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941.
We consider an operator function T in a Krein space which can formally be written as (0.1)but the last term on the right of (0.1) is replaced by a relatively form‐compact perturbation of a similar form. We study relations between the operator function T, a selfadjoint operator M in some Krein space, associated with T, and an operator which can be constructed with the help of the operator function –T–1. The results are applied to a Sturm‐Liouville problem with a coefficient depending rationally on the eigenvalue parameter. 相似文献
942.
In this paper, we study the existence of positive periodic solutions for singular second order equations x" + n2/4x+h(x) = p(t), where h has a singularity at the origin and n is a positive integer. We give an explicit condition to ensure the existence of positive periodic solutions when h is an unbounded perturbation at infinity by using qualitative analysis and topological degree theory. 相似文献
943.
Philippe Flajolet Xavier Gourdon Conrado Martínez 《Random Structures and Algorithms》1997,11(3):223-244
In a randomly grown binary search tree (BST) of size n, any fixed pattern occurs with a frequency that is on average proportional to n. Deviations from the average case are highly unlikely and well quantified by a Gaussian law. Trees with forbidden patterns occur with an exponentially small probability that is characterized in terms of Bessel functions. The results obtained extend to BSTs a type of property otherwise known for strings and combinatorial tree models. They apply to paged trees or to quicksort with halting on short subfiles. As a consequence, various pointer saving strategies for maintaining trees obeying the random BST model can be precisely quantified. The methods used are based on analytic models, especially bivariate generating function subjected to singularity perturbation asymptotics. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 : 223–244, 1997 相似文献
944.
Yufu Liu Xianjun Wang Langlang Xiong Xingchao Qi Zhen Lai Xuezhi Wang Yunlin Li Xunya Jiang 《Laser \u0026amp; Photonics Reviews》2024,18(2):2300740
Although the spin-controlled vortex generation and photonic spin-Hall effect of spin-flipped abnormal mode have been widely studied recently, the traditional method based on the metasurface is difficult to fabricate, and the efficiency of the spin-flipped abnormal mode is rather low due to process errors and intrinsic material loss. Here, a new method is proposed based on the insights into the topological singularity and special Bragger reflections resonant (BRR) mode of one-dimensional (1D) finite photonic crystals (PhCs) with anisotropic material to realize nearly perfect (100%) spin-conversion efficiency. For a finite 1D PhC with cell number N, there are 3N complete spin-conversion (CSC) and complete spin-maintained (CSM) channels. Two mechanisms of these CSC and CSM channels are revealed. The working bandwidths and the angular ranges of these CSC and CSM are also studied. Based on these theoretical findings, multi-angles and multi-frequencies perfect spin-conversion (-maintained) devices can be designed. At last, these theoretical results are confirmed by the numerical experiments based on finite-difference time-domain (FDTD) methods. This work paves the way to exploring the topological properties and polarization control of PhCs made of anisotropic dielectrics and provides a prospective method for the design of multi-channels spin optical devices. 相似文献
945.
徐玉梅 《高校应用数学学报(英文版)》2006,21(4)
This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blow-up result for C1 solution to Cauchy problem. 相似文献
946.
We show that defines a birational map and has no fixed part for some bounded positive integer m for any -lc surface X such that is big and nef. For every positive integer , we construct a sequence of projective surfaces , such that is ample, for every i, , and for any positive integer m, there exists i such that has nonzero fixed part. These results answer the surface case of a question of Xu. 相似文献
947.
On the Analytical Approach of Codimension-Three Degenerate Bogdanov-Takens (B-T) Bifurcation in Satellite Dynamical System 下载免费PDF全文
Muhammad Marwan Muhammad Zainul Abidin 《Journal of Nonlinear Modeling and Analysis》2023,5(4):667-681
In this paper, we have conducted parametric analysis on the dynamics of satellite complex system using bifurcation theory. At first, five equilibrium points $\mathcal{E}_{0,1,2,3,4}$ are symbolically computed in which $\mathcal{E}_{1,3}$ and $\mathcal{E}_{2,4}$ are symmetric. Then, several theorems are stated and proved for the existence of B-T bifurcation on all equilibrium points with the aid of generalized eigenvectors and practical formulae instead of linearizations. Moreover, a special case $\alpha_{2}=0$ is observed, which confirms all the discussed cases belong to a codimension-three bifurcation along with degeneracy conditions. 相似文献
948.