A maximum principle for combinatorial Yamabe flow

This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like a heat equation on graphs, but it can be shown to not satisfy the maximum principle. The notion of a parabolic-like operator is introduced as an operator which satisfies the maximum principle, but may not be parabolic in the usual sense of operators on graphs. A maximum principle is derived for the curvature of combinatorial Yamabe flow under certain assumptions on the triangulation, and hence the heat operator is shown to be parabolic-like. The maximum principle then allows a characterization of the curvature as well was a proof of long term existence of the flow.     

Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds

In this paper we consider eigenvalues of the Dirichlet biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this inequality, we study eigenvalues of the Dirichlet biharmonic operator on compact domains in a Euclidean space or a minimal submanifold of it and a unit sphere. We obtain universal bounds on the (k+1)th eigenvalue on such objects in terms of the first k eigenvalues independent of the domains. The estimate for the (k+1)th eigenvalue of bounded domains in a Euclidean space improves an important inequality obtained recently by Cheng and Yang.     

一类Poincaré方程的中心焦点判定

本文根据计算焦点量的一类递推公式和Poincare对称原理,以计算机代数为工具,得 到了一类Poincare方程的焦点量公式,并给出了原点为中心的条件.     

利用琼斯矩阵分析全偏振光通过旋光器件的邦加球表示

用琼斯矩阵表示旋光器件．用琼斯矢量表示偏振光．计算椭圆偏振光通过旋光器件后的琼斯矢量，分析椭圆偏振光通过旋光器件的邦加球表示。结果表明．用此法得到的结论与已有结论一致。     

The Poincaré Bifurcation of a Class of Planar Hamiltonian Systems

In this paper, we discuss the Poincare bifurcation of a class of Hamiltonian systems having a region consisting of periodic cycles bounded by a parabola and a straight line. We prove that the system can generate at most two limit cycles and may generate two limit cycles after a small cubic polynomial perturbation.     

交比和Poincare度量在平面拟共形映射下的偏差

研究(1)若f是 R²到 R²上的k -拟共形映射, 则对任意x₁,x₂,x₃,x_4∈R²有16^{\frac1k-1}(|(x₁,x_2, x₃,x₄)|+1)^{\frac1k}&;\leq&; \left|\left(f(x_1), f(x_2),f(x_3),f(x_4)\right)\right|+1\\&; \leq&; 16^{k-1}\left(|(x_1,x_2,x_3,x_4)|+1\right)^{k}; \end{eqnarray*}(2)若f是R²到R²上的k -拟共形映射, D是R²中的任一真子域,则对任意x₁,x₂∈D有\begin{eqnarray*}\frac1k\lambda_D(x_1,x_2)+4(\frac1k-1)\log2&;\leq&; \lambda_{f(D)} (f(x_1),f(x_2))\\&;\leq &;k\lambda_D(x_1,x_2)+4(k-1)\log2.\end{eqnarray*}了交比和Poincar\'e度量在平面拟共形映射下的偏差估计, 得到了如下两个结果.     

The Rényi–Ulam pathological liar game with a fixed number of lies

The q-round Rényi–Ulam pathological liar game with k lies on the set [n]{1,…,n} is a 2-player perfect information zero sum game. In each round Paul chooses a subset A[n] and Carole either assigns 1 lie to each element of A or to each element of [n]A. Paul wins if after q rounds there is at least one element with k or fewer lies. The game is dual to the original Rényi–Ulam liar game for which the winning condition is that at most one element has k or fewer lies. Define to be the minimum n such that Paul can win the q-round pathological liar game with k lies and initial set [n]. For fixed k we prove that is within an absolute constant (depending only on k) of the sphere bound, ; this is already known to hold for the original Rényi–Ulam liar game due to a result of J. Spencer.     

球面稳定同伦群的γ_tl_1g_0新元素族

首先给出了May谱序列E_1~(s,t,u)项的几个结果,然后利用这些结果和关于Ext_P~(s,t)(Z_p,Z_p)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂P~i(i≥0)生成的子代数)得出了乘积(?)t (?)g0∈Ext_A~(*,*)(Z_p,Z_p)(3≤t相似文献   

Application of Planar Poincaré Chart in polarization optics

A Planar Poincar Chart which describes the polarized state of light and its change as it through a polarized device is proposed in this paper. It provides a method for polarization analysis and polarization device design.     

四维空间中的异维环分支问题

利用局部活动坐标架法,讨论了四维空间中连接两个鞍点的异维环分支问题,在一些通有的假设下,分别得到了异维环保存、同宿环、周期轨存在的充分条件以及保存的异维环与分支出的周期轨共存(或不共存)的结果.