Classification problems for shifts on modules over a principal ideal domain

In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.

     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Finite element approximation of spectral problems with Neumann boundary conditions on curved domains

This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain . Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain in the framework of the abstract spectral approximation theory.

     

Markov-type Inequalities for Surface Gradients of Multivariate Polynomials

Let K ^d be a compact set with a smooth boundary and consider a polynomial p of total degree n such that p_C(K)1. Then we show that D_Tp(x)=o(n²) for any x Bd K and T a tangential direction at x. Moreover, the o(n²) term is given in terms of the modulus of smoothness of Bd K.     

Another generalization of weighted Ostrowski type inequality for mappings of bounded variation

A new generalization of weighted Ostrowski type inequality for mappings of bounded variation with a unified sharp bound is established.     

窄域上2D弱阻尼KdV方程的blow-up的研究

得到了2D的弱阻尼KdV方程在窄域上blow-up时间估计.     

Numerical methods for portfolio selection with bounded constraints

This work develops an approximation procedure for portfolio selection with bounded constraints. Based on the Markov chain approximation techniques, numerical procedures are constructed for the utility optimization task. Under simple conditions, the convergence of the approximation sequences to the wealth process and the optimal utility function is established. Numerical examples are provided to illustrate the performance of the algorithms.     

Mechanical properties of amphiphilic urethane acrylate ionomer hydrogels having heterophasic gel structure

Amphiphilic urethane acryale hydrogels containing ionic groups (dimethylolpropionic acid) were prepared by varying the molecular weight of the soft segment (polyether type) and the type of diisocyanate, and their mechanical properties were examined. They showed heterophasic gel structure composed of ionic hard domains induced by aggregation of the ionic groups and polyether soft domains comprising the urethane acrylate network. This heterophasic structure could be confirmed by dynamic mechanical analysis (DMA) and by wide-angle X-ray scattering analysis (WAXS); the crystallinity detected by WAXS and the transition peak of the ionic hard domains detected by DMA strongly suggested that there were ionic aggregates. These ionic aggregates acted as reinforcing fillers in the network, which eventually enhanced the tensile strength of the hydrogels. Above all, the tensile properties of the hydrogels were of interest in that the trends of the stress-strain curves were consistent with the rubbery ones. It is believed that the higher purity of the polyether soft domains resulted from the heterophasic gel structure imparting further elastomeric properties on the network. Received: 31 July 1998 Accepted in revised form: 15 October 1998     

Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains

We study the contractibility of the efficient solution set of strictly quasiconcave vector maximization problems on (possibly) noncompact feasible domains. It is proved that the efficient solution set is contractible if at least one of the objective functions is strongly quasiconcave and any intersection of level sets of the objective functions is a compact (possibly empty) set. This theorem generalizes the main result of Benoist (Ref.1), which was established for problems on compact feasible domains.The authors thank Dr. T. D. Phuong, Dr. T. X. D. Ha, and the referees for helpful comments and suggestions.