We consider two spaces of harmonic functions. First, the space H(U) of functions harmonic on a bounded open subset U of R and continuous to the boundary. Second, the space H0(K) of functions on a compact subset K of R n which can be harmonically extended on some open neighbourhood of K. A bounded open subset U of R is called stable if the space H(U) is equal to the uniform closure of H0(U ). We...

This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very “varied” class of problems, comprising sub-classes of problems ranging from trivial to undecidable. Solution methods for QP are very diverse, ranging from entirely co...

Cauchy problem of Cahn-Hilliard equation with inertial term in three-dimensional space is considered. Using delicate analysis its Green function and convolution nonlinear term, pointwise decay rate obtained.

A nonrigid rotor model is developed from the two-parameter quantum algebra U qp (u 2). [This model presents the U qp (u 2) symmetry and shall be referred to as the qp-rotor model.] A ro-tational energy formula as well as a qp-deformation of E2 reduced transition probabilities are derived. The qp-rotor model is applied (through fitting procedures) to twenty rotational bands of superdeformed nucl...

Throughout this paper we use the following notations. By Zp we denote the ring of p-adic rational integers, Q denotes the field of rational numbers, Qp denotes the field of p-adic rational numbers, C denotes the complex number field, and Cp denotes the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p−νp(p) = p−1. When one talks of q-exten...

Let p be a prime number with p ≡ 1(mod 2). Throughout this paper, Zp,Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. The p-adic norm | · |p is normalized as |p|p = 1 p . Let q be an indeterminate in Cp such that |1− q|p < p −1 p−1 . The q-extension of number x be defined as [x]q = 1−qx 1−q . Note that limq→1[...

We constructively prove the existence of almost complete problems under logspace manyone reduction for some small complexity classes by exhibiting a parametrizable construction which yields, when appropriately setting the parameters, an almost complete problem for PSPACE, the class of space efficiently decidable problems, and for SUBEXP, the class of problems decidable in subexponential time. O...

Building on foundations introduced in a previous paper, we give several p-adic analytic descriptions of the categories of étale Zp-local systems and étale Qp-local systems on an affinoid algebra over a finite extension of Qp (or more generally, over the fraction field of the Witt vectors of a perfect field of characteristic p). These include generalizations of Fontaine’s theory of (φ, Γ)-module...

in this paper, a pointwise pseudo-metric function on the l-realline is constructed. it is proved that the topology induced by this pointwisepseudo-metric is the usual topology.