The Eighth Congress of Romanian Mathematicians

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List of talks

I. Algebra and Number Theory

Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu

II. Algebraic, Complex and Differential Geometry and Topology

Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties

III. Real and Complex Analysis, Potential Theory

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

Special session: Optimization and Games Theory

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

Special session: Spectral Theory and Applications in Mathematical Physics

Special session: Dynamical Systems and Ergodic Theory

VI. Probability, Stochastic Analysis, and Mathematical Statistics

VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences

Special session: Mathematical Modeling of Some Medical and Biological Processes

Special session: Mathematical Models in Astronomy

VIII. Theoretical Computer Science, Operations Research and Mathematical Programming

Special session: Logic in Computer Science

IX. History and Philosophy of Mathematics

Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics 

(this list is in updating process)

ANGHEL Nicolae
University of North Texas, United States
Title: Fredholmness vs. Spectral Discreteness for First-Order Differential Operators (details)
In this talk we show that for essentially self-adjoint first-order differential operators $D$, acting on sections of bundles over complete (non-compact) manifolds, Fredholmness vs. Spectral Discreteness is the same as `$\exists c>0$, $D$ is $c$-invertible at infinity' vs. `$\forall c>0$, $D$ is $c$-invertible at infinity'. An application involving the spectral theory of electromagnetic Dirac operators is then given.
BADEA Gabriela
Ovidius University of Constanta, Romania
Title: On the summing properties of the multilinear operators on a cartezian product of $c_{0}\left(X\right)$ spaces (details)
In this talk we discuss the necessary and sufficient conditions for an operator defined on a Cartesian product of $c_{0}\left(X\right)$ to be summing, dominated or multiple s-summing. These three concepts are some possible extensions of the summing linear operators to the multilinear settings. Also, we consider the relationship with the nuclear multilinear operators, which is related to Swartz's theorem from the linear case. Some examples of such operators are also presented.
BOCA Florin - Petre
University of Illinois Urbana-Champaign, USA
Title: The distribution of rational numbers and ergodic theory (details)
Rational numbers in [0,1), or equivalently roots of unity on the unit circle, can be naturally ordered either by the size or their denominators, or by the sum of digits in their continued fraction representation. Their distribution is not random and appears to be controlled by four important types of measure-preserving transformations (Gauss, Farey, BCZ, Newman), with very different ergodic properties. Our talk will discuss connections between number theory and ergodic theory along these lines.
University Politehnica of Bucharest, Romania
Title: An example of twisted bi-Laplacian and its spectral properties (details)
\documentclass{article} \usepackage{amsmath,amssymb,amscd,amsthm,verbatim,alltt,amsfonts,array} %\usepackage[english]{babel} \usepackage{latexsym} \usepackage{amssymb} \title{An example of twisted bi-Laplacian and its spectral properties} \author{Viorel Catan\u a} \date{} \begin{document} \maketitle \newcommand{\omm}{\Omega} \newcommand{\om}{\omega} \newcommand{\ty}{\infty} \newcommand{\di}{\displaystyle} \newcommand{\va}{\varphi} \newcommand{\si}{\sigma} \newcommand{\ga}{\gamma} \newcommand{\gaa}{\Gamma} \newcommand{\na}{\nabla} \newcommand{\te}{\theta} \newcommand{\ld}{\ldots} \newcommand{\ov}{\over} \newcommand{\mm}{\medskip} \newcommand{\la}{\lambda} \newcommand{\su}{\subset} \newcommand{\qu}{\quad} \newcommand{\fo}{\forall} \newcommand{\al}{\alpha} \newcommand{\be}{\beta} \newcommand{\ep}{\varepsilon} \newcommand{\pa}{\partial} \newcommand{\ti}{\times} \newcommand{\de}{\delta} Let $L$ be the twisted Laplacian on $\mathbb{R}^2$, which is the second-order partial differential operator given by $L = - \Delta + \frac{1}{4} (x^2 + y^2) - i \left(x \frac{\pa}{\pa y} - y\frac{\pa}{\pa x} \right)$, where $\Delta = \di\frac{\pa^2}{\pa x^2} + \di\frac{\pa^2}{\pa y^2}$ is the Laplace operator, $H = - \Delta + \di\frac{1}{4} (x^2 + y^2)$ is the Hermite operator and $N = x \di\frac{\pa}{\pa y} - y \di\frac{\pa}{\pa x}$ is the rotation operator. It follows that the twisted Laplacian $L = H - iN$ is the Hermite operator perturbed by the partial differential operator $-iN$. Now, we introduce the renormalization of the twisted Laplacian $L$ to be the partial differential operator given by $P_m = \di\frac{1}{2} (L + 2m-1)$, $m \in \mathbb{N}^*$. So, the transpose $Q_m$ of $P_m$ is given by $Q_m = \di\frac{1}{2} (L^t + 2m-1)$, $m \in \mathbb{N}^*$, where $L^t = - \Delta + \di\frac{1}{4} (x^2 + y^2) + iN$ is the transpose of the twisted Laplacian $L$. The aim of this talk is to analyze the twisted bi-Laplacian $M_{m,n}$, $m,n \in \mathbb{N}^*$ defined by $M_{m,n} = Q_n P_m = P_m Q_n = \frac{1}{4} (H + iN + 2n-1)(H - iN + 2m-1)$, where $P_m$ and $Q_n$ commute because it can be shown easy that $H$ and $N$ commute. Based on the well-known spectral properties of the twisted Laplacian $L$ (see [2]) we can prove that the spectrum of $M_{m,n}$ is given by a sequence of isolated eigenvalues of finite multiplicity each of them. This fact is a consequence of the compactness of the resolvent of the twisted bi-Laplacian as an operator from $L^2 (\mathbb{R}^2)$ into $L^2 (\mathbb{R}^2)$. Moreover, the essential self-adjointness and global hypoellipticity in terms of a new two-parameter family of Hilbert spaces (in fact Sobolev spaces) are studied. Let us remark that when we take $m=n=1$ we recover the results in the paper [3] and that we can also state and prove similar assertions as above in an abstract setting (see [1]). \bigskip {\bf References} \medskip [1] V. Catan\u a, The Heat Kernel and Green Function of the Generalized Hermite Operator, and the Abstract Cauchy Problem for the Abstract Hermite Operator, in Pseudo-Differential Operators: Analysis, Applications and Computations, Operator Theory: Advances and Applications, Vol. 213 (2011), 155-171. [2] A. Dasguspta and M.W. Wong, Essential self-adjointness and global hypoellipticity of the twisted Laplacian, Rend. Sem. Mat. Univ. Pol. Torino, 66(2008), 75-85. [3] T. Gramchev, S. Pilipovic, L. Rodino, M.W. Wong, Spectral properties of the twisted bi-Laplacian, Arch. Math., 93(2009), 565-575. \end{document}
