Absolute ruin problems for the risk processes with interest and a constant dividend barrier

In this paper,the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated.First,integro-differential equations satisfied by the expected discounted dividend payments are derived.The explicit expressions are obtained when the individual claim size is expo-nential distributed.Second,the moment generating function of the discounted dividends is considered,and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived.Third,by a "differential" argument,the time to recovery to zero from a given negative surplus is considered.Finally,how long it takes for the surplus process to reach the dividend barrier is discussed.     

Multipolar model for collisional quantum interference on rotational energy transfer

A theoretical model of collisional quantum interference ( CQI) is developed in a diatom-diatom system based on the first-order Born approximation of time-dependent perturbation theory and the multipolar interaction potential. The transition cross section is obtained. The relations between the differential and integral interference angles are discussed. The key factors on the determination of the differential and integral interference angles are obtained. The changing tendency of the interference angles with the experimental temperatures is obtained.     

Electromechanical dynamics analysis and simulation on rollforming equipment with both sides variable cross-section

Electromechanical dynamics analysis and simulation on a rollforming equipment with both sides variable cross-section are discussed in this study.The system includes mechanical parts and electro-magnetism parts, and it is a strongly coupled electromechanical system.Based on a virtual work principle and given power,generalized forces of this system are obtained.By using Lagrange-Maxwell equations, a model of electromechanical dynamics is established.Differential equations of two-phase winding on d-q axis are obtained by Park transformation, which comes from three-phase winding equations on the A-B-C axis.This system is solved with the 4th order Runge-Kutta’ s method, and discrete solutions of all variables are obtained.Finally, by using Matlab language, the system is simulated.The results show that the proposed method works very well.     

无穷直线上含参变未知函数的Riemann边值问题

给出了无穷直线上一类含参变未知函数的Riemann边值问题的提法．讨论该问题的可解性，给出了该问题的可解性定理．     

Multi-Variable Non-Singular BEM for 2-D Potential Problems

A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations(BIEs) of the potential and its derivatives, where the nodal potential derivatives are considered independent of the nodal potential and flux. The system equation is solved to determine the unknown boundary potentials and fluxes, with high accuracy boundary nodal potential derivatives obtained from the solution at the same time. A modified Gaussian elimination algorithm was developed to improve the solution efficiency of the final system equation. Numerical examples verify the validity of the proposed algorithm.     

ON THE SOLUTION OF THE SINGULAR INTEGRAL EQUATIONS WITH BOTH CAUCHY AND CONVOLUTION KERNEL

The following equations are basic forms of C-K equation (which is simplified in the following as singu-lar integral equations with convolution, that is C-K equations):where a,b,a_j,b_j are known constants or known functions, and find its solution f L_P(R), {0} or {α,β}.There were rather complete investigations on the method of solution for equations of Cauchy type aswell as integral equations of convolution type. But there is not investigation to the C-K equations, nodoubt, such that is important.     

Electromagnetic tomography (EMT): image reconstruction based on the inverse problem

Starting from Maxwell's equations for inhomogeneous media, nonlinear integral equations of the inverse problem of the electromagnetic tomography (EMT) are derived, whose kernel is the dyadic Green's function for the EMT sensor with a homogeneous medium in the object space. Then in terms of ill-posedness of the inverse problem, a Tikhonov-type regularization model is established based on a linearization-approximation of the nonlinear inverse problem. Finally, an iterative algorithm of image reconstruction based on the inverse problem and reconstruction images of some object flows for simplified sensor are given. Initial results of the image reconstruction show that the algorithm based on the inverse problem is superior to those based on the linear back-projection in the quality of image reconstruction.     

Boundary Integral Equations and A Posteriori Error Estimates

Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing, Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations, Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hypersingular residuals are good a posteriori error indicators in many adaptive boundary element computations.     

Analysis of Helical Gear System Dynamic Response Based on Fuzzy Numbers

A non-linear dynamic model with the single degree of freedom of a helical gear pair introducing fuzzy numbers is developed. In this proposed model, time-variant mesh stiffness, which is a non-linear parameter, mesh damping and composite error of a pair of meshing tooth of the gear pair are all included. Mesh stiffness is calculated by expressing Bθ (τ) as a Fourier series. Π shape function is introduced as the membership function to characterize the fuzziness of the error. Fuzzy displacement dynamic response of the geared system at λ- level, which is a closed interval, is obtained by removing the fuzziness of the fuzzy differential equations and using Runge-Kutta numerical method. In fact, the fuzzy dynamic response and dynamic loading factor are all the interval functions related λ. The result obtained here can be used to the fuzzy dynamic optimization design course of the helical gear system. The main advantage of this method is to introduce the concept of fuzzy number for the first time to the a     

A generalized block-by-block method for the system of linear Volterra integral equations of the second kind

In this paper,we provide a generalized block-by-block method for constructing block-by-block systems to solve the system of linear Volterra integral equations of the second kind,and then deduce some of the special cases.Compared with the expansion method and He’s homotopy perturbation method,respectively,numerical examples are given to certify the effectiveness of the method.The results show that the block-by-block method is very effective,simple,and of high accuracy in solving the system of linear Volterra integral equations of the second kind.     

