修理工单重休假的Gnedenko系统算子性质

研究了一种Gnedenko系统,即由3个串联部件,一个温储备部件及一个修理工组成的系统,其中修理工可以单重休假.运用C₀半群的理论,证明了系统算子是稠定的预解正算子,得出了系统算子的共轭算子及其定义域,并证明了系统算子的增长界为0.最后运用了预解正算子中共尾的概念及相关理论,证明了系统算子的谱上界也是0.     

Benjamin方程的Bcklund变换、非线性叠加公式及无穷守恒律

利用屠格式求出了Benjamin方程的B cklund变换、精确孤波解、非线性叠加公式及其无穷守恒律·　这种算法具有普适性·     

A type of multi-component integrable hierarchy

A new isospectral problem is established by constructing a simple interesting loop algebra. A commutation operation of the loop algebra is as straightforward as the loop algebra ?_1. It follows that a type of multi-component integrable hierarchy is obtained. This can be used as a general method.     

An extension of the direct method and similarity reductions of a generalized Burgers equation with an arbitrary derivative function

In this paper,we extend the well-known direct method proposed by Clarkson and Kruskal for finding similarity reductions of partial differential equations.It follows that some new similarity reductions of the generalized Burgers equation,such as travelling wave reduction,logarithmic reduction,power reduction,rational fractional reduction,etc,are derived,in which some of these cannot be obtained solely by using the direct method.The similarity reductions obtained are interpreted by the nonclassical symmetry Lie group.     

Two expanding forms of a Lie algebra and their application

With the help of a known Lie algebra,two new high order Lie algebras are constructed.It is remarkable that they have different constructing approaches.The first Lie algebra is constructed by the definition of integrable couplings.the second one by an extension of Lie algebra,Then by making use of Tu scheme,a generalized AKNS hierarchy and another new hierarchy are obtained.As a reduction case of the first hierarchy,a kind of coupled KdV equation is presented.As a reduction case of the second one,a new coupled Schroedinger equation is given.     

Two types of traveling wave solutions to burgers-KdV equations

ＩｎｔｒｏｄｕｃｔｉｏｎＳｏｃａｌｌｅｄＢｕｒｇｅｒｓ＿ＫｄＶｅｑｕａｔｉｏｎｓａｒｅｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎｓｕｔ ｕｕｘ-αｕｘｘ βｕｘｘｘ =0 ,(1 )ｗｈｉｃｈｗａｓｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｉｎｔｒｏｄｕｃｅｄｗｈｅｎｏｎｅｓｔｕｄｉｅｄｓｏｍｅｐｈｙｓｉｃａｌｐｒｏｂｌｅｍｓｓｕｃｈａｓｌｉｑｕｉｄｆｌｏｗｓｗｉｔｈａｉｒｂｕｂｂｌｅｓ,ｔｈｅｆｌｕｉｄｉｎｔｈｅｅｌａｓｔｉｃｔｕｂｅｓａｎｄｓｏｏｎ ,ｗｈｅｒｅαａｎｄβｓｔａｎ…     

一类孤子方程族及其多个Hamilton结构

本文建立了一个含11个位势的新的等谱问题,得到了一组新的Lax对,由此得到一类新的孤子方程族.该族是Liouville可积的,具有4-Hamilton结构,且循环算子的共轭算子是一个遗传对称算子.另外,为确切说明所得方程族是一个4-Hamilton结构,在附录中证明了所得的4个Hamilton算子的线性组合恒为Hamilton算子.     

冬凌草甲素的电化学性质及电分析方法研究

研究了抗癌药物冬凌草甲素在悬汞电极上的电化学行为。在NaAc-NaOH(pH 7.8)的缓冲溶液中,冬凌草甲素有一受吸附控制的还原峰,峰电位为-1.150 V,峰电流与冬凌草甲素浓度在7.25×10-7~1.01×10-5mol/L范围内有良好的线性关系,检出限为1.45×10-7mol/L(S/N=3)。对冬凌草片剂实际样品中冬凌草甲素含量测定,结果满意。     

具有内部构造安全保障体系的冗余机器系统的解的半离散化分析

对具有内部构造安全保障体系的冗余机器系统中的修复率μ(x)用初等阶梯函数方法进行逼近,并给出了系统的半离散化模型,为进一步数值计算打下基础.     

一类S-mKdV方程族及其扩展可积模型

由loop代数的一个子代数出发，构造了一个线性等谱问题，再利用屠格式计算出了一类Liouvelle意义下的可积系统及其双Hamilton结构，作为该可积系统的约化，得到了著名的Schrdinger方程和mKdV方程，因此称该系统为S-mKdV方程族.根据已构造的的子代数，又构造了维数为5的loop代数的一个新的子代数，由此出发设计了一个线性等谱形式，再利用屠格式求得了S-mKdV方程族的一类扩展可积模型.利用这种方法还可以求BPT方程族、TB方程族等谱系的扩展可积模型.因此本方法具有普遍应用价值.最后作为特例，求得了著名的Schrdinger方程和mKdV方程的可积耦合系统.