & FARBE S.A. Bac˘au, COPANEX S.R.L. Bac˘au Scientific Commitee Mihai ANASTASIEI (Ia¸si), Nuri AKSEL (Germany), Vladimir BALAN (Bucure¸sti), Constantin BACUTA (U.S.A.), Wladimir-Georges BOSKOFF (Constant¸a), Dumitru BOTNARU (Moldavia), Vasile BRANZˆ ANESCU˘ (Bucure¸sti), Tassos BOUNTIS (Greece), Daniel BREAZ (Alba Iulia), Sergiu CATARANCIUC (Moldavia), Adrian CARABINEANU (Bucure¸sti), Victor CHEPOI (France), Ovidiu CARJˆ A˘ (Ia¸si), Acad. Mitrofan CIOBANU (Moldavia), Sanda CLEJA-T¸IGOIU (Bucure¸sti), Acad. Constantin CORDUNEANU ( U.S.A.), Adrian CONSTANTINESCU (Bucure¸sti), Piergiulio CORSINI (Italy), Ion CRACIUN˘ (Ia¸si), Matthias DEHMER (Germany), Narcisa APREUTESEI DUMITRIU (Ia¸si), Angelo FAVINI (Italy), Gabriel DIMITRIU (Ia¸si), Vladimir GERDT (Russia), Ioan DZITAC (Oradea), Bogdan KAZMIERCZAK (Poland), Constantin FETECAU˘ (Ia¸si), Victor LEPIN (Belarus), Paul GEORGESCU (Ia¸si), Boris LOGINOV (Russia), Acad. Marius IOSIFESCU (Bucure¸sti), Nenad MLADENOVICI (Great Britain), Gabriela MARINOSCHI (Bucure¸sti), Andrei MOROIANU (France), Acad. Solomon MARCUS(Bucure¸sti), Gheorghe MOROS¸ANU (Hungary), Acad. Radu MIRON(Ia¸si) Lidia PALESE (Italy), Ioana MOISIL (Sibiu), Mihail POPA (Moldavia), Costic˘aMOROS¸ANU (Ia¸si), Maido RAHULA (Estonia), Titus PETRILA (Cluj-Napoca), Kumbakonam RAJAGOPAL (U.S.A.), Constantin POPA (Constant¸a), Liliana RESTUCCIA (Messina), Vasile POSTOLICA˘ (Bac˘au), Ruggero Maria SANTILLI (U.S.A.), Vasile PREDA (Bucure¸sti), Dana SCHLOMIUK (Canada), Ioan STANCU MINASIAN (Bucure¸sti), Kiyoyuki TCHIZAWA (Japan), Mirela S¸TEFANESCU˘ (Constant¸a), Ioan TODINCA˘ (Moldavia), Dan TIBA (Bucure¸sti), Vladilen TRENOGIN (Russia), Acad. Ioan TOMESCU(Bucure¸sti), Nicolae VULPE (Moldavia), Mihai TURINICI (Ia¸si), Gheorghit¸˘aZBAGANU˘ (Bucure¸sti). Organizing Commitee: President: Ilie BURDUJAN Anca Veronica ION Vice President: Mihai TALMACIU Stelian ION Local Organizing Commitee: Faculty of Sciences, Bac˘au Elena NECHITA Valer NIMINET¸ Marcelina MOCANU Dan POPA Manuela GˆIRT¸U Simona VARLANˆ 3 Contents 1 Real,Complex,FunctionalandNumericalAnalysis 5 2 PDEswithApplicationsinMechanics,Biology,etc. 21 3 ODEs; Dynamical Systems 25 4 Probability Theory, Mathematical Statistics, Operations Research 31 5 Algebra, Logic, Geometry (with applications) 43 6 Mathematical Modeling 63 7 Computer Science 75 8 Education 83 9 Supplement 93 4 1. Real, Complex, Functional and Numerical Analysis 6 Real, Complex, Functional and Numerical Analysis Some connection between Pompeiu-Hausdorff convergences of nets and other well-known hyperconvergences Gabriela Apreutesei Faculty of Mathematics, ”Alexandru Ioan Cuza” University of Ia¸si, Romania e-mail: [email protected] Let (X,d) be a metric space and l (X) the family of closed non-void parts of X. One of the most used convergences for sequencesC of sets is Pompeiu-Hausdorff convergence. Sometimes is difficult to verify the properties of this convergence, so we find some conditions on sequences or nets (like monotonicity, boundedness or compactness) which assure the coincidence of Pompeiu- Hausdorff convergence with other well-known hyperconvergences: Kuratowski, Wijsman and Mosco convergences. Properties of nonlocal reaction-diffusion equations from population dynamics Narcisa Apreutesei Department of Mathematics and Informatics, ”Gheorghe Asachi” Technical University of Iasi, Romania e-mail: [email protected] Some models of integro-differential equations from population dynamics are presented and analyzed. The integral term describes the nonlocal consumption of resources. We are interested mainly in the bistable case. For some models, Fredholm property of the linearized operators is combined with the implicit function theorem to prove the existence of waves. This is available only for the case of small support of the integral, when the integro-differential operators are close to the differential operators. For some other models, Leray-Schauder method can be applied. This implies the construction of a topological degree for the corresponding operators and the establishment of a priori estimates of the solution. Multilevel methods for variational and quasi-variational inequalities Lori Badea ”Simion Stoilov” Institute of Mathematics of Romanian Academy, Bucharest, Romania e-mail: [email protected] This talk is an overview of some results concerning the global convergence rate of the standard multigrid method for the variational inequalities and variational inequalities conatining a term introduced by a contraction operator. Also, we estimate the convergence rate of the one- and two- level methods for