Riemann problem for a geometrical optics system

The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left(right)-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis.     

Uniform exponential attractor for nonautonomous partly dissipative lattice dynamical system

In this paper,we consider the existence of a uniform exponential attractor for the nonautonomous partly dissipative lattice dynamical system with quasiperiodic external forces.     

Efficient statistical inference for partially nonlinear errors-in-variables models

In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.     

Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line

In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.     

让学生欣赏数学美——“姐妹”双曲线与双曲线的“姐妹”圆

<正>你是sin我是cos,无论tan还是cot,我都一样爱你.你说我们是永不相交的平行线,我却只想下辈子与你,在非欧几何里相见.我们就是sin和cos总能形成的闭合曲线,我外冷你内热最终凝结成鲁珀特之泪平和一处,或在傅里叶变换里回望过去点滴或在裂纹扩展中开始未来星光.以上是在网上受到热捧的数学类理科生三行情诗作品之一.正如克莱因所说:"数学是人类最高超的智力成就,也是人类心灵最独特的创作,音乐能激励或抚慰人的情怀,绘画使人赏心悦目,诗歌能动人     

循环逆M-矩阵的判定

给出了循环逆M-矩阵的判定方法:如果一个n×n非负循环矩阵非正且不等于c0I,若存在一个正整数K是n的真因子,使得cjk0,j=0,1[,…,n-k]k,其余的ci等于0且Circ[c0,ck,…,cn-k]是一个逆M-矩阵,则A是一个逆M-矩阵.     

带有无界势和一般时间频率的非周期离散非线性Schr#246;dinger方程：无穷多个孤立子

本文研究下面的非周期离散非线性Schrödinger 方程：
-Δu_n + v_nu_n - ωun = g_n（u_n）,n ∈ Z,
其中V = {v_n}_n∈Z 和g_n 都是非周期的,当|n| → +∞ 时,v_n → +∞,并且时间频率ω ∈ R 可以满足下面的任何一种情形：（1）ω 属于算子-Δ + V 的一个有限谱间隔;（2）ω < inf σ（-Δ + V）;（3）ω ∈ σ（-Δ+ V）,其中σ（-Δ+ V）表示-Δ+ V的谱. 本文将用一些局部条件（在无穷远或零处）来代替一些全局条件. 利用变化的喷泉定理,当非线性项在无穷远处是超线性时,本文得到这个方程的无穷多个非平凡孤立子,并且,也得到指数衰减的孤立子的存在性.     

二元三次样条空间S31,2(Δmn(2)) 的样条拟插值

本文首先利用由两组具有局部最小支集的样条所组成的基函数,构造非均匀2 型三角剖分上二元三次样条空间S₃^1,2(Δ_mn⁽²⁾)的若干样条拟插值算子. 这些变差缩减算子由样条函数B_ij¹支集上5 个网格点或中心和样条函数B_ij²支集上5 个网格点处函数值定义. 这些样条拟插值算子具有较好的逼近性,甚至算子V_mn（f） 能保持近最优的三次多项式性. 然后利用连续模,分析样条拟插值算子V_mn（f）一致逼近于充分光滑的实函数. 最后推导误差估计.     

具有较少非循环子群共轭类的有限群

设G是有限群,用δ(G)表示群G的非循环子群的共轭类数,πr(G)表示整除|G|的素因子的集合.本文主要研究满足条件δ(G)≤|π(G)|+1的有限群,得到这类群可解,并给出它们的同构分类进一步证明,δ(G)=|π(G)|+2的有限非可解群必同构于A_5或SL(2,5).     

Morse理论及其在一类N-Laplacian方程中的应用

研究了一类次临界增长的N-Laplacian方程.利用Trudinger-Moser不等式和Morse理论,证明了在不具有山路引理的几何性质、不满足Ambrosetti-Rabinowitz条件及整体符号条件下,该方程非平凡解的存在性.