Nonlocal boundary value problem for fractional differential equations with p‐Laplacian

In this paper, we are concerned with the existence of positive solutions for the following nonlocal BVP of fractional DEs with p‐Laplacian operator By using the fixed point theorem in a cone, multiplicity solutions of the BVP are obtained. An example is also given to show the effectiveness of the obtained result. Copyright © 2013 John Wiley & Sons, Ltd.     

Orlicz mixed quermassintegrals

The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy-Kubota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.     

A projection subgradient method for solving optimization with variational inequality constraints

In this paper, we propose a projection subgradient method for solving some classical variational inequality problem over the set of solutions of mixed variational inequalities. Under the conditions that $T$ is a $\Theta $ -pseudomonotone mapping and $A$ is a $\rho $ -strongly pseudomonotone mapping, we prove the convergence of the algorithm constructed by projection subgradient method. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints.     

Orlicz–John ellipsoids

The Orlicz–John ellipsoids, which are in the framework of the booming Orlicz Brunn–Minkowski theory, are introduced for the first time. It turns out that they are generalizations of the classical John ellipsoid and the evolved _Lp$L_p$ John ellipsoids. The analog of Ball's volume-ratio inequality is established for the new Orlicz–John ellipsoids. The connection between the isotropy of measures and the characterization of Orlicz–John ellipsoids is demonstrated.     

判定离散Hopfield神经网络稳定性的新方法

寻求判断离散Hofield神经网络稳定性的新判据。具体考虑神经元的权值矩阵元素和阀值之间的关系，依此判断能量函数的收敛性，得到了一个与阀值无关、不需权值矩阵对称的新判据；在新判据的基础上作出数学变形和分析，并用线性方程的解去刻划稳定点的存在性，得到了稳定点存在的一个充要条件。最后将离散Hopfield神经网络的稳定点存在问题转化为在有限区域内连续函数的零点解的问题。     

一种改进的模糊阈值选取方法

提出了一种改进的模糊阈值选取方法。针对传统的模糊阈值法隶属函数窗宽不容易确定的出发点，结合传统的易于实现的阈值选取方法，巧妙的绕过了确定窗宽的问题，能够结合模糊阈值法和该传统阈值法各自所能达到的优点，并且方法非常简单，明了。实践证明，这种方法是行之有效的，并具有较强的场景适应能力。     

小麦液泡膜H~ -ATPase的Ca~(2 )激活特性

纯化小麦液泡膜H -ATPase,测定了纯化的小麦液泡膜H -ATPase 受Mg2 和Ca2 双重激活的特性及两种激活状态下酶的特性. Mg2 激活时酶水解活性受DCCD的抑制,受磷脂酰丝氨酸(PS)影响明显,ATP水解和泵质子活性相偶联.而在Ca2 激活时酶水解活性不受DCCD抑制,受PS影响微弱,Ca2 激活时ATP水解与泵质子活性解偶联. Mg2 和Ca2 对小麦液泡膜H -ATPase的激活作用不具有叠加效应.     

黄铜选择性溶解固相扩散机理的研究

采用恒电位暂态和旋转盘环电极等方法研究了α、α＋β以及β黄铜在硫酸钠、硫酸以及氯化钠的稀溶液中的阳极溶解过程．结果表明，在黄铜阳极溶解的初始阶段测得的ｉ－ｔ曲线遵循抛物线定律，求得ｉ－ｔ为一通过坐标原点的直线，证明了黄铜中锌的选择性溶解受固相扩散控制，计算出在上述溶液中黄铜中锌的扩散系数值在１０－１５～１０－１３ｃｍ２·ｓ－１数量级，介质成分和微量合金元素砷对扩散系数值有明显的影响．     

[0,1]区间上的r重正交多小波基

本文利用L2（R）上的紧支撑正交的多尺度函数和多小波构造出有限区间[0,1]上的正交多尺度函数及相应的正交多小波.本文构造的逼近空间Vj[0,1]与相应的小波子空间Wj[0,1]具有维数相同的特点,从而给它的应用带来巨大方便.最后给出重数为2时的[0,1]区间上的正交多小波基构造算例.