Plastic Torsion and Related Problems

A simple algorithm to calculate the maximum torsional load for a cylindrical shaft is presented. The algorithm is based on the notion of viscosity solutions to the eikonal equation, and is not restricted to simply-connected cross-sections. Applications to other, related problems, such as ferromagnetic thin films, and elastic buckling of thin film blisters are also discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Lyapunov-Like Solutions to Stability Problems for Discrete-Time Systems on Asymptotically Contractive Sets

This paper presents new criteria for stability properties of discrete-time non-stationary systems. The criteria are based on the concept of asymptotically contractive sets. As a result, general necessary conditions are established for asymptotic stability of the zero equilibrium state, the instantaneous asymptotic stability domain of which can be either time-invariant or time-varying and then possibly asymptotically contractive. It is shown that the classical Lyapunov stability conditions including the invariance principle by LaSalle cannot be applied to the stability test as soon as the system instantaneous domain of asymptotic stability is asymptotically contractive. In order to investigate asymptotic stability of the zero state in such a case novel criteria are established. Under the criteria the total first time difference of a system Lyapunov function may be non-positive only and still can guarantee asymptotic stability of the zero state. The results are illustrated by examples.     

在乘积域上的一类奇异积分算子的Lp有界性

本文讨论了乘积域Rn×Rm上一类带粗糙核的奇异积分算子的Lp(Rn×Rm)有界性。这里,Ω为原子Hardy空间H1a(Sn-1×Sm-1)中的函数,h为L∞(Lq)(R+×R+)中的径向函数,Φ(t)满足一定的增长条件。     

有界凸区域上的Dirichlet问题的正则性

本文主要讨论在有界凸区域上具Lipschitz连续系数的散度型椭圆算子的解的二阶导数的可积性问题．并且得到了相应的结论．     

Interaction of Polyunsaturated Fatty Acids with Cholesterol: A Role in Lipid Raft Phase Separation

Unequal affinity between lipids has been hypothesized to be a mechanism for the formation of microdomains/rafts in membranes. Our studies focus upon the interaction of cholesterol with polyunsaturated fatty acid (PUFA)-containing phospholipids. They support the proposal that steric incompatibility of the rigid steroid moiety for highly disordered PUFA chains, in particular docosahexaenoic acid (DHA), provides a sensitive trigger for lateral segregation of lipids into PUFA-rich/sterol-poor and PUFA-poor/sterol-rich regions. Solid state ²H NMR and x-ray diffraction (XRD) demonstrate that the solubility of cholesterol is reduced in 1-palmitoyl-2-docosahexaenoyl-phosphatidylethanolamine (16-0:22:6PE) bilayers. In mixed membranes of phosphatidylethanolamine (PE) with the lipid raft forming molecules egg sphingomyelin (SM) and cholesterol, diminished affinity of the sterol for 16:0-22:6PE relative to 1-palmitoyl-2-oleoylphosphatidylethanolamine (16:0-18:1PE) is identified by ²H NMR order parameters and detergent extraction. Phase separation of the PUFA-containing phospholipid from SM/cholesterol rafts is the implication, which may be associated with the myriad of health benefits of dietary DHA.     

Families of Finite Subsets of ℕ of Low Complexity and Tsirelson Type Spaces

We study Tsirelson type spaces of the form T[(ℳ︁_k, θ_k)^l_k=1] defined by a finite sequence (ℳ︁_k)^l_k=1 of compact families of finite subsets of ℕ. Using an appropriate index, denoted by i(ℳ︁), to measure the complexity of a family ℳ︁, we prove the following: If i(ℳ︁_k) < ω for all k = 1, …, l, then the space T[(ℳ︁_k, θ_k)^l_k=1] contains isomorphically some l_p, 1 < p < ∞, or c₀. If i(ℳ︁) = ω, then the space T[ℳ︁, θ] contains a subspace isomorphic to a subspace of the original Tsirelson's space.     

Ridged Domains,Embedding Theorems and Poincaré Inequalities

We study the embeddings E : W(X(Ω), Y(Ω)) ↪ Z(Ω), where X(Ω), Y(Ω) and Z(Ω) are rearrangement–invariant Banach function spaces (BFS) defined on a generalized ridged domain Ω, and W denotes a first–order Sobolev–type space. We obtain two–sided estimates for the measure of non–compactness of E when Z(Ω) = X(Ω) and, in turn, necessary and sufficient conditions for a Poincaré–type inequality to be valid and also for E to be compact. The results are used to analyse the example of a trumpet–shaped domain Ω in Lorentz spaces. We consider the problem of determining the range of possible target spaces Z(Ω), in which case we prove that the problem is equivalent to an analogue on the generalized ridge Γ of Ω. The range of target spaces Z(Ω) is determined amongst a scale of (weighted) Lebesgue spaces for “rooms and passages” and trumpet–shaped domains.     

Complex Powers of the Neumann Laplacian in Lipschitz Domains

Let L^q_r(Ω) be the usual scale of Sobolev spaces and let Δ_N be the Neumann Laplacian in an arbitrary Lipschitz domain Ω. We present an interpolation based approach to the following question: for what range of indices does map isomorphically onto L^q_r(Ω)/ℝ?     

Characterization of the singular part of the solution of Maxwell's equations in a polyhedral domain

The solution of Maxwell's equations in a non‐convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian. Copyright © 1999 John Wiley & Sons, Ltd.