Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

Mesure de l'Anisotropie des Indices de Réfraction des Cristaux Liquides: Interpretation des Différences Observées lors de I'Utilisation des Diverses Méthodes

Les différences observées dans la mesure des indices et des biréfrignences dans les cristaux liquides, lors de l'utilisation de deux séries de méthodes: utilisation de cuve prismatique à longueur d'onde fixe ou de cuves à faces parallèles à longueur d'onde variable sont relevées et confirmées.     

Variations of the elastic constants of InSb near the covalent-metallic transition

Abstract

The pulse-echo-overlap method was used to measure the longitudinal and transverse wave velocities in single-crystal (100) and (111) samples of InSb up to 3 GPa at room temperature. The peculiar variations of the elastic constants were observed near the covalent-metallic transition.     

Highly efficient water‐soluble visible light photoinitiators

The monoacylphosphineoxide (MAPO) salts Na‐TPO and Li‐TPO and the bisacylphosphineoxide (BAPO) salts BAPO‐ONa and BAPO‐OLi define an important and in the latter case a new class of water‐soluble photoinitiators (PIs) for radical polymerization. These compounds showed excellent water‐solubility of at least 29 g/L for Na‐TPO and up to 60 g/L for BAPO‐ONa in deionized water, thus exceeding the solubility of the state of the art PI for water‐based systems Irgacure 2959 ( I2959 ) 6‐ to 12‐fold. However, biocompatibility, storage stability, and reactivity were equally important to replace the state of the art compounds. Concerning these properties, the MAPO and BAPO salts were at least in the same range (biocompatibility, stability) or showed even better results (reactivity) and had the additional advantage of visible light initiation. Na‐TPO and Li‐TPO achieved double bond conversions of an aqueous solution of N‐acryloylmorpholine over 97% with broad band irradiation (320–500 nm), Li‐TPO showed additionally very good biocompatibility (LC₅₀ = 3.1 mmol/L) and BAPO‐OLi showed highest reactivity with visible light irradiation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 473–479     

An immersed smoothed point interpolation method (IS‐PIM) for fluid‐structure interaction problems

An immersed smoothed point interpolation method using 3‐node triangular background cells is proposed to solve 2D fluid‐structure interaction problems for solids with large deformation/displacement placed in incompressible viscous fluid. In the framework of immersed‐type method, the governing equations can be decomposed into 3 parts on the basis of the fictitious fluid assumption. The incompressible Navier‐Stokes equations are solved using the semi‐implicit characteristic‐based split scheme, and solids are simulated using the newly developed edge‐based smoothed point interpolation method. The fictitious fluid domain can be used to calculate the coupling force. The numerical results show that immersed smoothed point interpolation method can avoid remeshing for moving solid based on immersed operation and simulate the contact phenomenon without an additional treatment between the solid and the fluid boundary. The influence from information transfer between solid domain and fluid domain on fluid‐structure interaction problems has been investigated. The numerical results show that the proposed interpolation schemes will generally improve the accuracy for simulating both fluid flows and solid structures.     

Cauchy-type integral formula and Plemelj formula of hypermonogenic functions on unbounded domains

In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries.     

超空间上高阶Teodorescu算子

本文首先由超空间上Cauchy-Pompeiu公式定义了超空间上高阶Teodorescu算子,研究了此类算子的一些基本性质.其次,利用此类算子,我们得到了$k$-超正则函数的Almansi型展开. 最后运用这个展开,我们证明了$k$-超正则函数的Morera型定理、开拓定理和唯一性定理.