Aalborg University, Denmark
Title: On the construction of composite Wannier functions (details)
We give a constructive proof for the existence of an $N$-dimensional Bloch basis which is both smooth (real analytic) and periodic with respect to its $d$-dimensional quasi-momenta, when $1\leq d\leq 2$ and $N\geq 1$. The constructed Bloch basis is conjugation symmetric when the underlying projection has this symmetry, hence the corresponding exponentially localized composite Wannier functions are real. This is joint work with G. Nenciu (Bucharest) and I. Herbst (Charlottesville)
COSTARA Constantin
Ovidius University of Constanta, Romania
Title: Complex analysis and spectral isometries (details)
In this talk, we shall present some ideas and methods from complex analysis which can be used to obtain new results on linear maps on Banach algebras preserving the spectral radius.
University "Al. I. Cuza" of Iasi, Romania, Romania
Title: On weak linear spaces (details)
Non-linear spaces have been introduced and studied related to various problems in optimization, functional analysis, computer science, set-valued analysis. In this talk we present some properties of weak linear spaces and comparison results on different types of non-linear spaces.
Purdue University, USA
Title: A generalized Dixmier-Douady theory (details)
We show that the Dixmier-Douady theory of continuous field $C^*$-algebras with compact operators $K$ as fibers extends significantly to a more general theory of fields with fibers $A otimes K$ where $A$ is a strongly self-absorbing C*-algebra. An important feature of the general theory is the appearance of characteristic classes in higher dimensions. We give the following application of these results. Let $X$ be a locally compact space of finite covering dimension. Let $M_{mathbb{Q}}$ be the the universal UHF algebra. Any separable continuous field of C*-algebras over $X$ with all fibers abstractly isomorphic to $M_{mathbb{Q}}otimes K$ is locally trivial. The set of isomorphism classes of these fields becomes an abelian group with multiplication given by the tensor product. This group is isomorphic to $$H^1(X,mathbb{Q}^{times}_{+}) oplus H^3(X,mathbb{Q})oplus H^5(X,mathbb{Q})oplus cdots.$$
DANET Nicolae
Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, 124, Lacul Tei Blvd., 020396 Bucharest, Romania
Title: Closure sublinear operators and their use to the Dedekind completion of a Riesz space (details)
\documentclass{article} \begin{document} A \textbf{closure sublinear operator} on a Riesz space (vector lattice) $F$ is a \textbf{sublinear} operator $U:F\longrightarrow F,$ which is also a \textbf{closure operator} (that is, $(a)$ $U$ is extensive: $f\leq U(f);$ $% (b)$ $U$ is idempotent: $U(U(f))=U(f);$ and $(c)$ $U$ is increasing: $% f_{1}\leq f_{2}\Rightarrow U(f_{1})\leq U(f_{2})$) that commutes with the finite supremums, $U(f_{1}\vee f_{2})=U(f_{1})\vee U(f_{2}).$ Using $U$ we define a new operator $L:F\rightarrow F$ by putting $L(f)=-U(-f).$ The operator $L$ is a \textbf{dual closure} \textbf{operator} (the property $(a)$ becomes: $L(f)\leq f),$ \textbf{supralinear,} and commutes with finite infimums, $L(f_{1}\wedge f_{2})=L(f_{1})\wedge L(f_{2}).$ The aim of this paper is to study the properties of this pair $(U,L)$ of operators and to show how they can be used to construct the Dedekind completion of a Riesz space $G,$ if this is a Riesz subspace of a Dedekind complete Riesz space $E.$ \begin{thebibliography}{9} \bibitem{Danet2014} D\u{a}ne\c{t}, N.: \emph{Riesz spaces of normal semicontinuous functions}, Mediterr. J. Math. DOI 10.1007/s00009-014-0466-2, published online 23 September 2014. \bibitem{KaplanIV} Kaplan, S., \emph{The second dual of the space of continuous functions}, IV. Trans. Amer. Math. Soc. \textbf{113} (1964), 512-546. \bibitem{KaplanBook} Kaplan, S., \emph{The bidual of C(X)} I, North-Holland Mathematics Studies 101, Amsterdam, 1985. \end{thebibliography} \end{document}
DANET Rodica - Mihaela
Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, 124, Lacul Tei Blvd., 020396 Bucharest, Romania
Title: The most important challenge in the interval analysis. Historical notes and how we can overcome the barrier via extension results (details)
\documentclass{amsart} \begin{document} The paper brings into question the most important challenge in the Interval Analysis, namely that the existence of an opposite for some closed intervals in an arbitrary ordered vector space ceases to be true and the second distributive law for the usual algebraic operations remains true only under a restrictive condition. Firstly some historical notes related to the Interval Analysis are given. Secondly we show how we can overcome the limits imposed to the above mentioned challenge. We shall illustrate this with some extension results. In a previous paper we gave a theorem of the Mazur-Orlicz type. Now we give new results concerning some applications of this theorem in the Interval Analysis. We also give a new example that shows how we can correct the \textquotedblleft defect\textquotedblright\ of the addition that we mentioned above. \begin{thebibliography}{9} \bibitem{1} Anguelov, R., \textit{The algebraic structure of spaces of intervals-Contributions of Svetoslav Markov to\ interval analysis and its applications}, International Conference on Mathematical Methods and Models in Bioscience, 16-21 June, Sofia, Bulgaria, Biomath \textbf{2013}, Conference Book, 22-24 (2013). \bibitem{2} Aseev, S.M., \textit{Quasilinear operators and their application in the theory of multivalued mappings}, Proceedings of the Steklov Institute of Mathematics \textbf{2}, 23-52 (1986). \bibitem{3} D\u{a}ne\c{t}, N., D\u{a}ne\c{t}, R.-M., \textit{Existence and extensions of positive linear operators}, Positivity 13, 89-106 (2009). \bibitem{4} D\u{a}ne\c{t}, R-M., \textit{A Mazur-Orlicz Type Theorem in Interval Analysis and its Applications, Proceedings of the\ seventh Positivity conference, July 22-26, Leiden}, \textbf{2013} (to appear). \end{thebibliography} \end{document}
