On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain

We obtain the L_p–L_q maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ?ⁿ (n?2). The Robin condition consists of two conditions: v ? u=0 and αu+β(T(u, p)v – 〈T(u, p)v, v〉v)=h on the boundary of the domain with α, β?0 and α+β=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and non‐slip one when α=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd.     

四次函数实零点的完全判据和正定条件

本文给出了四次函数实零点的完全判据和正定条件,这一结果在研究多项式系统的奇点分析和分支问题时给出了可以实用的判据．     

关于矩阵条件数的一些结论

本文讨论了一些矩阵范数达到极小的充要条件,其主要结果如下:1.设?为m×n实矩阵,且具有n个线性无关的列,则求?广义逆谱条件数等于1的充要条件为?=cI,其中c为正常数.2.设?为n阶非异实矩阵,则矩阵A的求逆p-范数条件数等于1的充要条件为A=cpσ,其中c为正常数,σ是置换阵,其对角元都等于 1或-1.3.设?为n阶非异实矩阵,则矩阵4的求逆F-范数条件数等于1的充要条件为?=cU,其中c为正常数,U为正交阵.     

一类仓库货物储存模型经典解的存在唯一性

文章用特征线法给出一类仓库货物储存模型解的递推表达式,并证明其光滑性从而得到了经典解的存在唯一性。     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

Magnetic hysteresis of the magnetoresistance and the critical current density in polycrystalline YBa2Cu3O7−δ–Ag superconductors

A systematic study of the magnetic hysteresis in transport properties of polycrystalline YBa₂Cu₃O_7−δ–Ag compounds has been made based on two kinds of measurements at 77 K and under applied magnetic fields up to 30 mT: critical current density J_c(B_a) and magnetoresistance R(B_a). The R(B_a) curves show a minimum in their decreasing branch occurring at B=B_min which was found to be both the excitation current I_ex and the maximum applied magnetic field B_am dependent. In addition, for a certain value of B_am>5 mT, we have observed that B_min increases with increasing I_ex and reaches a saturation value. The J_c(B_a) curves show a maximum in decreasing applied magnetic fields occurring at B=B_max. We have also found that B_max increases with increasing B_am and reaches a saturation value. The minimum in the R(B_a) and the maximum in J_c(B_a) curves were found to be related to the trapped flux within the grains. All the experimental results are discussed within the context of the flux dynamics and transport mechanisms in these high-T_c materials.     

Optimally Stable Multivariate Bases

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogs of component-wise condition numbers for linear systems introduced by Skeel.     

Unusual current‐voltage characteristics of single crystalline and bicrystalline La0.7Ca0.3MnO3 films

The current‐voltage characteristics of single crystalline and bicrystalline La_0.7Ca_0.3MnO₃ films were measured and analyzed. Several epitaxial films, as well as 45° [001]‐tilt grain boundaries, display current‐voltage characteristics which are asymmetric with respect to polarity reversal of the bias current. One epitaxial film has a polarity dependent resistance of ～340kΩ and of ～670kΩ in forward and in reverse direction, respectively.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.