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.     

互补问题的一个修改算法

本文给出了一个修改的路径跟踪预测校正非内点算法 ,同时给出了一个新的中心路邻域的表示 .并在此基础上给出了全局和局部收敛性 ,最后给出的数值结果验证了其有效性     

线性码的重量分布

本文给出线性码重量分布之间很有用的一个关系,并给出一个应用。     

求解整数规划的单参数填充函数

本文给出了一个新的求解离散全局最优化问题的单参数填充函数,并给出了一个新的算法,同时给出了对几个测试问题的数据计算结果.     

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.     

Jordan不等式的改进及应用

给出了Jordan不等式的一个改进,并利用改进的结果给出杨乐不等式的一个推广     

“勾股定理的一个简洁证明”的姐妹篇

文[1],[2],[3]分别给出了勾股定理的“简短证明”,文[4]给出了“一个更为简短而且整洁的证明”.本文运用圆的基本知识再给出一个前所未见的简证.     

Choi不等式的一些研究和应用

1974年,Man-DuenChoi结合正定线性算子定义,给出了矩阵分析学中的一个重要不等式,这个不等式是Fiedler不等式的推广,利用一些正定矩阵的性质,给出Choi不等式的一个新的推到方法,并且用该不等式给出了Fiedler不等式的一个新证明.     

Ramsey数R_m(3)的计算及Schur数的新上界

利用抽屉原理,给出了Ramsey数Rm(3)的一个递推公式,得到Rm(3)准确值计算的一个具体表达式,并利用Rm(3)的计算公式给出了Schur数的一个新的上界。     

不完备证券市场中博弈未定权益的保值

考虑不完备证券市场中博弈未定权益(GCC)的保值问题,通过Kramkov关于上鞅的可选分解定理给出未定权益的上保值价格和下保值价格。指出关于买卖双方都存在着一个最优保值策略。给出价格的一个无套利区间,并针对前面的结论,给出几个性质以及在限制投资组合方面的一个应用。     

Bounds of the Hausdorff Measure of Sierpinski carpet

By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Solution of two-dimensional boundary-value problems of the theory of thin composite shells

Discrete analogues of the boundary-value problems of a two-dimensional refined theory of anisotropic shells taking into account the transverse shear deformation are presented. The systems of resolving equations in the general form are obtained for arbitrary nonshallow shells of variable curvature whose coordinate lines of the reduction surface may not coincide with the lines of principal curvatures. The algebraic problems of determining the stress-strain state in shells made of composite materials with stress concentrators under various kinds of loads are obtained as particular cases of the schemes presented. The results of calculating the stress concentration near a nonsmall circular hole in a transversely isotropic nonshallow spherical shell under internal pressure are presented. The dependences of stress concentration factors on the hole dimension and on a change in the shear stiffness of the shells are studied. A comparison between the calculation results obtained within the framework of the theories of shallow and nonshallow shells is given.Presented at the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Timoshenko Institute of Mechanics, Ukranian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 465–472, July–August, 2000.     

Comments on generalized Heron polynomials and Robbins’ conjectures

Heron’s formula for a triangle gives a polynomial for the square of its area in terms of the lengths of its three sides. There is a very similar formula, due to Brahmagupta, for the area of a cyclic quadrilateral in terms of the lengths of its four sides. (A polygon is cyclic if its vertices lie on a circle.) In both cases if A is the area of the polygon, (4A)² is a polynomial function of the square in the lengths of its edges. David Robbins in [D.P. Robbins, Areas of polygons inscribed in a circle, Discrete Comput. Geom. 12 (2) (1994) 223-236. MR 95g:51027; David P. Robbins, Areas of polygons inscribed in a circle, Amer. Math. Monthly 102 (6) (1995) 523-530. MR 96k:51024] showed that for any cyclic polygon with n edges, (4A)² satisfies a polynomial whose coefficients are themselves polynomials in the edge lengths, and he calculated this polynomial for n=5 and n=6. He conjectured the degree of this polynomial for all n, and recently Igor Pak and Maksym Fedorchuk [Maksym Fedorchuk, Igor Pak, Rigidity and polynomial invariants of convex polytopes, Duke Math. J. 129 (2) (2005) 371-404. MR 2006f:52015] have shown that this conjecture of Robbins is true. Robbins also conjectured that his polynomial is monic, and that was shown in [V.V. Varfolomeev, Inscribed polygons and Heron polynomials (Russian. Russian summary), Mat. Sb. 194 (3) (2003) 3-24. MR 2004d:51014]. A short independent proof will be shown here.     

Dynamic properties of composite laminates and panels with highly contrasting directions of anisotropy

An asymptotic analysis of the dynamic stress-strain state of a thin laminar packet of anisotropic layers is presented. The statement is nonclassical, since in layer materials the ratio of elastic moduli in the longitudinal and transverse directions can generate small parameters comparable to the relative half-thickness of the packet, as, for example, in high-strength unidirectional composites. Alternation of strong load-carrying layers and a relatively soft filler with a similar difference in the elastic moduli between the layers is also allowed. The averaged two-dimensional equations and the total stress tensor in the layers are determined. The results are classified with respect to the types of anisotropy and the indices of differences in the elastic moduli. It is shown that first-approximation models lead to kinematic relations similar to those of the theories of high-order shear strains. Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 605–614, September–October, 1999.     

On a notion of partially conditionally identically distributed sequences

A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence weaker than exchangeability, but equivalent to it in the presence of stationarity. We extend such notion to families of sequences. Paralleling the extension from exchangeability to partial exchangeability in the sense of de Finetti, we propose a notion of partially c.i.d. dependence, which is shown to be equivalent to partial exchangeability for stationary processes. Partially c.i.d. families of sequences preserve attractive limit properties of partial exchangeability, and are asymptotically partially exchangeable. Moreover, we provide strong laws of large numbers and two central limit theorems. Our focus is on the asymptotic agreement of predictions and empirical means, which lies at the foundations of Bayesian statistics. Natural examples of partially c.i.d. constructions are interacting randomly reinforced processes satisfying certain conditions on the reinforcement.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.