Existence results for a nonlinear coupled radiative–conductive heat transfer system

In this paper, we present existence results for a one-dimensional coupled system of nonlinear integro-differential equations on s="true">s="true">s="true">Ls="true">s="true">psup><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.642ex" height="2.086ex" viewBox="0 -796.9 1137.5 898.2" role="img" focusable="false" style="vertical-align: -0.235ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">s="true">s="true">se xlink:href="#MJMATHI-4C">se>s="true" transform="translate(681,410)">s="true">se transform="scale(0.707)" xlink:href="#MJMATHI-70">se>svg><script type="math/mml" id="MathJax-Element-1">s="true">s="true">s="true">Ls="true">s="true">psup>script>-spaces with <svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.853ex" height="2.317ex" viewBox="0 -747.2 4672.6 997.6" role="img" focusable="false" style="vertical-align: -0.582ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">s="true">se xlink:href="#MJMAIN-31">se>s="true" transform="translate(778,0)">se xlink:href="#MJMAIN-2264">se>s="true" transform="translate(1834,0)">se xlink:href="#MJMATHI-70">se>s="true" transform="translate(2615,0)">se xlink:href="#MJMAIN-3C">se>s="true" transform="translate(3672,0)">se xlink:href="#MJMAIN-221E">se>svg><script type="math/mml" id="MathJax-Element-2">script>. This system describes the steady-state combined radiative–conductive heat transfer. We reformulate the full coupled system as a fixed point problem. This formulation is applied to prove existence results for the radiation intensity and the temperature fields. We treat separately the cases <svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.52ex" height="2.317ex" viewBox="-38.5 -747.2 2376.6 997.6" role="img" focusable="false" style="vertical-align: -0.582ex; margin-left: -0.089ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">s="true">se xlink:href="#MJMATHI-70">se>s="true" transform="translate(781,0)">se xlink:href="#MJMAIN-3D">se>s="true" transform="translate(1837,0)">se xlink:href="#MJMAIN-31">se>svg><script type="math/mml" id="MathJax-Element-3">script> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.52ex" height="2.317ex" viewBox="-38.5 -747.2 2376.6 997.6" role="img" focusable="false" style="vertical-align: -0.582ex; margin-left: -0.089ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">s="true">se xlink:href="#MJMATHI-70">se>s="true" transform="translate(781,0)">se xlink:href="#MJMAIN-3E">se>s="true" transform="translate(1837,0)">se xlink:href="#MJMAIN-31">se>svg><script type="math/mml" id="MathJax-Element-4">script>. The analysis for <svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.52ex" height="2.317ex" viewBox="-38.5 -747.2 2376.6 997.6" role="img" focusable="false" style="vertical-align: -0.582ex; margin-left: -0.089ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">s="true">se xlink:href="#MJMATHI-70">se>s="true" transform="translate(781,0)">se xlink:href="#MJMAIN-3E">se>s="true" transform="translate(1837,0)">se xlink:href="#MJMAIN-31">se>svg><script type="math/mml" id="MathJax-Element-5">script> uses the Krasnosel’skii fixed point theorem, while the existence results in the case <svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.52ex" height="2.317ex" viewBox="-38.5 -747.2 2376.6 997.6" role="img" focusable="false" style="vertical-align: -0.582ex; margin-left: -0.089ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">s="true">se xlink:href="#MJMATHI-70">se>s="true" transform="translate(781,0)">se xlink:href="#MJMAIN-3D">se>s="true" transform="translate(1837,0)">se xlink:href="#MJMAIN-31">se>svg><script type="math/mml" id="MathJax-Element-6">script> are obtained via a new variant of that theorem for the weak topology established in Latrach et&nbsp;al. (2006).     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation s="true">s="true">s="true">ns="true">s="true">2sup>s="true">xs="true">+s="true">gstretchy="false" is="true">(s="true">xstretchy="false" is="true">)s="true">=s="true">pstretchy="false" is="true">(s="true">tstretchy="false" is="true">) with the critical situation that sup is="true">s="true">s="true">∫s="true">s="true">0s="true">s="true">2s="true">πsubsup>s="true">pstretchy="false" is="true">(s="true">tstretchy="false" is="true">)sup is="true">s="true">s="true">es="true">s="true">?s="true">is="true">ns="true">tsup>s="true">ds="true">tstretchy="true" maxsize="2.4ex" minsize="2.4ex" is="true">|s="true">=s="true">2stretchy="true" maxsize="2.4ex" minsize="2.4ex" is="true">|s="true">gstretchy="false" is="true">(s="true">+s="true">∞stretchy="false" is="true">)s="true">?s="true">gstretchy="false" is="true">(s="true">?s="true">∞stretchy="false" is="true">)stretchy="true" maxsize="2.4ex" minsize="2.4ex" is="true">| on g and p, where s="true">s="true">s="true">Ns="true">s="true">+sup>, is periodic and is bounded.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but s="true">s="true">s="true">Cs="true">s="true">1sup>) nonlinearities.     

