A tensor norm preserving unconditionality for -spaces

We show that, for each , there is an -tensor norm (in the sense of Grothendieck) with the surprising property that the -tensor product has local unconditional structure for each choice of arbitrary -spaces . In fact, is the tensor norm associated to the ideal of multiple -summing -linear forms on Banach spaces.

     

Evolution of hypersurfaces by the mean curvature minus an external force field

In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.     

脑胶质瘤磁共振弥散张量成像定量参数与VEGF、MMP-9表达的相关性

本研究旨在分析脑胶质瘤患者的磁共振弥散张量成像(DTI)参数与病变组织血管内皮生长因子(VEGF)和基质金属蛋白酶-9(MMP-9)表达的相关性,以及DTI参数对脑胶质瘤进行分级诊断的价值.根据病理分级将102例脑胶质瘤患者分为低级别组(47例)和高级别组(55例),均行MRI和DTI检查,定量测定表观弥散系数(ADC...     

一般矩阵函数的变差

设Sn是n次对称群,G为Sn的子群,χ是G的次数为1的特征标.如果A是一个n阶复变矩阵,定义一般矩阵函数dχG为dχG(A)=∑σ∈Gχ(σ)∏ni=1aiσ(i).本文用lp-算子范数(1≤p≤∞)的性质证明了一般矩阵函数变差的两个不等式.     

饮用水激光拉曼光谱的比较与分析

为了对我国目前饮用水的质量进行有效检测,对市面上几种常用品牌的饮用水以及实验室提供的蒸馏水等样品做了测量和计算。运用激光拉曼光谱的分析方法,测量了它们的激光拉曼光谱。同时,通过测量计算了样品在对称伸缩振动处拉曼谱的退偏度。结果表明,在水样品的对称伸缩振动处,其拉曼谱的相对强度大小和退偏度的大小有着相同的规律。对结果进行比较和分析后得出了如下结论：可以从拉曼光谱特征峰相对强度的大小和同一特征峰下退偏度的大小两方面来判断饮用水中矿物质含量的相对多少。为鉴定饮用水的质量提供了新的有效途径。     

The Groups of Symmetric Genus σ ≤ 8

Let G be a finite group. The symmetric genus σ (G) is the minimum genus of any compact Riemann surface on which G acts faithfully as a group of automorphisms. Here we classify the groups of symmetric genus σ, for all values of σ such that 4 ≤ σ ≤ 8. In addition, we obtain some general results about the partial presentations that groups acting on surfaces must have. We show that a group with even genus and no “large order” elements in its Sylow 2-subgroup has restrictions on its Sylow 2-subgroup. As a consequence, we show that if G is a 2-group with positive symmetric genus, then σ(G) is odd. The software package MAGMA was employed to help with the calculations, and the MAGMA library of small groups was essential to the classification.     

On warped product manifolds satisfying some curvature conditions

We determine curvature properties of pseudosymmetric type of certain warped product manifolds, and in particular of generalized Robertson–Walker spacetimes, with Einsteinian or quasi-Einsteinian fibre.     

Causal structure and algebraic classification of non-dissipative linear optical media

In crystal optics and quantum electrodynamics in gravitational vacua, the propagation of light is not described by a metric, but an area metric geometry. In this article, this prompts us to study conditions for linear electrodynamics on area metric manifolds to be well-posed. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structures in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. This classification, valuable in its own right, is then employed to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes. Physically, these results classify and drastically restrict the viable constitutive tensors of non-dissipative linear optical media.     

VARIATIONAL PROPERTIES OF THE INTEGRATED MEAN CURVATURES OF TUBES IN SYMMETRIC SPACES

61. IntroductionLet P be a submanifold of an n-dimensional riemannian manifold AI. Expressions fOrthe kth integrated mean curvatures, M^P(t), (i. e. the integral of tho kth mcan curvature,k = 0, 1,' l n -- l), of a tubular hypersurface P of radius t about P, in terms of theRiemann curvature tensor of P. are calculated when AI is Euclidean or a rank one symmetricspace[5'13"1. Moreover, when P is a closed convex hypersurface of thc n-dimensional spaceof constant curvature A', Santal6 has…