Stable Stationary Harmonic Maps to Spheres

For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S^k. We show that the singular set of stable-stationary harmonic maps from B5 to 83 is the union of finitely many isolated singular points and finitely many HSlder continuous curves. We also discuss the minimization problem among continuous maps from B^n to S^2.     

Generalized Solution of a Kind of Nonparametric Curvature Evolution with Boundary Condition

The existence and uniqueness of the generalized solution for a kind of nonparametric curvature flow problem are obtained. This kind of curvature flow problem describes the evolution of graphs with speed depending on the reciprocal of the Gauss curvature.     

Inverse-preserving Linear Maps Between Spaces of Matrices over Fields

Suppose F is a field different from F2, the field with two elements. Let Mn（F） and Sn（F） be the space of n × n full matrices and the space of n ×n symmetric matrices over F, respectively. For any G1, G2 ∈ {Sn（F）, Mn（F）}, we say that a linear map f from G1 to G2 is inverse-preserving if f（X）^-1 = f（X^-1） for every invertible X ∈ G1. Let L （G1, G2） denote the set of all inverse-preserving linear maps from G1 to G2. In this paper the sets .L（Sn（F）,Mn（F））, L（Sn（F）,Sn（F））, L （Mn（F）,Mn（F）） and L（Mn （F）, Sn （F）） are characterized.     

一类阶为偶数的高斯和显式计算的注记

给出指数2情形下阶数为2l_1~(r1)l_1~(r2)的高斯和的显式计算公式.证明方法直接利用Stickelberger理想分解定理,进而结果独立于其他指数2情形高斯和的结果而成立.     

EXISTENCE PROBLEMS OF ADDITIVE SELECTION MAPS FOR ANOTHER TYPE SUBADDITIVE SET-VALUED MAP

In this paper,we consider the following subadditive set-valued map F:X → P 0 (Y):F r ∑ i=1 x i + s ∑ j=1 x r+ j rF r ∑ i=1 x i r + sF s ∑ j=1 x r+ j s, x i ∈ X,i=1,2,,r + s,where r and s are two natural numbers.And we discuss the existence and unique problem of additive selection maps for the above set-valued map.     

Vibrational resonance in biological nonlinear maps

We investigate vibrational resonance in two different nonlinear maps driven by a biharmonic force: the Bellows and the Rulkov map. These two maps possess dynamical features of particular interest for the study of these phenomena. In both maps, the resonance occurs at the low-frequency of the biharmonic signal as the amplitude of the high-frequency signal is varied. We also consider an array of unidirectionally coupled maps with the forcing signal applied to the first unit. In this case, a signal propagation with several interesting features above a critical value of the coupling strength is found, while the response amplitude of the ith unit is greater than the first one. This response evolves in a sigmoidal fashion with the system number i, meaning that at some point the amplitudes saturate. The unidirectional coupling acts as a low-pass filter for distant units. Moreover, the analysis of the mean residence time of the trajectory in a given region of the phase space unveils a multiresonance mechanism in the coupled map system. These results point at the relevance of the discrete-time models for the study of resonance phenomena, since analyses and simulations are much easier than for continuous-time models.     

Sign or root of unity ambiguities of certain Gauss sums

Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite field with q elements. Recently, the problem of explicit evaluation of Gauss sums in the small index case has been studied in several papers. In the process of the evaluation, it is realized that a sign (or a root of unity) ambiguity unavoidably occurs. These papers determined the ambiguities by the congruences modulo L, where L is certain divisor of the order of Gauss sum. However, such method is unavailable in some situations. This paper presents a new method to determine the sign (root of unity) ambiguities of Gauss sums in the index 2 case and index 4 case, which is not only suitable for all the situations with q being odd, but also comparatively more efficient and uniform than the previous method.     

广义de Sitter空间中法向Lorentzian超曲面的nullcone Gauss映射的奇点

利用奇点理论研究了广义de Sitter空间中具有Lorentzian法空间的一类超曲面.介绍了这类超曲面的局部微分几何,定义了nullcone Gauss映射及nullcone高度函数族,进而研究了nullcone高度函数族的性质及nullcone高斯映射的几何意义,最后研究了这类超曲面的通有性质.     

Gauss型函数方程与Moskovitz幂型平均值的新特征

针对Moskovitz幂型平均值,探讨了Gauss型函数方程的求解.得到了它的新特征.作为应用,给出并验证了调和平均、几何平均、算术平均和反调和平均的Gauss特征.     

靶流形为球面子流形的调和映射的量子化现象(英文)

本文研究了调和映射和极小子流形的量子化性质.通过运用谱分解方法,获得了靶流形为球面子流形的调和映射的量子化性质,然后将其应用到球面的极小子流形的高斯映射,得到了极小子流形的第二基本形式的量子化性子.