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1.
We prove the global existence of weak solution pair to the initial boundary value problem for a system of m-Laplacian type diffusion equation and nonlinear wave equation. The interaction of two equations is given through nonlinear source terms f(u,v) and g(u,v).  相似文献   
2.
Despite the tremendous efforts devoted to the structural analysis of hydrogel microspheres (microgels), many details of their structures remain unclear. Reported in this study is that thermoresponsive poly(N‐isopropyl acrylamide) (pNIPAm)‐based microgels exhibit not only the widely accepted core–shell structures, but also inhomogeneous decanano‐sized non‐thermoresponsive spherical domains within their dense cores, which was revealed by temperature‐controlled high‐speed atomic force microscopy (TC‐HS‐AFM). Based on a series of experiments, it is concluded that the non‐thermoresponsive domains are characteristic for pNIPAm microgels synthesized by precipitation polymerization, and plausible structures for microgels prepared by other polymerization techniques are proposed.  相似文献   
3.
The Sr 3d X-ray photoelectron spectroscopy (XPS) spectrum of Sr-containing hydroxyapatite (SHAp) overlaps completely with the P 2p spectrum. Thus, the chemical state identification of Sr in SHAp is a challenging task. In this work, the Sr 3d spectrum was isolated from the overlapping spectra for analyzing the chemical state of Sr using a generic peak-fitting method. The SHAp layers containing various Sr concentrations were produced on a Ti substrate using a chemical treatment process with a calcium phosphate slurry that included Sr (NO3)2. The distribution of the constituent elements changed according to the Sr concentration, implying that the chemical state of Sr varied with concentration. The isolation of the Sr 3d XPS spectrum was conducted via spectral deconvolution using the P 2p spectrum corresponding to HAp. The isolated Sr 3d spectrum revealed that the chemical state of Sr was in SrO and Sr-substituted HAp states, and their ratio varied with the Sr concentration in the layer. The SrO to Sr-substituted HAp ratios affected the Sr ion releasing behavior from the SHAp layer, supporting the validity of the obtained analytical results.  相似文献   
4.
We conduct kinetic Monte Carlo simulations for the conservative climb motion of a cluster of self-interstitial atoms (SIAs) towards another SIA cluster in BCC–Fe; the conservative climb velocity is inversely proportional to the fourth power of the distance between them, as per the prediction based on Einstein’s equation. The size of the climbing cluster significantly affects its conservative climb velocity, while the size of the cluster that originates the stress field does not. The activation energy for the conservative climb is considerably greater than that derived in previous studies and strongly dependent on the climbing cluster size. The results presented in this study are the atomistic evaluation of the behaviour of SIA clusters through three-dimensional motion, which cannot be achieved using molecular dynamics techniques alone.  相似文献   
5.
We prove the existence of global decaying solutions to the exterior problem for the Klein–Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity. To derive the required estimates of solutions we employ a ‘loan’ method.  相似文献   
6.
Anisotropic morphologies and the phase behaviour of a hydrogen-bonded LC polymer obtained by photopolymerization in two kinds of LC solvent are discussed. The hydrogen-bonded LC monomer, 4-(6-acryloyloxyhexyloxy) benzoic acid (A6OBA), was photopolymerized in 4-cyano-4′-hexyloxybiphenyl (6OCB) and in 4-cyano-4′-undecyloxybiphenyl (11OCB), which show a nematic phase and a smectic A phase, respectively. After photo-polymerization, the LC media were removed by extraction and the pure polymer was observed by scanning electron microscopy. SEM images showed that the polymer possessed fibrous morphology with a fibre diameter of a few micrometers, based on polymerization-induced phase separation. The overall geometries reflected typical LC characteristics such as schlieren and focal-conic fan textures. It was found that the hydrogen bond between benzoic acid groups in the monomer was rigid enough to fix the anisotropic phase-separated structure forming during the early stage of phase separation; however, it could not permanently maintain the fibre structure due to dissociation at elevated temperature. X-ray measurements revealed that a well developed layer structure of the hydrogen-bonded mesogen existed in the polymer obtained from the smectic phase of 11OCB, whereas a polymer layer structure could develop only partially from the nematic phase of 6OCB.  相似文献   
7.
We propose two methods to enclose the solution of an ordinary free boundary problem. The problem is reformulated as a nonlinear boundary value problem on a fixed interval including an unknown parameter. By appropriately setting a functional space that depends on the finite element approximation, the solution is represented as a fixed point of a compact map. Then, by using the finite element projection with constructive error estimates, a Newton-type verification procedure is derived. In addition, numerical examples confirming the effectiveness of current methods are given.  相似文献   
8.
We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Fréchet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods.

We already derived such a theorem in [11 N. Yamamoto ( 1998 ). A numerical verification method for solutions of boundary value problems with local uniqueness by Banach's fixed-point theorem . SIAM J. Numer. Anal. 35 : 20042013 .[Crossref] [Google Scholar]], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations.  相似文献   
9.
Abstract

A variety of cyclic and acyclic ethers are efficiently reacted with acyl chlorides or acyl bromides to afford the ether-cleaved compounds of ω-chloro-or ω-bromoesters under high pressure conditions. The reactivity of ethers is found to be roughly depend on the basicity of the ether oxygen atom.  相似文献   
10.
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