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81.
Tomohiro Okuma 《Compositio Mathematica》1998,110(3):263-276
This paper studies the second pluri-genus of surface singularities. We give a formula for this invariant of a Gorenstein singularity, and several inequalities relating the invariant with the Milnor number, Tjurina number and the modality of a hypersurface singularity. 相似文献
82.
Fuyi Li Zhanping Liang Qi Zhang Yuhua Li 《Journal of Mathematical Analysis and Applications》2007,327(2):1010-1028
In this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett-Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638-654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations. 相似文献
83.
We consider three different models of linear differential equations and their isomonodromic deformations. We show that each
of the models has its own specificity, although all of them lead to the same final result. It turns out that isomonodromic
deformations are closely related to the Hamiltonian structure of both classical mechanics and quantum mechanics.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 143–151, January, 2007. 相似文献
84.
85.
A singular function boundary integral method (SFBIM) is proposed for solving biharmonic problems with boundary singularities. The method is applied to the Newtonian stick–slip flow problem. The streamfunction is approximated by the leading terms of the local asymptotic solution expansion which are also used to weight the governing biharmonic equation in the Galerkin sense. By means of the divergence theorem the discretized equations are reduced to boundary integrals. The Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers, the values of which are calculated together with the singular coefficients. The method converges very fast with the number of singular functions and the number of Lagrange multipliers, and accurate estimates of the leading singular coefficients are obtained. Comparisons with the analytical solution and results obtained with other numerical methods are also made. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
86.
87.
在文献「1」基础上,针对工程中难于求解的多材料交接点裂纹尖应力奇性分析问题,在于哈密顿原理,通过分离变量与共轭辛本征函数地求解,利用材料间的界面连接条件与坐标变换关系,建立了应力奇性与本征函数求解的解析表达式。由于采取裂纹面接触区模型,因而不再发生振荡奇异性。 相似文献
88.
Atsushi Wada Hiroyuki Ohminato Takashi Yonemura Yoko Miyamoto Mitsuo Takeda 《Optical Review》2005,12(6):451-455
Seidel comatic aberration is an important cause of deformation for a Laguerre--Gaussian (LG) beam. In addition, mono-axial
comatic aberration, whose phase modulation depends only on one transverse coordinate, is also an important cause of beam deformation.
Deformation of an LG beam by such aberrations is analyzed through numerical simulation based on the angular spectrum method.
It is also shown that for holographically generated LG beams quadratic spatial variation of grating pitch can produce seidel
and mono-axial comatic aberrations. An example of an experimentally generated LG beam with mono-axial comatic aberration is
reported. 相似文献
89.
把实轴上具一阶奇性解的特征奇异积分方程及其相联方程的求解化为实轴上具一阶奇性解的Riemann边值问题讨论,对后者在提法、奇点的对待和典则函数的理解方面作了与传统有所不同的处理,对前者通过对解和可解条件的简化及等价性的讨论,得到解和可解条件的简化形式及推广的Noether定理。 相似文献
90.
Lilia Yu. Kolotilina 《Numerical Algorithms》2006,42(3-4):247-280
Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed. 相似文献