一类二阶非线性中立型泛函微分方程的振动性

本文通过引入参数函数,结合完全平方术,研究了一类二阶非线性中立型泛函微分方程解的振动性,所得结果推广了已有文献的部分结果.     

一类二阶非线性微分方程解的振动性

讨论一类二阶非线性中立型微分方程,通过引入参数函数,结合完全平方技术,给出了该类方程解振动的判别准则,改进并推广了已有文献中的相应结果.     

含三角函数的一般形式对偶积分方程组的理论解

将Copson法推广、应用于一般形式的对偶积分方程组的求解。首先引入函数进行方程组变换,其次引入未知函数的积分变换实现退耦。应用Abel反演变换,使方程组正则化为Fredholm第二类积分方程组,并由此给出对偶积分方程组的一般性解。给出的解法和理论解,作为求解复杂的对偶积分方程组另一种有效的解法,可供求解复杂的数学、物理、力学中的混合边值问题参考。     

两对边简支单向变刚度矩形板的弯曲问题

本文通过做未知函数变换，将两对边简支单向变刚度矩形板在任意横向分布载荷作用下的弯曲问题归结为求解第二类的Ｖｏｌｔｅｒｒａ积分方程。对上述积分方程，建议了二次样条函数的近似解法，求得了问题的渐近解析解。为了检验方法的有效性并说明其应用，对线性变厚度的形做了数值计算，所得结果和精确解符合得很好。     

二元积分不等式的若干推广及应用

在本文中,我们主要研究一类具有时滞的二元非线性积分不等式. 在不要求已知函数的单调性和可微性的条件下,通过将不等式中的函数单调化和积分号外函数作常量化的方法, 给出这类不等式中未知函数的估计, 并且以推论形式给出相应的一元积分不等式中未知函数的解的估计. 最后, 利用该估计证明了一类积分方程和一类微分方程的解的有界性.     

两相材料倾斜裂纹的界面应力场

采用Muskhelishvili复变函数的方法,将两相材料倾斜裂纹问题归结以裂纹表面位错密度函数和未知量的Cauchy型奇异积分方程的求解。通过Cauchy型奇异积分的主部分析,得到倾斜裂纹接触界面时性态指数的特征方程,给出的数值结果可对奇异积分方程进行数值求解。根据两相材料倾斜裂纹在界面上产生的应力场与位错密度函数的关系,得到界面常规应力场及奇性应力场表达式。最后对两相材料的界面应力场进行了数值求解和分析,数值结果令人满意。     

一类含有未知导函数的三重积分不等式中未知函数的估计

研究了一类非线性三重积分不等式,其中被积函数中含有未知函数及其导函数,积分项外包含了非常数项.利用变量替换技巧、放大技巧和反函数技巧等分析手段,给出了三重积分-微分不等式中未知函数的显上界估计,推广了已有结果.最后举例说明所得结果可以用来研究微分-积分方程解的估计.     

具有任意次非线性项的演化方程的有理函数积分法

引入了一种求解具有任意次非线性项的演化方程精确解的有理函数积分法,该方法将未知函数的一阶导数展开为未知函数的多项式,通过齐次平衡法确定多项式的次数,然后利用有理函数积分法求解未知函数.通过对Klein-Gordon 方程和广义 Fithugh-Nagumo方程求解,表明所引入的有理函数积分法的有效性与便捷性.     

汶川地震断层应力强度因子分析超奇异积分法

 地震作为复杂瞬态断裂破坏物理过程,其机制研究是一个多学科交叉问题;同震断层处应力/能量积累释放规律,为从断裂角度研究地震机制提供了一个切入点;应力强度因子（应力角度）和应变能强度因子（能量角度）是断裂力学/物理学的两个最基本的参数。本文应用非线性边界元和主部分析法,将汶川地震断层破坏过程转化为解以断层位移间断为未知函数超奇异积分方程组问题,定义了断层处应力强度因子;利用有限部积分概念及体积力法,为方程组建立了数值解法,编制了Fortran程序,得到断层处应力强度因子数值结果;通过研究应力强度因子随断层位置变化规律,分析了汶川地震断层破坏过程;结合应变能强度因子理论,通过对宏微观电磁破坏过程进一步深入模拟研究可得到电磁辐射破坏变化规律,为地震短临预测提供理论支持和帮助。     

一类新的非线性时滞积分不等式及其应用

在文献(C.J.Chen,W.S.Cheung,D.Zhao.J.Inequ.Appl.,2009,2009:258569.)的基础上研究了一类更广泛的非线性时滞积分不等式,增加了两项非线性因子.尤其是参考文献中不等式右端的第一个积分项只含有未知函数的线性因子,而研究的不等式右端的第一个积分项包含了未知函数的非线性因子.最后,把研究不等式得到的结果用于研究微分方程解的估计.