Heinz type inequalities for mappings satisfying Poisson’s equation

In this paper, we study the Heinz type inequalities for mappings satisfying Poisson’s equation. Some results generalize the ones obtained by Partyka and Sakan.     

Delay of terminal current in systems with abruptly changed Hamiltonian

The current response for the parameter change of a mesoscopic system is a practical issue for future's circuit design. Nowadays most considered cases are various types of bias modulation, while the effect of change of conductor Hamiltonian is seldom addressed. In this paper, we investigate the response of ballistic transport induced by a sudden change of the conductor Hamiltonian. We formulize the terminal current in language of non-equilibrium Green's function. Our method is applied to one-dimensional tight-binding chains and we find that the terminal current has a delay to the Hamiltonian change. The amount of delay is not determined by the velocity of incident electrons in the bias window, but depends on the tight-binding hopping energy γ. The delay of current response at the detecting point away from where the Hamiltonian changes is s="true">s="true">s="true">γs="true">s="true">?s="true">1sup>, where C is a constant independent of the system.     

Non-trivial 1d and 2d Segal–Bargmann transforms

Special generating functions and Mehler's formula for the univariate complex Hermite polynomials are obtained and next employed to introduce and study some one- and two-dimensional integral transforms of Segal–Bargmann type in the framework of some specific functional Hilbert spaces; including the so-called generalized Bargmann–Fock spaces that are realized as <span class="NLM_disp-formula-image inline-formula">script>src="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/gitr20/2019/gitr20.v030.i07/10652469.2019.1593407/20190428/images/gitr_a_1593407_ilm0001.gif"}' />script>src="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gitr20/2019/gitr20.v030.i07/10652469.2019.1593407/20190428/images/gitr_a_1593407_ilm0001.gif"}" /><span class="mml-formula">span>span><span class="NLM_disp-formula inline-formula">src="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />span>-eigenspaces of a special magnetic Schrödinger operator.     

Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law s="true">s="true">s="true">vs="true">s="true">?s="true">σsup>. The validity of the equation has been rigorously proved in ss="workspace-trigger">[22] taking as a starting point a particle model and for values of the exponent , but the model can be expected to be valid, on heuristic grounds, for . The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

The Duskin nerve of 2-categories in Joyal's cell category Θ2

We give an explicit and purely combinatorial description of the Duskin nerve of any <svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.861ex" height="2.709ex" viewBox="0 -847.3 2953.9 1166.2" role="img" focusable="false" style="vertical-align: -0.741ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">se xlink:href="#MJMAIN-28">se>s="true" transform="translate(389,0)">se xlink:href="#MJMATHI-72">se>s="true" transform="translate(1063,0)">se xlink:href="#MJMAIN-2B">se>s="true" transform="translate(2063,0)">se xlink:href="#MJMAIN-31">se>s="true" transform="translate(2564,0)">se xlink:href="#MJMAIN-29">se>svg><script type="math/mml" id="MathJax-Element-1">script>-point suspension 2-category, and in particular of any 2-category belonging to Joyal's cell category s="true">s="true">s="true">Θs="true">s="true">2sub><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.862ex" height="2.341ex" viewBox="0 -794.4 1232.4 1007.7" role="img" focusable="false" style="vertical-align: -0.495ex;">stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)">s="true">s="true">s="true">se xlink:href="#MJMAIN-398">se>s="true" transform="translate(778,-150)">s="true">se transform="scale(0.707)" xlink:href="#MJMAIN-32">se>svg><script type="math/mml" id="MathJax-Element-2">s="true">s="true">s="true">Θs="true">s="true">2sub>script>.     

High-throughput lipidomics analysis to discover lipid biomarkers and profiles as potential targets for evaluating efficacy of Kai-Xin-San against APP/PS1 transgenic mice based on UPLC–Q/TOF–MS

Lipid metabolism has a significant function in the central nervous system and Alzheimer's disease (AD) is an age-related senile disease characterized by central nerve degeneration. The pathological development of AD is closely related to lipid metabolism disorders. To reveal the influence of Kai-Xin-San (KXS) on lipid metabolism in APP/PSI transgenic mice and potential therapeutic targets for treating AD, brain tissue samples were collected and analyzed by high-throughput lipidomics based on UPLC–Q/TOF-MS. The collected raw data were processed by multivariate data analysis to discover the potential biomarkers and lipid metabolic profiles. Compared with the control wild-type mouse group, nine potential lipid biomarkers were found in the AD model group, of which seven were up-regulated and two were down-regulated. Orally administrated KXS can reverse the changes in these potential biomarkers. Compared with the model group, a total of six differential metabolites showed a recovery trend and may be potential targets for KXS to treat AD. This study showed that high-throughput lipidomics can be used to discover the perturbed pathways and lipid biomarkers as potential targets to reveal the therapeutic effects of KXS.