DEACONU Valentin
University Of Nevada, Reno, USA
Title: Symmetries of graph C*-algebras (details)
Given a discrete locally finite graph $E=(E^0, E^1, r, s)$, we consider symmetries of the associated $C^*$-correspondence ${\mathcal H}_E$ and of the graph algebra $C^*(E)$, defined using actions and representations of a group $G$. Examples include self-similar actions of groups on trees. We study the fixed point algebra $C^*(E)^G$ and the crossed product $C^*(E)\rtimes G$. The group $G$ acts also on the $AF$-core $C^*(E)^{\mathbb T}$ and $C^*(E)^{\mathbb T}\rtimes G\cong (C^*(E)\rtimes G)^{\mathbb T}.$ If $G$ is finite, then $C^*(E)\rtimes G$ is isomorphic to the $C^*$-algebra of a graph of $C^*$-correspondences, constructed using orbits and characters of the stabilizer groups. Some of the results can be extended to actions and representations of groupoids.
DUMITRASCU Constantin Dorin
Adrian College, USA
Title: A direct proof of K-amenability for a-T-menable groups (details)
For amenable groups, the maximal group $C^*$-algebra $C^*(G)$ and the reduced groups $C^*$-algebra $C^*_r(G)$ are isomorphic. In the early 1980's, Cuntz, for discrete groups, then Julg and Valette, for non-discrete groups, introduced a weaker concept of $K$-amenability, which implies the isomorphism of these two group $C^*$-algebras at the level of $K$-theory. In the late 1990's, Higson and Kasparov proved the Baum-Connes conjecture for all the a-T-menable groups. These are groups that admit a continuous affine isometric and metrically proper action on some real Hilbert space $H$. As a consequence of the Baum-Connes conjecture, it follows that the a-T-menable groups are $K$-amenable. In this presentation we give a new proof of this result. Our approach is new in at least two aspects. First, we construct a homotopy between the unit $1_G$ in the representation ring of $G$ and a Fredholm $G$-module whose representations are weakly contained in the left-regular representation. Second, we perform our computations in the new bivariant $K$-theory for $C^*$-algebras, called $KE$-theory, constructed by the presenter. This is joint work with Nigel Higson.
University of Central Florida, United States
Title: Fourier series on fractals (details)
We present some recent results and open questions on the harmonic analysis and Fourier series on fractal measures.
al Farabi Kazakh national University, Kazakhstan
Title: Supersymmetry, nonassociativity, and Big Numbers (details)
The nonassociative generalization of supersymmetry is considered. Using a special choice of the parameters, it is shown that the associator of the product of four supersymmetry generators is connected with the angular momentum operator. The associator of four supersymmetry generators has the coefficient $sim hbar/ ell_0^2$ where $ell_0$ is some characteristic length. Two cases are considered: (a) $ell_0^{-2}$ coincides with the cosmological constant; (b) $ell_0$ is the classical radius of electron. It is also shown that the scaled constant is of the order of $10^{-120}$ for the first case and $10^{-30}$ for the second case. The possible manifestation and smallness of nonassociativity is discussed. The connection of operator decomposition to the hidden variables theory and alternative quantum mechanics is discussed.
Czech Academy of Sciences, Czech Republic
Title: Approximating quantum graphs by Schr\"odinger operators on thin networks (details)
\documentclass[11pt]{article} \usepackage{amssymb} \pagestyle{empty} \begin{document} \title{Approximating quantum graphs by Schr\"odinger operators on thin networks} \author{Pavel Exner} \date{Doppler Institute for Mathematical Physics \\ and Applied Mathematics, Prague} \maketitle \noindent Quantum graph models are extremely useful but they also have some drawbacks. One is related to the physical meaning of the vertex coupling. The self-adjointness requirement alone leaves a substantial freedom expressed through parameters appearing in the conditions matching the wave function at the graph vertices. It is a longstanding problem whether one can motivate their choice by approximating the graph Hamiltonian by operators on a family of networks, i.e. systems of tubular manifolds the transverse size of which tends to zero. It appears that the answer depends on the conditions imposed on tube boundaries. In this talk we present a complete solution for Neumann networks: we demonstrate that adding properly scaled potentials and changing locally the graph topology, one can approximate any admissible vertex coupling. The result comes from a common work with Taksu Cheon, Olaf Post, and Ond\v{r}ej Turek. \\ [1em] \emph{Mailing addresses:} \\ Department of Theoretical Physics, NPI \\ Czech Academy of Sciences \\ CZ-25068 \v{R}e\v{z} -- Prague; \\ Department of Physics, FNSPE \\ Czech Technical University \\ B\v{r}ehov\'{a} 7 \\ CZ-11519 Prague \\ [1em] \emph{E-mail:} \\ \end{document}
University of Bremen, Germany
Title: Conformal ending measures on limit sets of Kleinian groups (details)
