~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.     

一阶混合单调脉冲微分方程解的存在性

脉冲微分方程理论是微分方程的一个重要分支，混合单调迭代技术是其重要基础之一。在Banach空间中，利用混合单调迭代技术及Shaulder不动点定理，考虑混合单调脉冲微分方程初值问题，给出方程解和藕合最大最小解的存在性定理及单调迭代方法。     

广义Morrey空间中奇异积分算子和极大算子的加权不等式

证明了广义极大算子和奇异积分算子在广义Merrey空间中的加权不等式，并且还得到了极大算子无权不等式的特征。     

一类广义Bent型S-Box的构造

S-box是密码理论与实践中十分重要的一种装置 ,它的密码性能由其分量函数所决定 .于是 ,选择适当的分量函数来构造 S-box就成了一个重要的研究课题 .在一定意义上 ,Bent函数是最优良的密码函数 .本文通过函数序列半群和置换群来构造其任何非零线性组合为 Bent函数与线性函数之和的函数组 ,从而可由 Bent函数构造出具有高度非线性度和其他良好性状的 S-box     

M.Riesz定理的注记

设u(z)是单位圆内的实值调和函数 ,若 p_平均Mp(r ,u) =12π∫2π0｜u(reiθ) ｜pdθ1 p <∞ ,则称u(z) ∈hp( 1

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