Infinitely many solutions for the prescribed curvature problem of polyharmonic operator

We consider the following prescribed curvature problem for polyharmonic operator: $$\left\{\begin{array}{llll} D_{m} u = \tilde{K}(y)|u|^{m^*-2}u\; {\rm in}\; \mathbb{S}^N\\ u \quad\; >0\qquad\quad\quad\quad\quad{\rm on}\; \mathbb{S}^N\\ u \quad\; \in H^{m}(\mathbb{S}^N), \end{array} \right.$$ where ${m^*=\frac{2N}{N-2m}, N\geq 2m+1,m \in \mathbb{N}_{+}, \tilde{K}}$ is positive and rationally symmetric, ${\mathbb{S}^N}$ is the unit sphere with the induced Riemannian metric ${g=g_{\mathbb{S}^N},}$ and D _m is the elliptic differential operator of 2m order given by $$\begin{array}{lll}D_m={\prod\limits_{k=1}^m}{\left(-\Delta_g+\frac{1}{4}(N-2k)(N+2k-2)\right)}\end{array}$$ where Δ _g is the Laplace-Beltrami operator on ${\mathbb{S}^N}$ . We will show that problem (P) has infinitely many non-radial positive solutions, whose energy can be arbitrary large.     

On algebraic Riccati equations associated with M-matrices

We consider the algebraic Riccati equation for which the four coefficient matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible singular M-matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M-matrix. Under a regularity assumption on the M-matrix K, we show that the Riccati equation still has a minimal nonnegative solution. We also study the properties of this particular solution and explain how the solution can be found by existing methods.     

Existence of subharmonic solutions and homoclinic orbits for a class of even higher order differential equations

Using the variational structure and the Z ₂ group index theory we establish the existence of subharmonic solutions and homoclinic solutions for a class of even higher order differential equation.     

Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.     

Random strict convexity and random uniform convexity in random normed modules

Based on the analysis of stratification structure on random normed modules, we first present random strict convexity and random uniform convexity in random normed modules. Then, we establish their respective relations to classical strict and uniform convexity: in the process some known important results concerning strict convexity and uniform convexity of Lebesgue-Bochner function spaces can be obtained as a special case of our results. Further, we also give their important applications to the theory of random conjugate spaces as well as best approximation. Finally, we conclude this paper with some remarks showing that the study of geometry of random normed modules will also motivate the further study of geometry of probabilistic normed spaces.     

Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic

The psi function ψ(x) is defined by ψ(x)=Γ^′(x)/Γ(x), where Γ(x) is the gamma function. We give necessary and sufficient conditions for the function ψ^″(x)+[ψ^′(x+α)]² or its negative to be completely monotonic on (−α,∞), where . We also prove that the function [ψ^′(x)]²+λψ^″(x) is completely monotonic on (0,∞) if and only if λ1. As an application of the latter conclusion, the monotonicity and convexity of the function e^pψ(x+1)−qx with respect to x(−1,∞) are thoroughly discussed for p≠0 and .     

金属包层对称平面单轴晶体波导的模式场(Ⅱ)

对于晶体光轴平行于波导界面的结构,讨论了光在金属包层对称平面单轴晶体波导(波导层是单轴晶体,两个波导界面均为金属)内的传输特性.解析地得到了这种结构下波导模式场的精确解.模式场的性质因单轴晶体的性质不同而异.对于正单轴晶体,波导的主模是横电波,任何频率的光波均可激励该模式;当频率满足一定条件时,波导内传输单模,否则,将激励起高阶模式.高阶模既非TE波,也非TM波,而是两者耦合而成的混合模.对于负单轴晶体,波导的主模是一种混合模,该模式同样可被任何频率的光波所激励;当频率满足一定条件时,波导内传输单模,否则 关键词： 平面金属波导 单轴晶体 模式场 混合模     

交换环上的单模的射影性与内射性

在本短文中主要研究了交换环上的单模的射影性与内射性之间的关系。主要证明了:交换环上射影单模必是一个内射模;若该环是一个Noether环,则反之亦成立。     

山西省农民家庭消费水平和结构分析

本文利用统计计量学方法对山西省农民家庭消费水平和消费结构的变化及原因进行了实证分析。建立了山西省农民人均消费的消费函数和山西省农民总消费支出与食品、衣着、住房、日用品、燃料及文化生活服务支出的关系模型，并通过模型分析解释了农民的消费结构，也为决策者提供一些有效的参考资料。     

Ge组分分布对基区杂质非均匀分布的SiGe HBT温度特性的影响

众所周知, 双极型晶体管的设计主要是基区的设计. 一般而言, 基区的杂质分布是非均匀的. 本文首先研究了非均匀的杂质高斯分布对器件温度分布、增益和截止频率的温度特性的影响, 发现增益和截止频率具有正温度系数, 体内温度较高. 随后研究了基区Ge组分分布对这些器件参数的影响. 均匀Ge组分分布和梯形Ge组分分布的SiGe 异质结双极型晶体管增益和截止频率具有负温度系数, 具有较好的体内温度分布. 进一步的研究表明, 具有梯形Ge组分分布的SiGe 异质结双极型晶体管, 由于Ge组分缓变引入了少子加速电场, 不但使它的增益和截止频率具有较高的值, 而且保持了较弱的温度敏感性, 在增益、特征频率大小及其温度敏感性、体内温度分布达到了很好的折中.