The dynamics of geometrically finite hyperbolic manifolds is well understood by means of Patterson-Sullivan theory. For geometrically infinite manifolds, or manifolds given by infinitely generated Kleinian groups, nonrecurrent dynamics becomes the "thick part" of dynamics, not only in the sense of measure but often also Hausdorff dimension. Patterson-Sullivan measures work well for divergence type groups at the critical exponent. Conformal measures of exponent above the critical one were known to exist by earlier work of Sullivan using methods from Harmonic Analysis, but were explicitely constructed only a few years ago by Anderson, Tukia and myself. Such conformal ending measures naturally work well when the Poincare series converges and are thus suitable for studying nonrecurrent dynamics in hyperbolic manifolds. In my talk I will present the construction, properties and some first applications of such conformal ending measures.
Nihon University, Japan
Title: Some inequalities related to operator means (details)
We give some operator inequalities among arithmetic mean, geometric mean and harmonic mean. In addition, we show some unitarily invariant norm ineqauities, which give tight bound for logarithmic mean.
IMAR, Romania
Title: Interpolation for completely positive maps (details)
We obtain necessary and sufficient conditions for solvability, as well as a parametrization of all solutions, for a problem of interpolation for completely positive maps between matrix spaces. Numerical approximation methods are also discussed.
GOK Omer
Yildiz Technical University, ISTANBUL, TURKEY, TURKEY
Title: On Boolean Algebras of Projections of Finite Multiplicity (details)
let X be a Banach C(K)-module, where K is a compact Hausdorff space and the homomorphism m is continuous.In this talk, we give the equivalent conditions for reflexivity of the dual space X'. References. 1. A.Kitover, M.Orhon,Reflexivity of Banach C(K)-modules via the reflexivity of Banach lattices, Positivity, 18(2014), 475-488.
University Politehnica of Bucharest and "Simion Stoilow" Institute of Mathematics of the Romanian Academy, Romania, Romania
Title: Pro-C*-correspondences (details)
We associate a pro-C*-algebra to a pro-C*-correspondence and show that this construction generalizes the construction of crossed products by Hilbert pro-C*-bimodules and the construction of pro-C*-crossed products by strong bounded automorphisms. This is a joint work with I. Zarakas (University of Athens)
Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Title: Ergodic and metric properties of certain invariant measures on fractals (details)
I will give several recent results about invariant measures on fractals, obtained either from non-invertible dynamical systems with some hyperbolicity, or from conformal (finite or infinite) iterated function systems with overlaps.
Arak University, Iran
Title: On a generalization of Ciric fixed point in best approximation (details)
In this paper at first Ciric fixed point theorem is extended, then common fixed point for Banach operator pairs satisfying extended Ciric type contraction conditions are obtained without the assumption of linearity or affinity of either T or I. In particular we extend the main theorem due to Hussain. We also provide an application to an integral equation.
University of Bucharest, Romania
Title: Non singular automorphisms and dimension spaces (details)
We show that if T is (measure theoretically isomorphic to) an adic transformation defined on a Bratteli diagram endowed with a Markov measure then we can associate explicitly a matrix valued random walk and a dimension space. We explain how certain properties of nonsingular automorphisms can be translated in terms of dimension spaces and we give concrete examples. This talk is part of a joint work with Thierry Giordano and David Handelman.
University of Illinois, Chicago, USA
Title: On some criteria for quantum and stochastic confinement (details)
In this talk we will present several recent results concerning criteria ensuring the confinement of a quantum or a stochastic particle to a bounded domain in $mathbb R^n$. These criteria are given in terms of explicit growth and/or decay rates for the diffusion matrix and the drift potential close to the boundary of the domain. As an application of the general method, we will discuss several cases, including some where the background Riemannian manifold (induced by the diffusion matrix) is geodesically incomplete. These results are part of an ongoing joint project with G. Nenciu (IMAR, Bucharest, Romania).
Université de Lorraine and Pennsylvania State University, France
Title: Essential spectrum of N-body Hamiltonians with asymptotically homogeneous interactions (details)
We prove a HWZ-type theorem for the essential spectrum of N-body type Hamiltonians with two-body interactions that are asymptotically homogeneous of order zero at infinity. This generalizes the classical case of Coulomb potentials (for which the homogeneous part at infinity is zero). The techniques of proof use representations of certain associated C^*-algebras.
NOMURA Takaaki
Kyushu University, Japan
Title: Realizing homogeneous cones through oriented graphs (details)
In this talk, we realize any homogeneous convex cone by assembling uniquely determined subcones. These subcones are realized in the cones of positive-definite real symmetric matrices of minimal possible sizes. The subcones are found through the oriented graphs drawn by the data of the given homogeneous cones. Several interesting examples of our realizations of homogeneous convex cones will be also presented.
OLTEANU Cristian Octav
Politehnica University of Bucharest, Romania
Title: On Markov moment problem and its applications (details)
