Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2,1)

This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by Hölder continuous functions with Hölder index greater than 1/2. The results can be applied to the case of equations whose noisy inputs are given by a fractional Brownian motion $B^H$ with covariance operator Q, provided that $H\in (1/2,1)$ and $\mathrm{tr}(Q)$ is sufficiently small.     

Superconvergence analysis of the Galerkin FEM for a singularly perturbed convection–diffusion problem with characteristic layers

We analyze the superconvergence property of the Galerkin finite element method (FEM) for elliptic convection–diffusion problems with characteristic layers. This method on Shishkin meshes is known to be almost first‐order accurate (up to a logarithmic factor) in the energy norm induced by the bilinear form of the weak formulation, uniformly in the perturbation parameter. In the present paper the method is shown to be almost second‐order superconvergent in this energy norm for the difference between the FEM solution and the bilinear interpolant of the exact solution. This supercloseness property is used to improve the accuracy to almost second order by means of a postprocessing procedure. Numerical experiments confirm these results. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A family of regular vertex operator algebras with two generators

For every m ∈ ℂ ∖ {0, −2} and every nonnegative integer k we define the vertex operator (super)algebra D _m,k having two generators and rank . If m is a positive integer then D _m,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that D _m,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.      

Spin transition in heptanuclear star-shaped iron(III)–antimony(V) NCS- and CN-bridged compounds

The precursor [Fe^III(L)Cl] (LH₂ = N,N′-bis(2′-hydroxy-benzyliden)-1,6-diamino-3-azahexane) has been prepared and Mössbauer spectroscopy assigned a high-spin (S = 5/2) state at room temperature. The precursor is combined with the bridging units [Sb^V(X)₆]^? (X = CN^?, NCS^?) to yield star-shaped heptanuclear clusters [(LFe^III–X)₆Sb^V]Cl₅. The star-shaped compounds are in general high-spin systems at room temperature. On cooling to 20 K some of the iron(III) centers switch to the low-spin state as indicated by Mössbauer spectroscopy, i.e. multiple electronic transitions. While the cyano-bridged complex performs a multiple spin transition the thiocyanate-compound shows no significant population at both temperatures.     

An integer programming model for hierarchical workforce scheduling problem

In this paper, an integer programming model for the hierarchical workforce problem under the compressed workweeks is developed. The model is based on the integer programming formulation developed by Billionnet [A. Billionnet, Integer programming to schedule a hierarchical workforce with variable demands, European Journal of Operational Research 114 (1999) 105–114] for the hierarchical workforce problem. In our model, workers can be assigned to alternative shifts in a day during the course of a week, whereas all workers are assigned to one shift type in Billionnet’s model. The main idea of this paper is to use compressed workweeks in order to save worker costs. This case is also suitable for the practice. The proposed model is illustrated on the Billionnet’s example problem and the obtained results are compared with the Billionnet’s model results.     

Variational Problems in Domains with Cusp-Points and the Finite Element Method

A variational problem in a two-dimensional domain with cusp-points corresponding to a linear elliptic boundary value problem is formulated and the unique existence of its solution is proved. The corresponding finite element method using triangular finite C ⁰-elements with polynomials of the first degree is analyzed and both the convergence (under the assumptions sufficient for the existence of the exact solution) and the maximal rate of convergence 𝒪(h) are proved.     

On a Sturm–Liouville type problem with retarded argument

In this work, a Sturm–Liouville‐type problem with retarded argument, which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. Copyright © 2012 John Wiley & Sons, Ltd.     

On adjacent-vertex-distinguishing total coloring of graphs

In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number of some graphs such as cycle, complete graph, complete bipartite graph, fan, wheel and tree.     

Strong Feller Property of Sticky Reflected Distorted Brownian Motion

Using Girsanov transformations we construct from sticky reflected Brownian motion on \([0,\infty )\) a conservative diffusion on \(E:=[0,\infty )^n\), \(n \in \mathbb {N}\), and prove that its transition semigroup possesses the strong Feller property for a specified general class of drift functions. By identifying the Dirichlet form of the constructed process we characterize it as sticky reflected distorted Brownian motion. In particular, the relations of the underlying analytic Dirichlet form methods to the probabilistic methods of random time changes and Girsanov transformations are presented. Our studies of the mathematical model are motivated by its applications to the dynamical wetting model with \(\delta \)-pinning and repulsion.