Classification of semispaces according to their types in infinite-dimensional vector spaces

It is shown that each semispaceC X naturally generates a relation of complete preorder onX with respect to which the pair (X C, C) is a cut ofX. By identifying the type of the semispace with the type of the cut generated by this semispace, the semispaces are classified according to their types. The obtained classification extends the classification of semispaces in finite-dimensional vector spaces due to Martinez-Legaz and Singer to infinite-dimensional spaces.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 191–198, August, 1998.     

Triangular truncation and its extremal matrices

The triangular truncation operator is a linear transformation that maps a given matrix to its strictly lower triangular part. The operator norm (with respect to the matrix spectral norm) of the triangular truncation is known to have logarithmic dependence on the dimension, and such dependence is usually illustrated by a specific Toeplitz matrix. However, the precise value of this operator norm as well as on which matrices can it be attained is still unclear. In this article, we describe a simple way of constructing matrices whose strictly lower triangular part has logarithmically larger spectral norm. The construction also leads to a sharp estimate that is very close to the actual operator norm of the triangular truncation. This research is directly motivated by our studies on the convergence theory of the Kaczmarz type method (or equivalently, the Gauß‐Seidel type method), the corresponding application of which is also included. Copyright © 2016 John Wiley & Sons, Ltd.     

(λ,μ)-模糊子环和理想的进一步讨论

在(λ,μ)-模糊子群的基础上,进一步刻画了(λ,μ)-模糊子环和理想.详细讨论了(λ,μ)-模糊子环和理想的性质,以及它们与截集的关系,给出了相应结论.     

The distance function from the boundary in a Minkowski space

Let the space be endowed with a Minkowski structure (that is, is the gauge function of a compact convex set having the origin as an interior point, and with boundary of class ), and let be the (asymmetric) distance associated to . Given an open domain of class , let be the Minkowski distance of a point from the boundary of . We prove that a suitable extension of to (which plays the rôle of a signed Minkowski distance to ) is of class in a tubular neighborhood of , and that is of class outside the cut locus of (that is, the closure of the set of points of nondifferentiability of in ). In addition, we prove that the cut locus of has Lebesgue measure zero, and that can be decomposed, up to this set of vanishing measure, into geodesics starting from and going into along the normal direction (with respect to the Minkowski distance). We compute explicitly the Jacobian determinant of the change of variables that associates to every point outside the cut locus the pair , where denotes the (unique) projection of on , and we apply these techniques to the analysis of PDEs of Monge-Kantorovich type arising from problems in optimal transportation theory and shape optimization.

     

Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics.     

CPML在空中核爆电磁脉冲三维数值模拟中的应用

在分析不同类型完全匹配层(PML,perfectl ymatched layer)特点的基础上,选用了卷积形式PML(CPML,convolutional perfectly matched layer)截断空中核爆电磁脉冲(NEMP,nuclear electromagnetic pulse)数值模拟的开放边界.从自由空间中电磁波的平面波解和分裂形式的PML出发,构造了未分裂形式的PML,应用付里叶变换的卷积定理,推导出三维旋转椭球-双曲正交坐标系下CPML介质中电磁场的迭代形式的离散方程.获得了很好的截断效果,展示了CPML在NEMP数值模拟中的应用前景.     

圆波导劈形端口辐射器的数值分析

 高功率微波运用的圆波导劈形端口辐射器(Vlasov-Nakajima辐射器)的辐射场可视为由平开口圆波导的辐射场和在该辐射场中的劈形圆波导段的散射场叠加而成。运用等效电磁流原理数值求解Kirchhoff-kottler积分获得圆波导TM₀₁模的辐射场,再应用物理光学方法计算劈形段的散射场,并将计算的远场方向图与实验结果比较,获得较满意的一致。     

How to Extend the Concept of Convexity Cuts to Derive Deeper Cutting Planes

A new type of cutting plane, termed a decomposition cut, is introduced that can be constructed under the same assumptions as the well-known convexity cut. Therefore it can be applied in algorithms (e.g. cutting plane, branch-and-cut) for various problems of global optimization, such as concave minimization, bilinear programming, reverse-convex programming, and integer programming. In computational tests with cutting plane algorithms for concave minimization, decomposition cuts were shown to be superior to convexity cuts.     

关于“解一维热传导方程的高精度的隐式差分格式”一文的评注

本文指出了文[1]中存在的几个问题。     

核子配对壳模型计算中的多体效应

戴断到Ｓ,Ｄ子空间的核子配对壳模型用于原子核＾１２８－１３４Ｘｅ和＾１３０－１３６Ｂａ的计算。为考虑多体效应,Ｓ,Ｄ对分别用变分法和Ｔａｍｍ－Ｄａｎｃｏｆｆ近似给定。用一个含有三个参数的哈密顿量系统地描述了Ｘｅ和Ｂａ同位素的能谱,本征态和电磁跃迁的强度。所得结果和实验结果符合得较好,并且在一定程度上改善了用表面δ相互作用决定的Ｓ,Ｄ对所得结果中的不足之处。