We give necessary and sufficient conditions for the existence of a solution of a multidimensional real classical Markov moment problem, in an unbounded subset which is a Cartesian product of closed intervals. One obtains a characterization in terms of quadratic forms. To this end, we apply polynomial approximation results on such a Cartesian product. Next, we consider applications of a sufficient condition to approximating geometrically the solutions of some nonlinear systems with infinite many equations and unknowns (inverse problems solved starting from the moments). Thus, one solves problems studied in the literature by some other methods. Our way of treating these problems works in several dimensions. In the end, one considers a problem not necessarily involving polynomials.
"Transilvania" University of Brașov, Romania
Title: On equivalence of K-functionals and weighted moduli of continuity (details)
We study the best constants which can appear in the inequalities between the weighted modulus of continuity and the corresponding $K$-functional, in special case where the weight functions are convex or concave. \begin{thebibliography}{99} \bibitem {CL} R. De Vore, G.G. Lorentz, Constructive approximation, Springer, Berlin, New York, 1993. \bibitem {DT} Z. Ditzian, V. Totik, Moduli of smousness, Springer, Berlin, New York, 1987. \bibitem {Go} Gonska, H. H., On approximation in spaces of continuous functions. Bull. Austral. Math. Soc. 28 (1983), no. 3, 411–432. \bibitem{JS} Johnen, H., Scherer, K., On the equivalence of the $K$ -functional and moduli of conti- nuity and some applications, Constructive Theory of Functions of Several Variables, Vol. 571 (1977) of Lecture Notes in Mathematics, Springer, Berlin, 119 - 140. \bibitem {Ko} N.P. Korneichuk, The best uniform approximation of certain classes of continuous functions, Dokl. {\bf 141}, (1961) 304-307, (AMS Transl. {\bf 2}, 1254-1259). \bibitem{MS} Mitjagin, B. S. and Semenov, E. M., Lack of interpolation of linear operators in spaces of smooth functions, (Russian), Math. USSR-Izv. {\bf 41} (1977), no. 6, 1289-1328. \bibitem {PR04} R. P\u alt\u anea, Approximation theory using positive linear operators, Birkhauser, Boston, 2004. \end{thebibliography}
IMAR, Romania
Title: Almost commuting permutations are near commuting permutations (details)
We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations.
PILLET Claude - Alain
Université de Toulon, France
Title: Conductance and AC Spectrum (details)
We characterize the absolutely continuous spectrum of the one-dimensional Schr\"odinger operators $h=-\Delta+v$ acting on $\ell^2(\mathbb{Z}_+)$ in terms of the limiting behaviour of the Landauer-B\"uttiker and Thouless conductances of the associated finite samples. The finite sample is defined by restricting $h$ to a finite interval $[1,L]\cap\mathbb{Z}_+$ and the conductance refers to the charge current across the sample in the open quantum system obtained by attaching independent electronic reservoirs to the sample ends. Our main result is that the conductances associated to an energy interval $I$ are non-vanishing in the limit $L\to\infty$ iff ${\rm sp}_{\rm ac}(h)\cap I\neq\emptyset$.
POPA Ioan - Lucian
"1 Decembrie 1918" University of Alba Iulia, Romania
Title: Nonuniform Exponential Trichotomies in Terms of Lyapunov Functions (details)
The aim of this paper is to give characterizations in terms of Lyapunov functions for nonuniform exponential trichotomies of nonautonomous and noninvertible discrete-time systems.
POPA Nicolae
Simion Stoilow Institute of mathematics Romanian Academy, Romania
Title: Abel-Schur multipliers on Banach spaces of infinite matrices (details)
We consider a class of multipliers extending the Schur multipliers class of matrices. We get some similar results with those of [1] and [9]. In particular we obtain a new proof of the necessity of a well-known theorem of Hardy-Littlewood. (See [14], [13], [10].) References [1] J.M. Anderson, J. Clunie and Ch. Pommerenke, On Bloch function and normal func- tions, J. Reine Angew. Math. 270(1974), 12–37. [2] J.M. Anderson and A. Shields, Coefficient multipliers of Bloch functions, Trans. Amer. Math. Soc. 224(1976), 255–265. [3] S. Barza, L. E. Persson and N. Popa, A Matriceal Analogue of Fejer’s theory, Math. Nach. 260(2003), 14–20. [4] G. Bennett, Schur multipliers, Duke Math. J., 44(1977), 603-639. [5] I. C. Gohberg, M. G. Krein, Introduction to the theory of linear nonselfadjoint op- erators, Translations of mathematical Monographs, Vol. 18 American mathematical Society, providence, R. I. 1969. [6] G.H. Hardy, J. E. Littlewood, Theorems concerning mean values of analytic and harmonic functions , Quart. J. of Math. Oxford Ser. 12(1941), 221-256. [7] D. Krtinic, A matricial analogue of Fejers theory for different types of convergence, Math. Nachr., 280(2007), no. 13-14, 1537 1542. [8] M. Jevti ́ and M. Pavlovi ́, On multipliers from H p to q , 0 < q < p < 1, Arch. Math., 56(1991), 174–180. [9] A. Matheson, A multiplier theorem for analytic functions of slow mean groth, Proc.Amer. Math.Soc., 77(1979), 53-57. [10] M. Mateljevic, M. Pavlovic, Multipliers of H p and BM OA. Pacific J. Math. 146(1990), 71-84. [11] L.E. Persson and N. Popa, Matrix Spaces and Schur Multipliers: Matriceal Harmonic Analysis, World Scientific, 2014. [12] N. Popa, Matriceal Bloch and Bergman-Schatten spaces, Rev. Roumaine Math. Pures Appl., 52(2007), 459–478. [13] W. T. Sledd, On Multipliers of H p Spaces, Indiana Univ. Math. J., 27(1978), 797-803. [14] E. M. Stein and A. Zygmund, Boundedness of translation invariant operators on Hoelder spaces and LP-spaces, Ann. Math., 85(1967), 337-349. [15] K. Zhu, Operator theory in Banach function spaces, Marcel Dekker, New York, 1990.
POPESCU Marian - Valentin
Technical University of Civil Engineering Bucharest,, Romania
Title: Collectively coincidence results in some classes of topological spaces (details)
