The Principal Floquet Bundle and Exponential Separation for Linear Parabolic Equations

We consider linear nonautonomous second order parabolic equations on bounded domains subject to Dirichlet boundary condition. Under mild regularity assumptions on the coefficients and the domain, we establish the existence of a principal Floquet bundle exponentially separated from a complementary invariant bundle. Our main theorem extends in a natural way standard results on principal eigenvalues and eigenfunctions of elliptic and time-periodic parabolic equations. Similar theorems were earlier available only for smooth domains and coefficients. As a corollary of our main result, we obtain the uniqueness of positive entire solutions of the equations in     

管内均相湍流燃烧加速的数值模拟

通过均相流体模型、湍流k 模型和EBU(EddyBreak Up) Arrhenius燃烧模型 ,选用Simple格式对管中戊烷和空气的燃烧实例进行了数值求解。其结果反映了燃烧导致的爆炸过程中管内流场各参数的变化规律 ,揭示了管内燃烧、流动、湍流之间的正反馈耦合关系 ,并与实验结果和相关数值结果基本相符。     

求解线性方程组的一种新方法

将线性方程组的一般系数矩阵转化为对称正定矩阵，从而把原线性方程组的求解问题转化为一个等价变分问题的极少值点寻优问题，借助对分寻优法进行求解。算例结果表明，本文方法不仅对于良态线性方程组的求解问题是有效的，而且对于病态线性方程组的求解问题同样是有效的。     

Theoretical Contributions of Complex Systems to Positive Psychology and Health: A Somewhat Complicated Affair

Health has historically eluded consistent definition and baffled people's attempts at self-improvement. This paper argues for the central role of Somewhat complicated nonlinear dynamical systems in modeling both positive psychology and physical health. Whether personal attributes or behaviors are salutogenic or harmful is dependent on context and intensity. In addition, people simultaneously and relatively independently seek sometimes-contradictory outcomes. This establishes the place of intrapsychic conflict in health. The paper proposes that the good life emerges from systems composed of coupled modular components, potentially capable of chaotic behavior. Positive psychology and healthy physiology derive from linked regulative systems that are relatively loosely-coupled, distributed, and that rely on heuristic processes rather than algorithms guaranteeing solution to pursue well-being. The adoption of these Somewhat complicated models does not require theories of health to be intricate, nor to employ mechanisms with fractal structure; complex function can emerge from simple systems. Potentially healthy systems attributes are addressed, including current interest in healthy chaos, and an illustrative model is developed.     

薄壳算子对称性和正定性的充要条件

本文从一般薄壳方程组出发，证明了薄壳算子的对称性和正定性。并给出了这两种性质存在的充要条件。最后指出本文的证明方法及结论具有一般性。     

卢瑟福公式中正负号问题的探讨

分析了某些理论力学教材在推导卢瑟福公式过程中,处理正负号问题不完善的地方,并给出了一种新的推导方式,从而达到对卢瑟福公式全面完整的认识。     

半正定差分方程正解的存在性

利用锥压缩与锥拉伸不动点定理,在非线性项具有负下界和非减性条件下,讨论了一类二阶半正定非线性差分方程正解的存在性,改进和推广了现有差分方程的一些结果,并将所获得的结果应用于一个具体的二阶半正定非线性差分方程中.     

椭圆曲线y~2=px(x~2+2)在p≡1(mod 8)时的正整数点

设p是适合p≡1(mod 8)的奇素数.运用二次和四次Diophantine方程的性质给出了椭圆曲线E:Y²=px(x2=px(x²+2)有正整数点(x,y)的判别条件,并且证明了:当p<100时,该曲线没有正整数点.     

一类四阶非线性微分方程两点边值问题的正解

应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得了一类四阶非线性常微分方程两点边值问题{-u(4)(t)t=f(t,u(t)),≤t≤1,u(0)=u′(0)=u′(1)=u′″(1)=0正解的存在性.     

分数阶微分方程积分边值问题多个正解的存在性

研究了带有积分边值条件的分数阶微分方程的边值问题.利用LeggettWilliams不动点定理,以及一些分析技巧得到了这类分数阶微分方程边值问题多个正解的存在性.