一类非线性Schr(o)dinger方程的非协调有限元分析

在半离散格式下研究一类带幂次非线性项的Schr(o)dinger方程的非协调矩形EQrot1元方法.直接利用插值技巧和该单元的两个特殊性质(相容误差比插值误差高一阶及其插值算子与传统的Ritz投影是一致的),给出相应的收敛性分析及误差估计.     

An image joint compression-encryption algorithm based on adaptive arithmetic coding

Through a series of studies on arithmetic coding and arithmetic encryption, a novel image joint compression- encryption algorithm based on adaptive arithmetic coding is proposed. The contexts produced in the process of image compression are modified by keys in order to achieve image joint compression encryption. Combined with the bit-plane coding technique, the discrete wavelet transform coefficients in different resolutions can be encrypted respectively with different keys, so that the resolution selective encryption is realized to meet different application needs. Zero-tree coding is improved, and adaptive arithmetic coding is introduced. Then, the proposed joint compression-encryption algorithm is simulated. The simulation results show that as long as the parameters are selected appropriately, the compression efficiency of proposed image joint compression-encryption algorithm is basically identical to that of the original image compression algorithm, and the security of the proposed algorithm is better than the joint encryption algorithm based on interval splitting.     

利用概率分布巧证不等式

文[1]巧妙地建立一维离散型随机变量X的概率分布,并利用其方差的非负性(D(X)=E(X2)-(E(X))2≥0,当且仅当X服从退化分布时等号成立)给出了柯西不等式的一种构造证法,笔者读后颇受启发,也尝试用该法证明了一些不等式,写在这里与读者分享.     

例谈隐含的轨迹问题

在江苏省数学高考中,动点轨迹问题的要求低.考纲选修部分只要求了解,必修部分甚至没有求.在实际教学中,我们对这一问题的处理,既不象以前一样必欲穷尽其中的各种技巧,也不能避不谈,忽视其中的基本方法.其原因有以下三点:(1)求动点轨迹方程是解析几何的基本问题.解析几何的基本思想是用代数的方法来研究几何题,它的基本方法是坐标法,即通过坐标把几何问表示成代数形式,然后通过代数方程来表示和研曲线.此两者相辅相成,缺一不可.(2)解决几何中的动态问题是解析几何的基意义所在,也最能体现其作为一种数学方法的优性.笛卡尔与费马创立解析几何的初衷,便是为了究变量数学.在高中解析几何中,点、直线与圆是     

直来直去证明不等式

文[1]通过构造长方体,利用代换方法证明了一些代数和三角不等式,读后很受启发,构造与变更,实现了问题的转化,获得证明不等式的一种有效途径.笔者的持续思考是,对于这些不等式,能不能直来直去的给出更加简明的证明方法呢?经探究是可简化的,这只要进行适度的代数变形,利用均值不等式、柯西不等式以及放缩技巧,笔者从高中教材基础知识出发给出直接证法,作为一份课程资源,供读者学习时参考.     

On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus

In the present paper, the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given. In the meantime, the solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov’s positive annulus in ?³.     

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.     

ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a Cr(r > 1) cons...     

MATHEMATICAL ANALYSIS OF WEST NILE VIRUS MODEL WITH DISCRETE DELAYS

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics,...