Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media

This paper presents a new nonlinear reaction–diffusion–convection system coupled with a system of ordinary differential equations that models a combustion front in a multilayer porous medium. The model includes heat transfer between the layers and heat loss to the external environment. A few assumptions are made to simplify the model, such as incompressibility; then, the unknowns are determined to be the temperature and fuel concentration in each layer. When the fuel concentration in each layer is a known function, we prove the existence and uniqueness of a classical solution for the initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. We construct monotone iterations of upper and lower solutions and prove that these iterations converge to a unique solution for the problem, first locally and then, in time, globally.     

Completion of R2 with a Conformal Metric as a Closed Surface

In this paper,we obtain some asymptotic behavior results for solutions to the prescribed Gaussian curvature equation.Moreover,we prove that under a con-formal metric in R2,if the total Gaussian curvature is 4π,the conformal area of R2 is finite and the Gaussian curvature is bounded,then R2 is a compact C1,α surface after completion at ∞,for any α ∈(0,1).If the Gaussian curvature has a Holder decay at in-finity,then the completed surface is C2.For radial solutions,the same regularity holds if the Gaussian curvature has a limit at infinity.     

The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction

The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols

While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called ‘verification theorems’ and ‘viscosity solutions’ provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.     

Ft-Raman Study of Three Synthetic Solid Solutions Formed by Orthorhombic Sulfates: Celestite-Barytes,Barytes-Anglesite and Celestite-Anglesite

Abstract

In the present work, three different solid solutions whose end-members are the orthorhombic sulfates celestite (SrSO₄), barytes (BaSO₄) and anglesite (PbSO₄) are studied using FT-Raman spectroscopy. Sulfate anion symmetric internal modes have been examined in detail by means of band-shape analysis and component fitting procedures. the symmetric stretching mode v₁(A₁) changes its wavenumber position linearly with the cationic composition of the samples which further confirms the ideal character of the solid solutions studied. the corresponding full-width at half-height is strongly increased in the central components of the different solid solutions which can be understood as an effect of the positional disorder induced by random cationic substitution. Similar results are observed in the symmetric bending mode, v² (E). the study of the low frequency spectral region permits one to differentiate translational modes of the sulfate anion, which changes its wavenumber position when the alkali-earth metal ion changes from rotational modes. This permits the tentative band assignment of the anglesite rotational Raman bands at 134 and 152 cm^?1, which were previously not assigned.     

修正的BBM方程新的精确解

应用进一步修正的简单方程法对修正的 Benjamin -Bona -Mahoney (mBBM )方程进行求解,给出了mBBM方程新的精确类孤波解,取定某些参数值,便可得到精确孤波解.这种方法也可用于寻找其它常系数以及变系数非线性发展方程(组)的精确解,具有一定的普适性.     

Er3＋-Yb3＋-Mo6＋共掺杂ZrO2-Al2 O3固溶体的上转换发光

采用共沉淀法制备了一系列Al2 O3含量由低到高的ZrO2-Al2 O3固溶体,并研究了固溶体的晶相结构以及稀土Er3＋在固溶体中的上转换发光增强机制。XRD结果表明固溶体为四方晶相ZrO2结构,Al2 O3的最高固溶度约为20 mol％。上转换发光光谱分析表明,Er3＋掺杂ZrO2室温下具有绿色上转换荧光发射,通过共掺杂Yb3＋和M o6＋离子,使得Er3＋掺杂ZrO2的绿色上转换发光强度增强了约20倍,获得了明亮的黄绿色上转换发光。基质ZrO2通过与Al2 O3固溶形成复合氧化物,由于产生的大量氧空位缺陷的能级与Er3＋的4 F7/2能级高度相接近,增强了Yb3＋-MoO2-4基团（2 F7/2,3 T2）能级向Er3＋的4 F7/2能级的能量传递。通过形成固溶体复合氧化物基质材料,使得Er3＋的绿色上转换发光在获得20倍增强的基础上又提高了8倍。绿色与红色上转换发光比例的变化也提高了材料的色纯度,上转换发光由黄绿色变为纯绿色。     

周期脉冲作用下Logistic映射的复杂动力学行为及其分岔分析

研究了两种周期脉冲作用下Logistic映射的复杂动力学行为. 随着参数的变化, 该系统产生平衡解、周期解、混沌等现象, 且该系统可经级联倍周期分岔到达混沌. 通过构造Poincaré 映射, 对周期脉冲作用下Logistic映射进行了分岔分析. 最后基于Floquet理论揭示了该系统周期解的分岔机理. 关键词： Logistic映射 脉冲 周期解 分岔机理     

PERSISTENCE AND PERIODIC SOLUTIONS FOR NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH IMPULSES

In this paper, a nonautonomous Predator-prey model with functional response and impulses is studied. By using comparison theorem and the mono-tonicity, some sufficient conditions which guarantee the permanence and asymptotic behavior of this system are obtained.     

Existence of three positive solutions for boundary value problems with p-Laplacian

By using fixed point theorem, we study the following equation g(u^′′(t))+a(t)f(u)=0 subject to boundary conditions, where g(v)=|v|^p−2v with p>1; the existence of at least three positive solutions is proved.