The ellipsoidal coordinates and the square root characteristics of the displacement jumps across the crack surface are cleverly used in the hypersingular integral equations for an arbitrary planar crack embedded into the infinite three dimensional homogeneous elastic solid.

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Advanced course covering topics selected from: semimartingale theory, stochastic integrals, homogeneous chaos expansions, stochastic differential equations, Malliavin calculus, infinite dimensional processes, functional central limit theorems, Feynman-Kac formula, Feynman integral.

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Fourier analysis consists of Fourier series which can solve limited one-dimensional space Heat-conduction question and Fourier integral which can solve infinite one-dimensional space Heat-conduction question. This is more systematic compared with the other methods, and embodies corresponding beauty of Mathematics to Physics.

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A.Cayleys modern thought that looked matrix upon as a hypercomplex developed to the early days of the 20~ century from the end of the 19~ century. Infinite matrix theory and the matrix theory on abstract region investigated further since the development on integral equation and modern physics.

凱萊把超復(fù)數(shù)視為矩陣的思想在19世紀(jì)未至20世紀(jì)初得到發(fā)展taoseav1，由于積分方程的發(fā)展以及近代物理的需要數(shù)學(xué)家們開始了對無限矩陣?yán)碚撊蘸磺悠怠⒃貙儆诔橄笥虻木仃嚨难芯俊?/p>

Thus we available defined a fuzzy Henstock integral on infinite interval.

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However, due to the oscillation and singularity of the integrand of Green's function and that integral interval is infinite, it is difficult to compute the function and to control the accuracy.

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Gerber-Shiu discounted penalty function is studied and a solution is obtained to the iuntegro-differertial eqution which is in the form of an infinite series by means of integral transform.

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It has important significance to consider backward stochastic Volterra type integral equation in infinite dimensional space.By a similar calculation as in the second part,we study this kind of equations driven by cylindrical Brownian motion under non-Lipschitz condition.

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In this paper, we will introduce the weighted modulus of smoothness and the weighted K-functional to discuss the direct and the converse theorems, the local saturation results on the simultaneous approximation on an infinite interval with Jacobi-weight by the integral operator, the lin...

本文利用帶權(quán)光滑模與帶權(quán)K--泛函討論定義在無窮區(qū)間上的積分型算子Gamma算子線性組合對空間L_∞(0精品福利99，∞)中函數(shù)的帶Jacobi權(quán)同時逼近的正逆定理以及局部飽和結(jié)果，還討論了Gamma算子的強(qiáng)逆不等式5月婷婷综合网。

Functional differential equation; evolutional equations about population;neutral integral equation; cone; fixed point index; infinite delay; m -accretive operator; random fixed point; condensing map

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