\begin{document} In this paper we investigate some collectively fixed-point and coincidence results for multimaps defined on some topological spaces. \textit{Firstly} we refer to results obtained with convexity assumptions in the \textit{Fr% \'{e}chet space} setting (which obvoiusly includes the \textit{Banach space} setting). \textit{Secondly} we refer to results obtained without convexity assumptions, in the \textit{acyclic finite dimensional ANR} setting. \textit{% Thirdly} we consider some results also obtained without convexity assumptions, in the \textit{finite dimensional Riemannian manifolds} and, in particular, in the\textit{\ finite dimensional Hadamard manifolds}. \begin{thebibliography}{9} \bibitem{1} Aliprantis, C. D. and Border, K. C., \textit{Infinite dimensional analysis, a Hitchhiker's Guide}, Third ed. Springer Verlag, Berlin, Heidelberg, New York 2006. \bibitem{2} Andres, J. and G\'{o}rniewicz, L., \textit{Topological Fixed Point Principles for Boundary Value Problems}, Kluwer Academic Publishers, Dordrecht 2003. \bibitem{3} do Carmo, M. P., \textit{Riemannian Geometry }(translated by F. Flaherty)\textit{, }in\textit{\ Mathematics; Theory and Applications }(Eds. R.V. Kadison, I.M. Singer)\textit{\ }Birkh\"{a}user, Boston, Basel, Berlin 1992. \bibitem{4} D\u{a}ne\c{t}, R.-M., Popescu, M.-V. and Popescu, N., \textit{% Coincidence results with compactness assumptions for families of correspondences containing upper semi-continuous multimaps, and their applications}, Romanian Journal of Mathematics and Computer Science, Vol \textbf{3}, Issue 2, 164-184 (2013). \bibitem{5} D\u{a}ne\c{t}, R.-M.; Popescu, M.-V., Popescu, N., \textit{From Fr\'{e}chet Spaces to Riemannian Manifolds via Equilibrium Results with and without Convexity Assumptions}, Proceedings of the International Conference Riemannian Geometry and Applications in Engineering and Economics -- RIGA \textbf{2014}, Bucharest, May 19-21 (Eds. A. Mihai, I. Mihai), Bucharest University Press, 65-86 (2014). \bibitem{6} Hu, S.-T., \textit{Theory of Retracts}, Wayne State Univ. Press. Detroit 1965. \end{thebibliography} \end{document}
"Vasile Alecsandri" University of Bacau, ROMANIA
Title: ISAC'S CONES (details)
documentclass{amsart} %%% remove comment delimiter ('%') and specify encoding parameter if required, %%% see TeX documentation for additional info (cp1252-Western,cp1251-Cyrillic) %usepackage[cp1252]{inputenc} %%% remove comment delimiter ('%') and select language if required %usepackage[english,spanish]{babel} usepackage{amssymb} usepackage{amsmath} usepackage[dvips]{graphicx} %%% remove comment delimiter ('%') and specify parameters if required %usepackage[dvips]{graphics} begin{document} title{ISAC'S CONES } author{Vasile Postolicu a {Romanian Academy of Scientists,} {``Vasile Alecsandri'' University of Bacu au,} {Faculty of Sciences,} {Department of Mathematics, Informatics and Educational Sciences,} {Bacu au, România,} {e-mail~: }} date{ } maketitle textbf{ Abstract. }This is a very short research work representing an homage to the regretted Professor George Isac, Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. 17000, Kingston, Ontario, Canada, K7K 7B4. Professor Isac introduced the notion of ``nuclear cone'' in 1981, published in 1983 and called later as ``supernormal cone'' since it appears stronger than the usual concept of ``normal cone''. For the first time, we named these convex cones as ``Isac's Cones'' in 2009 , after the acceptancetextbf{ }on professor Isac's part. This study is devoted to Isac's cones, including significant examples, comments and several pertinent references, with the remark that this notion has its real place in Hausdorff locally convex spaces not in the normed linear spaces, having strong implications and applications in the efficiency and optimization. Isac's cones represent the largest class of convex cones in separated locally convex spaces ensuring the existence and important properties for the efficient points under completeness instead of compactness. textbf{ Mathematics Subject Classification (2000):} Primary 46A03. Secondary 46A40. textbf{ Keywords textit{: }}textit{Isac's (nuclear or supernormal) cone, topology, locally convex space. } vspace{0.5cm} textbf{ Selected References} 1. Isac, G. - textit{Points critiques des systémes dinamiques. Cônes nucléaires et optimum de} textit{Pareto},textit{ }Research Report, Royal Military College of St. Jean, Québec, Canada, 1981. 2. Isac, G. - textit{Sur l'existence de l'optimum de Pareto, }Riv. Mat. Univ. Parma, 4(9),1983, p. 303 - 325. 3. Postolicu a V. - textit{Approximate Efficiency in Infinite Dimensional Ordered Vector Spaces}. International Journal of Applied Management Science (IJAMS), Vol. 1, No. 3, 2009, p. 300 -- 314. 4. Postolicu a V. - textit{Isac's Cones in General Vector Spaces.} Published as Chapter 121, Category: Statistics, Probability, and Predictive Analytics, vol.3, p.1323-1342, in Encyclopedia of Business Analytics and Optimization -- 5 Vols., 2014. end{document}
RADU Remus
Stony Brook University, U.S.A.
Title: Semi-indifferent dynamics (details)
We consider complex H\'enon maps that have a semi-indifferent fixed point with eigenvalues $\lambda$ and $\mu$, where $|\lambda|=1$ and $|\mu|<1$. At a semi-parabolic parameter (i.e. when $\lambda$ is a root of unity) we have a good understanding of this family: for small Jacobian, the dynamics of the Julia set of the H\'enon map fibers over the dynamics of a certain polynomial Julia set. This is joint work with R. Tanase. The situation when $\lambda=\exp(2\pi i \alpha)$ and $\alpha$ is irrational is more complex as it depends on the arithmetic properties of $\alpha$. When $\alpha$ is the golden mean, we show that the H\'enon map with small Jacobian has a Siegel disk whose boundary is homeomorphic to a circle; the proof is based on renormalization of commuting pairs. This is joint work with D. Gaydashev and M. Yampolsky. We will explain where these maps sit in the whole parameter space of complex H\'enon maps and explore other directions.
Aalborg University, Denmark
Title: Analytic Perturbation Theory of Embedded Eigenvalues (details)
