Locally Completely Regular Epigroups

The object of the article is to characterize epigroups which are locally completely regular. Some subclasses of such epigroups are also described.     

Characterizations of proximinal,semichebychevian and chebychevian subspaces in real normed spaces

A simple model optimal control problem for continuous casting with state-space constraints is approximated, as usual, by a penalty method and by a numerical discretization of the nonlinear heat equation. The convergence of the approximate problems directly to the original problem is proven under a stability criterion linking the penalty parameter with the discretization parameters. For this purpose, known discretization error estimates for the Stefan problem are extended for the case of time varying boundary conditions.     

局部传输信息不等式和曲率维数条件的等价性

本文得到了曲率维数条件CD(ρ,∞) 和CD(0, n)与相应的局部传输信息不等式的等价性.     

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order $H^m(\mathbb {H}^n), m\in \mathbb {N}^n,$ under the heat kernel transform on $\mathbb {H}^n,$ using direct sum and direct integral of Bergmann spaces and certain unitary representations of $\mathbb {H}^n$ which can be realized on the Hilbert space of Hilbert‐Schmidt operators on $L^2(\mathbb {R}^n).$ We also show that the image of Sobolev space of negative order $H^{-s}(\mathbb {H}^n), s(>0) \in \mathbb {R}$ is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on $\mathbb {H}^n$ under the heat kernel transform.     

Rumor spreading on random regular graphs and expanders

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well‐studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. In this paper we consider random networks where each vertex has degree d ≥ 3, i.e., the underlying graph is drawn uniformly at random from the set of all d ‐regular graphs with n vertices. We show that with probability 1 ‐ o(1) the push model broadcasts the message to all nodes within (1 + o(1))C_d lnn rounds, where Particularly, we can characterize precisely the effect of the node degree to the typical broadcast time of the push model. Moreover, we consider pseudo‐random regular networks, where we assume that the degree of each node is very large. There we show that the broadcast time is (1 + o(1))Clnn with probability 1 ‐ o(1), where \begin{align*}C = \lim_{d\to\infty}C_d = \frac{1}{\ln2} + 1\end{align*}. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

On locally spherical polytopes of type {5, 3, 5}

There are only finitely many locally projective regular polytopes of type {5, 3, 5}. They are covered by a locally spherical polytope whose automorphism group is J₁×J₁×L₂(19), where J₁ is the first Janko group, of order 175560, and L₂(19) is the projective special linear group of order 3420. This polytope is minimal, in the sense that any other polytope that covers all locally projective polytopes of type {5, 3, 5} must in turn cover this one.     

On a class of binary linear completely transitive codes with arbitrary covering radius

An infinite class of new binary linear completely transitive (and so, completely regular) codes is given. The covering radius of these codes is growing with the length of the code. In particular, for any integer ρ≥2, there exist two codes in the constructed class with d=3, covering radius ρ and lengths and , respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described.     

Continuity and generators of dynamical semigroups for infinite Bose systems

For a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations (CCR) we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von Neumann algebra associated with a representation of the CCR. Then the explicit form of the generators of the extended semigroups is calculated.     

Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations

This paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations. Upon making some suitable assumptions, the existence and uniqueness of a weighted pseudo almost periodic solution is obtained. To illustrate our main result, we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional-differential equations with feedback control.