variational inequalities of the second kind and of the quasi-variational inequalities. The methods are introduced as subspace correction algorithms in a reflexive Banach space, where general convergence results are derived. These algorithms become multilevel and multigrid methods by introducing the finite element spaces. In this case, the error estimates are written in function of the number of subdomains and the overlapping parameter for the one- and two-level methods, and in function of the number of levels for the multigrid methods. For the one- and two-level methods, we comparatively illustrate the convergence rates of by numerical experiments. Also, the obtained convergence rates for the multigrid methods are compared with those existing in the literature for the complementarity problems. CAIM 2014, Bac˘au, September 18-21, 2014 7 About extensions with p-remainders Laurent¸iu I.Calmut¸chi Tiraspol State University, Republic of Moldova e-mail: [email protected] We use the terminology from [5]. Any space is considered to be a non-empty completely regular T1-space. If X is a dense subspace of a space Y , then Y is called an extension of X and the subspace Y X is called remainder of X. Denote by βX the Stone-Cechˇ compactification of the space X. Let\ X∗ = βX X. Fix a space\X. Let Y and Z be two extensions of the space X. We consider that Y Z if there exists a continuous mapping f : Z Y such that f(x)= x for any x X. If f is a homeomorphism≤ of Z onto Y , then we say that the→ extensions Y and Z are equivalent.∈ We identify the equivalent extensions. Any non-empty family of extensions of the space X is a partially ordered set and briefly is called a poset. E A space X is a paracompact p-space if there exist a metrizable space Y and a perfect mapping g : X Y of X onto Y [2]. Let−→X be a space and d a pseudumetric on X. For each x X and each real number rr > 0 put K(x) = y X : d(x,y) = 0 and V (x,d,r) = y X ∈: d(x,y) < r . There exist a set X/d, a metric{ d¯ ∈on X/d and a mapping} π : X/d such{ ∈ that d(x,y) = d¯(π} (x), π (y)) for each d −→ d d x,y X. The pseudometric d is called a k-metric if the mapping πd is perfect. If the mapping πd is continuous,∈ then the pseudometric d is called a continuous pseudometric on X. Any pseudometric is considered to be continuous. A pseudometric d is called a complete k-metric if d is a k-metric and(X/d, d¯) is a complete metric space. On a space there exists a complete k-metric if and only if it is a paracompact Cech-completeˇ -space. An extension Y of a space X is called a (complete) p-extension if on Y there exists a (complete) k-metric d such that πd(X) πd(Y X)= . Proposition 1. Let Y be∩ a p-extension\ ∅ of a space X. Then X, Y and Y X are paracompact p-spaces. \ Theorem 2. For a space X the following assertions are equivalent: 1. X is a Lindel¨of p-space. 2. For X there exists a p-extension Y which is a Lindel¨of p-space. 3. Any p-extension Y of X is a Lindel¨of p-space. 4. There exists a compactification bX of X such that bX X is a paracompact p-space. 5. For any compactification bX of X the remainder bX \X is a Lindel¨of p-space. 6. On X there exists some totally bounded k-metric. \ Theorem 3. If d is a k-metric on a space X then there exist a complete p-extension Y of X and a complete k-metric ρ on Y such that d(x,y)= ρ(x,y) for each ρx,y X and πρ(X) πρ(Y X)= . In this case we say that ρ is a completion of the k-metric d. ∈ ∩ \ ∅ We mention that a completion ρ of a k-metric d, in general, is not unique. Let Ec(X,d) is the family of all complete p-extension (Y, ρ) of X, where ρ is a completion of the k-metric d. Obviously that Ecp(X,d) is a poset. Theorem 4. If d is a k-metric on a space X, then Ecp(X,d) is a complete upper-lattice with a maximal element (mX,dm) and X mX βX, where βX is the Stone-Cechˇ compactification of X. Some similar problems of the theory⊆ of⊆ extensions of spaces were examined in [1, 3, 4, 5, 6]. Bibliography [1] C. C. Alexander, Metrically isolated sets, Amer. Math. Monthly 78 (1971), 892-895. 8 Real, Complex, Functional and Numerical Analysis [2] A. V. Arhangel’skii, Open and near open mappings. Connections between spaces, Trudy Moskov. Matem. Ob-va, 15 (1966, 181-223 (English translation: Trans. Mosk. Math. Soc. 15 (1966), 204-250). [3] A. V. Arhangel’skii, Mappings and spaces, Uspehy Matem. Nauk 21:4 (1966) 133-184 (English translation: Russian Math. Surveys 21:4 (1966), 115-162).
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  • The Structure and Two Complexities of Economic Choice Semiautomata
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