椭球的Orlicz质心体(英文)

主要研究了Lutwak等所引入的Orlicz质心体(Lutwak E,Yang D,Zhang G.Orliczcentroid bodies.J.Differential Geom.,2010,84:365-387).利用Orlicz质心体在线性变换下的不变性,证明了椭球的Orlicz质心体仍是椭球.作为例子,计算了当取两个特定的凸函数时单位球的Orlicz质心体的支持函数.     

非自治p(t)-拉普拉斯系统周期解的存在性

本文研究一类非自治p(t)-Laplace系统.利用鞍点定理和极小作用原理,获得了周期解存在的充分条件,推广和改进了文献[8]中的结果.     

关于新几何体Γ_(-p)K的几个不等式

本文研究了新几何体Γ_(-p)K与L_p-质心体和L_p-John椭球有关的几个有趣不等式,包括L_p-Busemann-Petty质心不等式的一种隔离,同时探讨了新几何体Γ_(-p)K的单调性．     

相对于余挠对的维数(英文)

本文介绍了右R-模的F-维数(C-维数)以及环R上整体F-维数(C-维数).利用同调方法,给出了平坦模维数的新刻画.另外,得到了von Neumann正则环和完全环的新刻画.     

关于可构成实数在Lω1中分布的几个定理

任何一个可构成实数都是在L_ω1中构成的。本文指出,并不是L_ω1前面的每一层都会产生新的实数,并用元数学的方法(或者就是模型的方法)对这样的层作了宏观上的描述。     

混合新几何体Γ_(-p，i)K的不等式

近来,Lutwak,Yang和Zhang提出了新几何体Γ_(-p)K的概念,获得一些结论.本文引入混合新几何体Γ_(-p,i)K的概念,即新几何体是它的特殊类,得到了混合新几何体的一些性质,并建立了相关的不等式.     

关于Orlicz凸体的收敛性的注(英文)

本文研究了Orlicz投影体和Orlicz质心体的性质.利用几何分析的方法,获得了Orlicz投影算子和Orlicz质心算子的连续性.     

关于Petty投影不等式猜想Lp-版本的几个不等式

本文研究了关于投影不等式的Petty猜想这个凸体理论中的一个著名公开问题.利用凸体的Lp-Brunn-Minkowski-Firey理论,建立了Petty投影不等式猜想的Lp-版本的几个不同精度的不等式,推广了已有文献的结论.     

关于一类弱Berwald的(α,β)-度量

本文研究了一类重要的形如F=α +εβ +β arctan(β/α) (ε为常数)的弱Berwald (α, β)-度量.利用S-曲率公式,获得了这类度量为弱Berwald度量的充要条件.并且还证明了F为具有标量旗曲率的弱Berwald度量当且仅当它们为Berwald度量且旗曲率消失.     

SL(2,R)上一类极大算子的(H∞,s1,L1)型

本文我们引入了函数类B_δ(G//K)={φ∈L¹(G//K)||φ(t)|≤Δ^-1(t)(1+t)^1-δ,δ>0),对f∈L^p(G//K),1≤p≤∞,和极大算子(?),证明了这类算子是(H_∞,s¹,L¹)型的.     

Lp-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables

The properties of L₂-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of L₂-approximable sequences since 1976 when Moussatat introduced a narrower notion of L₂-generated sequences. The method relies on a study of certain linear operators in the spaces L_p and l_p. A criterion of L_p-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.     

在险值与Lp-空间上的连续一致风险度量

本文研究了在险值和L^p-空间上的连续一致风险度量之间的关系.利用凸集分离定理和截尾逼近方法,获得了在险值可以用L^p-空间上的连续一致风险度量表示的结果,并且得到了L^p-空间上的表示定理的一种新的证明方法.它们分别是文献[2]的相关结论从L^∞-空间到L^p-空间上的推广和对Inoue^[4]做的一些补充证明.     

Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous data

In this paper we investigate vector-valued parabolic initial boundary value problems , subject to general boundary conditions in domains G in with compact C ^2m -boundary. The top-order coefficients of are assumed to be continuous. We characterize optimal L ^p -L ^q -regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on and the Lopatinskii–Shapiro condition on are necessary for these L ^p -L ^q -estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.      

Counting cycles and finite dimensional L norms

We obtain sharp bounds for the number of n-cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. We prove sharp estimates on both ∑_i=1ⁿx_i^k and ∑_i=1ⁿ|x_i|^k, subject to the constraints that ∑_i=1ⁿx_i²=C and ∑_i=1ⁿx_i=0.     

On -topological vector spaces generated by a co-tower of L-topological vector spaces

In this paper, a characterization for an I(L)-topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I(L)-topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I(L)-topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I(L)-topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too.     

Distributions of class Lα

L_α (0 α 1) is a class of infinitely divisible distributions defined by restricting the measure in the Levy-Khinchin formula to a special form. When α = 1, L_α is just the classical class L. Several properties for L_α classes, which are similar to the most important properties for the class L, are established. Also, a conjecture of Wolfe about unimodality of some L_α distributions is disproved by giving a counterexample.     

Additive L-theory

The cobordism groups of quadratic Poincaré complexes in an additive category with involution are identified with the Wall L-groups of quadratic forms and formations in , generalizing earlier work for modules over a ring with involution by avoiding kernels and cokernels.     

The L p -curvature images of convex bodies and L p -projection bodies

Associated with the L _p -curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L _p -projection bodies are established. As a natural extension of a result due to Lutwak, an L _p -type affine isoperimetric inequality, whose special cases are L _p -Busemann-Petty centroid inequality and L _p -affine projection inequality, respectively, is established. Some L _p -mixed volume inequalities involving L _p -projection bodies are also established.     

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.     

环Fp+vFp上互补对偶常循环码

本文研究了环F_p+vF_p上互补对偶（1-2v）-常循环码.利用环F_p+vF_p上（1-2v）-常循环码的分解式C=vC_1-v ⊕（1-v）C_v,得到了环F_p+vF_p上互补对偶（1-2v）-常循环码的生成多项式.然后借助从F_p+vF_p到F_p²的Gray映射,证明了环F_p+vF_p上互补对偶（1-2v）-常循环码的Gray像是F_p的互补对偶循环码.