Very Hyperbolic Polynomials

A real polynomial in one variable is hyperbolic if it has only real roots. A function f is a primitive of order k of a function g if f ^(k) = g. A hyperbolic polynomial is very hyperbolic if it has hyperbolic primitives of all orders. In the paper, we prove a property of the domain of very hyperbolic polynomials and describe this domain in the case of degree 4.     

三类多双曲复方程组的Riemann-Hilbert边值问题

用函数论的方法研究了三类超定双曲型方程组的解,即三类多双曲复方程组在一般柱形域上的Riemann-Hilbert边值问题的提法,可解条件,解的表示,唯一性和存在性.     

确定有限域上给定周期的不可约多项式的个数以及利用低次不可约多项式构造高次不可约多项式

主要利用较献[4]更为简明的方法证明了有关有限域Fq(q为一个素数幂）上的以l为周期的n次不可约多项式的个数的结论。另外，本结合结合初等数论知识得到了前面这个结论的几个推论，并对利用低次不可约多项式构造高次不可约多项式进行了研究。     

四维Minkowski空间中类空超曲面的双曲高斯映射的奇点

介绍了四维Minkowski空间中类空超曲面的局部理论,定义了类空超曲面上的双曲高斯映射,双曲高度函数及距离平方函数,给出了一些定理的详细证明.介绍了一种证明高度函数是Morse族的新方法并应用Arnold等建立的Lagrange奇点理论对类空超曲面的双曲高斯映射的奇点进行了分类.     

唯一分解整环R上不可约多项式的一个判别准则

本获得了一个判别唯一分解整环R及其商域Q上的n次（n＞2)多项式不可约的充分条件。     

Hyperbolicity, heterodimensional cycles and Lyapunov exponents for partially hyperbolic dynamics

We prove a dichotomy of C² partially hyperbolic sets with one-dimensional center direction admitting no zero Lyapunov exponents, either hyperbolicity over the supports of ergodic measures or approximation by a heterodimensional cycle. This provides a partial result to the C¹ Palis Conjecture that claims a dichotomy, hyperbolicity or homoclinic bifurcations in a dense subset of the space of C¹ diffeomorphisms. Moreover, a theorem of Ma?é applied in the proof is modified to have an additional property concerning the Hausdorff distance between a periodic orbit and the support of a hyperbolic ergodic measure.     

Bezout Rings,Polynomials, and Distributivity

Let A be a ring, be an injective endomorphism of A, and let be the right skew polynomial ring. If all right annihilator ideals of A are ideals, then R is a right Bezout ring is a right Rickartian right Bezout ring, (e)=e for every central idempotent eA, and the element (a) is invertible in A for every regular aA. If A is strongly regular and n 2, then R/x ⁿ R is a right Bezout ring R/x ⁿ R is a right distributive ring R/x ⁿ R is a right invariant ring (e)=e for every central idempotent eA. The ring R/x ² R is right distributive R/x ⁿ R is right distributive for every positive integer n A is right or left Rickartian and right distributive, (e)=e for every central idempotent eA and the (a) is invertible in A for every regular aA. If A is a ring which is a finitely generated module over its center, then A[x] is a right Bezout ring A[x]/x ² A[x] is a right Bezout ring A is a regular ring.     

Radon, Cosine and Sine Transforms on Real Hyperbolic Space

New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 1dn−1, in terms of polynomials of the Laplace–Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms.     

Discreteness Criterions of Isometric Subgroups for Quaternionic Hyperbolic Space

In this paper, we give analogue of Jörgensen's inequality for nonelementary groups of isometries of complex hyperbolic 2-space generated by two elements, one of which is either loxodromic or boundary elliptic for the same group of isometries of quaternionic hyperbolic 2-space. And we give a sufficient condition for a nonelementary subgroup of isometries of quaternionic hyperbolic 2-space generated by two elements one of which is parabolic not to be discrete.     

Integrally Closed Domains,Minimal Polynomials,and Null Ideals of Matrices

Abstract

We show that every element of the integral closure D′ of a domain D occurs as a coefficient of the minimal polynomial of a matrix with entries in D. This answers affirmatively a question of Brewer and Richman, namely, if integrally closed domains are characterized by the property that the minimal polynomial of every square matrix with entries in D is in D[x]. It follows that a domain D is integrally closed if and only if for every matrix A with entries in D the null ideal of A, N _D (A)?=?{f?∈?D[x]?∣?f(A)?=?0} is a principal ideal of D[x].     

唯一分解整环R上不可约多项式的若干结构

本文在唯一分解整环Ｒ上引入隐含同余和非隐含同余概念．从而获得Ｒ上多项式不可约性的若干结构．一百多年来首次对著名的Ｅｉｓｅｎｓｔｅｉｎ不可约定理作出重要推广     

求解双曲守恒律方程的三阶修正模板WENO格式北大核心CSCD

为了降低经典的三阶加权本质无振荡(WENO)格式的数值耗散,提出了一种新的三阶WENO格式的修正模板近似方法.改进了经典WENO-JS格式中各候选模板上数值通量的一阶多项式逼近,通过加入二次项使模板逼近达到三阶精度.计算了相应的候选通量,并且通过引入可调函数φ(x),使得新的格式具有ENO性质.最后给出了一系列数值算例,证明了该方法的有效性.     

三步完全可化约拟线性双曲组型方程组的整体经典解

本文对三步完全可化约拟线性双曲型方程组的整体经典解进行讨论，得到了整体经典解的存在性．这一结果说明非线性特征向量也可能引发奇性．     

退化高阶伯努利多项式与广义等幂和多项式的对称等式

研究了退化伯努利多项式与广义等幂和多项式的对称关系,获得了关于多个退化高阶伯努利多项式与广义等幂和多项式的若干对称关系.     

Hyperbolic Programs, and Their Derivative Relaxations

We study the algebraic and facial structures of hyperbolic programs, and examine natural relaxations of hyperbolic programs, the relaxations themselves being hyperbolic programs.     

Upper and Lower Bounds on Resonances for Manifolds Hyperbolic Near Infinity

For a conformally compact manifold that is hyperbolic near infinity and of dimension n + 1, we complete the proof of the optimal O(r ⁿ⁺¹) upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we establish a Poisson formula expressing the regularized wave trace as a sum over scattering resonances. This leads to an r ⁿ⁺¹ lower bound on the counting function for scattering poles.