We are interested in the behaviour of embedded eigenvalues of (analytic) families of self-adjoint operators $\{H(\xi)\}_\xi$ as a function of the parameter $\xi$. Kato's analytic perturbation theory does not apply directly on embedded eigenvalues. The investigation of the essential spectrum of a Schrödinger operator via spectral deformation techniques such as dilation analyticity is well-developed. In this talk, we present some new abstract results in which analytic perturbation theory for embedded eigenvalues is made available by the aid of a Mourre estimate and local spectral deformation. In particular, we show that given certain conditions on $\{H(\xi)\}_\xi$, embedded eigenvalue clusters are branches of analytic functions. The conditions are verifiable in non-trivial cases; as an example an abstract two-body system is considered.
SAH Ashok Kumar
University of Delhi, India
Abstract. In this paper we study frame-like properties of a wave packet system by using hyponormal operators on L2 (R). We present necessary and sufficient conditions in terms of relative hyponormality of operators for a system to be a wave packet frame in L2 (R). We illustrate our results with several examples and counter-examples.
SAVOIE Baptiste
DIAS-STP Dublin, Ireland
Title: A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit. (details)
The original formulation of \textit{the Bohr-van Leeuwen (BvL) theorem} states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude-Lorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from $-\infty$ to $\infty$ what makes the free energy density magnetic-field-independent. When considering the classical Maxwell-Boltzmann electron gas, it is often admitted that the BvL theorem holds on condition that the potentials modeling the interactions are particle-velocities-independent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the many-body interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this article is to give within the linear-response theory a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas subjected to a class of translational invariant external potentials.
Yildiz Technical University, Turkey
Title: About The Regularized Trace Of A Self Adjoint Differential Operator (details)
In this paper , We find a regularized trace formula of the Sturm Liouville operator with a bounded operator coefficient.
Sardar Vallabhbhai National Institute,Surat Gujarat, India
Title: On approximation properties of generalization of Kantorovich-type discrete q-Beta operators (details)
The present paper deals with the Stancu type generalization of the Kantorovich discrete $q$-Beta operators. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation.
SPARBER Christof
University of Illinois at Chicago, USA
Title: Weakly nonlinear time-adiabatic theory (details)
We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations. That is, to non- linear Schrödinger equations in which, either, the nonlinear coupling constant or, equivalently, the solution is asymptotically small. To this end, a notion of criticality is introduced at which the linear bound states stay adiabatically stable, but nonlinear effects start to show up at leading order in the form of a slowly varying nonlinear phase modulation. In addition, we prove that in the same regime a class of nonlinear bound states also stays adiabatically stable, at least in terms of spectral projections.
STAMATE Elena - Cristina
"Octav Mayer" Institute of Mathematics, Iasi, Romania
Title: Vector integrals for multifunctions (details)
In this paper we present a new Pettis-Sugeno type integral of vector mutifunctions relative to a vector multisubmeasure and present several classic properties. Some comparative results with other generalization for the integrals of Pettis-Lebesgue, Aumann-Sugeno and Choquet-Pettis type are also established.
Title: Commutation and Splitting Theorems for von Neumann Algebras (details)
The Splitting Theorem for factors of Ge & Kadison (Inventiones Math., 1996) is extended for von Neumann Algebras and the Tomita Commutation Theorem is extended for tensor products over commutative subalgebras. Both these results appear as direct consequences of a general commutation theorem for tensor products over (arbitrary) subalgebras.
"Transilvania" University of Brasov, Romania
Title: On some second order moduli of continuity (details)
\documentclass[11pt,twoside]{article} \usepackage[utf8]{inputenc} \headheight 35pt \addtolength{\oddsidemargin}{-0.3cm} \addtolength{\evensidemargin}{-2.0cm} \setlength{\topmargin}{0cm} \setlength{\textheight}{21cm} \setlength{\textwidth}{15cm} \begin{document} \thispagestyle{empty} % TITLE \centerline{\large{\bf On some second order moduli of continuity }}% <--TITLE \medskip % Author \centerline{\bf Maria TALPĂU DIMITRIU} \centerline{Faculty of Mathematics and Informatics, \textit{Transilvania} University of Braşov, Romania} \centerline{e-mail:} \bigskip \begin{abstract} In this paper we study the equivalence of two second order moduli of continuity defined for the Lipschitz continuous functions and a suitable generalized K-functional. \\ 2010 \textit{Mathematics Subject Classification:} 26A15, 41A36, 41A44. \textit{Key words:} Moduli of smoothness, K-functional, Lipschitz function. \end{abstract} %--------------------------------------------------------------------------- \textbf{Acknowledgement} \emph{This paper is supported by the Sectoral Operational Programme Human Resources Development (SOP HRD), financed from the European Social Fund and by the Romanian Government under the project number POSDRU/159/1.5/S/134378.