关于多项式映射自同构恒等集的一个注记

本文给出了判定一个仿射代数集是否是一个自同构恒等集的充分条件.作为一个推论,我们给出了Mckay-Wang的一个问题的一个新证明.我们也给出了一些具体的例子来说明主要的定理.     

关于自相似集的Hausdorff测度的一个判据及其应用

讨论了满足开集条件的自相似集。对于此类分形，用自然覆盖类估计它的Hausdorff测度只能得到一个上限，因而如何判断某一个上限就是它的Hausdorff测度的准确值是一个重要的问题。本文给出了一个判据。作为应用，统一处理了一类自相似集，得到了平面上的一个Cantor集－Cantor尘的Hausdorff测度的准确值，并重新计算了直线上的Cantor集以及一个Sierpinski地毯的Hausdorff测度。     

关于Goldie环的一些注记

本文给出了一个判别准则来判定一个(半)素右Goldie环是否是一个左Goldie环,同时也考虑了一个拟生成元与其自同态环之间的关系。     

关于P.Crawleg和R.P.Dilworth的公开问题

本文讨论了P.Crawleg和R.P.Dilworth提出的一个公开问题,研究了偏序集的带有固定点的保序映射,并且给出了若干充分或必要条件,使得一个偏序集的每一个保序映射都至少有一个固定点。     

一个Lie代数的子代数及其相关的两类Loop代数

本文构造了Lie代数A2的一个子代数A2,通过选取恰当的基元阶数得到相应的一个loop代数A2,由此设计一个等谱问题,利用屠格式得到了一个新的Liouville可积的Hamilton方程族.作为其约化情形,得到了一个非线性有理分式型演化方程.再由一个矩阵变换,得到了换位运算与A2等价的Lie代数A1的一个子代数A1,将A1再扩展成一个新的高维loop代数G,利用G获得了所得方程族的一类扩展可积系统.     

周期多尺度分析的特征及它的一个应用

在这篇文章里，我们研究了周期多尺度分析的性质，给出了尺度函数序列的一个特征．这个特征能够使我们从一个尺度函数序列得到另一个尺度函数序列．最后，我们给出了主要结果的一个应用．     

截断切割问题的参数规划模型

对一个截断切割问题,本文给出了一个参数网络规划模型,总结了[3]中的解法,并给出了一个实例.     

论四元数矩阵的正定性

本文给出了正定四元数矩阵的定义，同时给出了正定四元数矩阵的一个充要条件，一个必要条件，一个充分条件。     

一类二阶泛函微分方程的周期边值问题

讨论了一类二阶泛函微分方程的周期边值问题,给出了上、下解的一个新的概念,并且得到了一个新的比较结果.同时,修正了相关文献中的一个错误.     

完备Brouwerian格上Fuzzy关系方程有极小解的条件

本文在有限论域上对完备Brouwerian格上Fuzzy关系方程极小的存在问题作了探讨，首先构造了Fuzzy关系方程有解但无极小解的一个例子，然后在解集非空时给出了对Fuzzy关系方程的每一个解都存在一个小于等于它的极小解的一个充分条件及一个充要条件，特别地，在充分条件下给出了一类Fuzzy关系方程所有极小解的个数的公式。     

Necessary Condition for a Strong Relative Minimum for Singular Optimal Control

A necessary condition is developed for a strong relative minimum for a first-order singular optimal control. It is shown that the strong condition is identical with the existing weak condition, namely, the generalized Legendre-Clebsch condition. It is conjectured that the strong condition for a second-order singular control will be the same as the corresponding weak condition.     

A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines

We establish a sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. The sufficient condition relates to a sufficient condition for the weak stability of the fluid networks that correspond to the queueing networks under consideration. In addition, we establish a necessary condition for the network to have a continuous diffusion limit; the necessary condition is to require a reflection matrix (of dimension equal to the number of stations) to be completely-S. When applied to some examples, including generalized Jackson networks, single station multiclass queues, first-buffer-first-served re-entrant lines, a two-station Dai–Wang network and a three-station Dumas network, the sufficient condition coincides with the necessary condition.     

