Dual mixed Orlicz–Brunn–Minkowski inequality and dual Orlicz mixed quermassintegrals

The dual Orlicz–Brunn–Minkowski inequality is extended from volume to dual quermassintegrals. As application, a dual mixed log-Brunn–Minkowski inequality is obtained. Moreover, dual Orlicz mixed quermassintegrals are defined and a dual Orlicz–Minkowski inequality and a dual mixed log-Minkowski inequality are established.     

真商群为s-自对偶群的有限p-群

如果有限群G的每个子群与G的某个商群同构,则称群G为s-自对偶群.如果s-自对偶群G的每个商群与G的某个子群同构,则称群G为自对偶群.本文分类了每个真商群均为s-自对偶群的有限p-群.作为推论,本文还分类了每个真截段均为s-自对偶群的有限p-群,每个真商群均为自对偶群的有限p-群,以及每个真截段均为自对偶群的有限p-群...     

关于对偶Steiner多项式的根的注记

受凸体的Steiner多项式的启发,定义了星体的对偶Steiner多项式,并利用对偶Aleksandrov-Fenchel不等式讨论了对偶Steiner多项式的根.进而,得到了关于对偶Steiner多项式的根的一些不等式,这些不等式恰好是关于Steiner多项式的根的不等式的对偶形式.     

Sparse Dual Frames and Dual Gabor Functions of Minimal Time and Frequency Supports

Exploitation of the optimality of (non-exact) frames from a sparse dual point of view is presented. Sparse dual frames and dual Gabor functions of the minimal time and/or frequency supports are studied and constructed through the notion of sparse representations. Conditions on the sparsest dual frames and the dual Gabor functions of the minimal time and/or frequency supports are discussed. Algorithms and examples are provided.     

INEQUALITIES FOR MIXED INTERSECTION BODIES

In this paper, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the dual Brunn-Minkowski inequalities) are established for mixed intersection bodies.     

二重数值积分公式的高精度对偶公式及其应用

给出了计算二重积分的Simpson公式与两点高斯公式的对偶公式的构造过程,得到与之对应的高精度对偶修正解,提高了二重数值积分公式的计算精度,同时给出了二重积分的一种估值方法.最后,应用于几个典型的数值算例,计算结果表明：对偶修正解比对应的数值积分公式及其对偶公式的解有更高的计算精度和更快的收敛速度.     

Dual Orlicz–Brunn–Minkowski theory

In this paper, a dual Orlicz–Brunn–Minkowski theory is presented. An Orlicz radial sum and dual Orlicz mixed volumes are introduced. The dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality are established. The variational formula for the volume with respect to the Orlicz radial sum is proved. The equivalence between the dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality is demonstrated. Orlicz intersection bodies are defined and the Orlicz–Busemann–Petty problem is posed.     

广义概率对偶犹豫模糊语言幂集结算子在多属性决策中的应用

在对偶犹豫模糊语言集、概率对偶犹豫模糊集和广义幂集结算子的基础上,研究了在概率对偶犹豫模糊语言环境下的广义幂集结算子问题。首先,给出了概率对偶犹豫模糊语言集的定义、运算规则、得分函数、精确函数、距离测度、熵。然后,定义了广义概率对偶犹豫模糊语言幂集结算子,并研究其具有的性质。其次,提出了一种决策方法来解决集结数据之间存在相互关系的概率对偶犹豫模糊语言多属性决策问题。最后,结合相关案例验证了该方法的有效性和可行性。     

Optimal dual frames for erasures

For any given frame (for the purpose of encoding) in a finite dimensional Hilbert space, we investigate its dual frames that are optimal for erasures (for the purpose of decoding). We show that in general the canonical dual is not necessarily optimal. Moreover, optimal dual frames are not necessarily unique. We present some sufficient conditions under which the canonical dual is the unique optimal dual frame for the erasure problem. As an application, we get that the canonical dual is the only optimal dual when either the frame is induced by a group representation or the frame is uniform tight.     

Joint Similarities and Parameterizations for Dilations of Dual g -frame Pairs in Hilbert Spaces

In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.     

集值随机过程的投影

本文研究了集值可积变差随机过程的可选和可料对偶投影．当Ｂａｎａｃｈ空间Ｘ具有ＲＮＰ,其对偶空间Ｘ＊可分时,证明了Ｐｗｋｃ（Ｘ）值的可积变差过程存在唯一的可选和可料对偶投影．最后讨论了集值随机过程对偶投影的性质．     

Optimal dual frames for erasures II

We continue the investigation on optimal dual frames for erasures. We obtain an necessary and sufficient condition under which the canonical dual frames are the unique optimal dual frames for erasures. We examine several special simple conditions under which the canonical dual is either not optimal or it is optimal dual but not unique one.     

The study of dual integral equations with generalized Legendre functions

Closed form solutions for dual integral equations involving generalized Legendre functions as kernels are obtained. Connected to these dual integral equations an exact solution for dual integral equations involving sine functions as kernels is also obtained. Properties of generalized Legendre functions and the inversion theorem for the generalized Mehler-Fock transforms are used to obtain the solution of dual integral equations     

对偶导集及其应用

借助对偶范畴的思想和方法在点集拓扑学中引入了对偶导集概念,讨论了对偶导集和对偶导集运算的相关性质.并以此为基础引入了对偶连通空间的概念,讨论了对偶连通空间和连通空间之间的关系,借此给出了不连通空间的几个等价刻画.为拓扑空间的研究提供了新的途径.     

平移积分几何中的对偶运动公式

本文利用对偶混合体积建立平移积分几何中的对偶运动公式.这些公式是将关于均质积分的基本运动公式推广到对偶均质积分和对偶混合体积情形.     

Second order duality and symmetric duality for non-linear programs in complex space

A second order dual to a non-linear program with linear constraints in complex space over arbitrary polyhedral convex cones is presented and appropriate duality theorems are established. Also, a pair of second order non-linear symmetric dual programs is formulated and appropriate duality results are proved. It is shown that a second order dual gives a better bound for the objective function than does the first order dual. Some special cases are discussed.     

Distance regular graphs arising from dimensional dual hyperovals

In [12], A. Pasini and S. Yoshiara studied the distance regular graphs constructed from the Yoshiara dual hyperovals. In this note, we prove that the incidence graphs of the semibiplanes constructed from dimensional dual hyperovals are distance regular graphs if the dual hyperovals are doubly dual hyperovals (DDHOs). This generalizes the result in [12].     

Dual Quaternion Involutions and Anti-Involutions

An involution or anti-involution is a self-inverse linear mapping. In this paper, we present involutions and anti-involutions of dual quaternions. In order to do this, quaternion conjugate, dual conjugate and total conjugate are defined for a dual quaternion and these conjugates are used in some transformations in order to check whether involution or anti-involution axioms are being satisfied or not by these transformations. Finally, geometric interpretations of real quaternion and dual quaternion involutions and anti-involutions are given.     

基于对偶犹豫模糊语言变量的多属性决策方法

首先定义了对偶犹豫模糊语言变量,然后给出其运算规则、得分值函数、精确值函数、比较规则以及对偶犹豫模糊语言变量的加权算术平均算子、有序加权算术平均算子和混合平均算子。针对属性值为对偶犹豫模糊语言变量的多属性决策问题,提出了一种基于对偶犹豫模糊语言变量集结算子的多属性决策方法。最后,结合国家电网公司合作单位选择问题,验证了该方法的有效性和可行性。