} \begin{thebibliography}{99} \bibitem{Ce71} Censor, E., \emph{Quantitative results for positive linear approximation operators}, J. Approx. Theory \textbf{4}(1971), 442-450 \bibitem{De69} DeVore, R. A., \emph{Optimal convergence of positive linear operators}, Proceedings of the Conference on the Constructive Theory of Functions, Budapest, 1969 \bibitem{Go84} Gonska, H. H., \emph{On approximation of continuously differentiable functions by positive linear operators}, Bull. Austral. Math. Soc. \textbf{27}(1983), 73-81 \bibitem{GoMe} Gonska, H. H., Meier, J., \emph{On approximation by Bernstein-type operators: best constants}, Studia Sci. Math. Hungar. \textbf{22}(1987), no. 1-4, 287–297 \bibitem{JoSc} Johnen, H., Scherer, K., \emph{On the equivalence of the $K$ -functional and moduli of continuity and some applications}, Constructive Theory of Functions of Several Variables, Vol. {\bf 571} (1977) of Lecture Notes in Mathematics, Springer, Berlin, 119 - 140. \bibitem{Pa97} Păltănea, R., \emph{New second order moduli of continuity}, In: Approximation and optimization (Proc. Int. Conf. Approximation and Optimization, Cluj-Napoca 1996; ed. by D.D. Stancu et al.), vol I, Transilvania Press, Cluj-Napoca, (1997), pp. 327-334. \bibitem{Pa04} Păltănea, R., \emph{Approximation theory using positive linear operators}, Birkh\"{a}user, 2004 \bibitem{MTD1} Talpău Dimitriu, M., \emph{Estimates with optimal constants using Peetre’s $K$-functionals}, Carpathian J. Math. \textbf{26} (2010), No. 2, 158 - 169 \end{thebibliography} \end{document}
Stony Brook University, U.S.A.
Title: Stability and continuity of Julia sets in $\mathbb{C}^2$ (details)
We discuss some continuity results for the Julia sets $J$ and $J^{+}$ of the complex H\'enon map, which is a polynomial automorphism of $\mathbb{C}^2$. We look at the parameter space of strongly dissipative H\'enon maps which have a fixed point with one eigenvalue $(1+t)\lambda$, where $\lambda$ is a root of unity and $t$ is real and sufficiently small. These maps have a semi-parabolic fixed point when $t$ is $0$, and we use techniques that we have developed for the semi-parabolic case to describe nearby perturbations. We prove a two-dimensional analogue of radial convergence for polynomial Julia sets and show that the H\'enon map is stable on $J$ and $J^{+}$ when $t$ is nonnegative. This is joint work with Remus Radu.
University of Tuebingen, Germany
Title: Peierls substitution for subbands of the Hofstadter model (details)
I start with a brief review of recent results on Peierls substitution for magnetic Bloch bands obtained jointly with Silvia Freund. Then I will show how these results can be applied to subbands of the Hofstadter model.
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucuresti, Romania
Title: On the maximal function model of a contraction operator (details)
The maximal function of a contraction operator $T\in\cal{L(H)}$ arises in the factorization process of an operator valued semispectral measure, i.e. it is the $L^2$-bounded analytic function attached to $T$ and has the form $M_T(\lambda)=D_{T^*}(I-\lambda T^*)^{-1}$, where $\lambda\in\mathbb D$ and $D_T$ is the defect operator of $T$. In the the particular $C_{.0}$ case, the Sz.-Nagy--Foias functional model reduces to the functional representation given by the maximal function $M_T(\lambda)$, i.e. $\textbf{H}=M_T{\cal H} \subset H^2({\cal D}_{T^*})$, where $(M_Th)(\lambda)=M_T(\lambda)h$. In this case $M_T$ becomes an isometry, and the functional model for $T^*$ is given by the restriction of the backward shift to \textbf{H}, and can be expressed with the maximal function of $T$ as $\textbf{T}^*=\frac{1}{\lambda}[M_T(\lambda)h-M_T(0)h]$. Analogously, the maximal function of $T^*$ has the form $M_{T^*}(\lambda)=D_T(I-\lambda T)^{-1}$, and for the discrete linear system generated by the rotation operator $R_T=\begin{bmatrix} T &D_{T^*}\\ D_T &-T^*\end{bmatrix}$ the operators $M_T$ and $M_{T^*}$ become the controllability and the observability operators, respectively. Some other properties of the maximal function are analyzed, and partial results on a functional model of the maximal function are given.
VASILESCU Florian - Horia
University of Lille 1, France
Title: Square Positive Functionals in an Abstract Setting (details)
In the framework of spaces of functions on measurable spaces, and using techniques from the theory of finite-dimensional commutative Banach algebras, as well as Hilbert space methods, we discuss integral representations of square positive functionals, extending and completing some older results concerning the positive Riesz functionals in finite-dimensional spaces of polynomials.
ZSIDO Laszlo
University of Rome "Tor Vergata", Italia
Title: Hilbert Space Geometry problems occurring in the Tomita-Takesaki Theory (details)
Each normal weight on a von Neumann algebra is (by a result of U. Haagerup) the pointwise least upper bound of the majorized bounded linear functionals. This is a basic ingredient in the treatment of the fundamental facts of the Tomita-Takesaki Theory, but is not enough to reduce the case of general faithful, semi-finite, normal weights to the case of (everywhere defined) faithful normal linear functionals. In the talk we propose a "spatial" approximation of an arbitrary faithful, semi-finite, normal weight $\varphi$ on a von Neumann algebra $M$ with bounded normal functionals. Essentially we approximate $\varphi$ with its (bounded) restrictions $\varphi_e$ to the reduced von Neumann algebras $eMe\,$, where $e\in M$ are projections with $\varphi (e)<+\infty\,$. Difficulties arise because in general we don't have $\varphi (eae)\leq\varphi (a)$ for every $a\in M^+$, and because the family of all projections of finite weight is not upward directed. We are approximating appropriately the identity operator on the Hilbert space $H_\varphi$ of the GNS representation of $\varphi$ with the orthogonal projections onto the Hilbert spaces of the GNS representations of the functionals $\varphi_e$ (considered subspaces of $H_\varphi$) and succeed to reduce the fundamentals of the Tomita-Takesaki Theory for general faithful, semi-finite, normal weights to the case of bounded functionals.