A criterion for checking if a convex set belongs to the union of a finite number of convex sets

A necessary and sufficient condition for the inclusion of a convex compact set in the union of a finite number of convex sets is proved. This condition obtained using the convex analysis techniques is a condition on the maximin of a given function. Using the dynamic programming, checking this condition is reduced to evaluating a set of functions and checking a condition for their values. The reduced form of the criterion is more convenient from the computational point of view.     

参数曲线的全局凸性判别条件

基于平面曲线的二次微商,导出了二重点的判别条件,结合参数曲线的局部凸性条件,得到了参数闭曲线的充要条件。给出了参数曲线的拐点判别条件,从而得到了参数曲线局部凸的充要条件。     

Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.     

Comparison between exact thermal boundary condition and harmonic mean conductivity condition at the solid–fluid interface for finite thickness shrouded non-isothermal fin array

A numerical study is made comparing the exact thermal boundary condition and a harmonic mean conductivity condition at the solid–fluid interface for a finite thickness shrouded non-isothermal fin array. Results highlight that there exists a significant deviation of pressure drop across the length of the fin for the exact thermal boundary condition, which is as high as 20% as compared to that obtained using the harmonic mean conductivity condition. The exact thermal boundary condition forecasts relatively more non-isothermal fin as compared to a harmonic mean conductivity condition. The greater the fin spacing the larger the non-isothermal behavior of the fin and it also depends upon Grashof number as well as inlet fluid velocity. The larger the Grashof number the greater is the non-isothermal behavior of fin. The greater the inlet velocity, the larger is the non-isothermal behavior of fin. Bulk fluid temperature is over predicted by as much as 13% by the harmonic mean conductivity condition for larger fin spacing with highest Grashof number coupled with larger velocity. This deviation is only 6% for smaller fin spacing. Overall Nusselt number is over predicted for the harmonic mean conductivity condition as compared to exact thermal boundary condition. This over prediction is limited to about 8%.     

A condition for diagonalization modulo arbitrary norm ideals

We give a spectral condition which is sufficient for the simultaneous diagonalization of a commuting tuple of self-adjoint operators modulo a given norm ideal. For diagonalization modulo certain norm ideals this condition is also necessary, while for other norm ideals this condition seems to be close to being necessary. Moreover, this condition is easy to verify in applications.     

A new necessary condition for optimality of systems with time delay

A new necessary condition for optimality of nonsingular control problems with time delay is developed. This condition accounts for the interaction of the different delays in the control vector. A necessary condition for optimality of singular control problems with time delay is also obtained as a corollary of the new condition.     

Optimal control with delays and mixed initial condition

This paper studies optimal control problems with unfixed initial instant for systems described by differential equations with variables delays and mixed initial condition. The mixed initial condition means that at the initial instant of time, some coordinates of the trajectory do not coincide with the corresponding coordinates of the initial function (a discontinuous part of the initial condition), whereas the others coincide (a continuous part of the initial condition). The authors prove necessary optimality conditions for the control and the initial function for the initial and final instants of time. From these conditions should be isolated the condition for the initial instant containing the effect of mixed initial condition. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 58, Optimal Control, 2008.     

A Class of Potentials for Which Exact Semiclassical Quantization Can Be Achieved

We consider a class of potentials for which the exact semiclassical quantization is achieved by a certain modification of the quantization condition. A list of potentials for which the new quantization condition is exact coincides with the list of potentials for which the spectrum is determined by the factorization method. We construct a one-parameter family of quantization conditions including the supersymmetric WKB condition as a special case. The new condition allows considering the interrelations between different modifications of the leading approximation and their validity ranges and also allows developing new approximate methods for calculating spectra.