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11.
N. S. Kazak E. G. Katranji I. A. Utkin A. A. Ryzhevich A. N. Khilo 《Journal of Applied Spectroscopy》2004,71(5):697-701
The phenomenon of self-diffraction of Bessel light beams (BLB) in a nonlinear liquid medium has been studied experimentally and theoretically for the first time. Diffraction maxima which do not correspond to integer orders for an induced periodic structure have been registered. It has been shown that the appearance of these maxima is due to the initial BLB modulation, which can be caused by the departure of the axicon refracting surface from the ideal conical surface, as well as by the imperfection of the form of the Gaussian beam incident on the axicon. 相似文献
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13.
The problem of generating a matrix A with specified eigen‐pair, where A is a symmetric and anti‐persymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by ??????En. The optimal approximation problem associated with ??????En is discussed, that is: to find the nearest matrix to a given matrix A* by A∈??????En. The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
14.
Ren-Cang Li. 《Mathematics of Computation》2003,72(242):715-728
This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.
15.
16.
薛儒英 《浙江大学学报(理学版)》1991,(2)
本文讨论了半线性椭圆方程△u+f(u)=0在三种边界条件下正解的存在性和唯一性,给出了正解存在和唯一的一些条件. 相似文献
17.
A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved. 相似文献
18.
G. A. Watson 《Advances in Computational Mathematics》1994,2(4):393-405
The orthogonal Procrustes problem involves finding an orthogonal matrix which transforms one given matrix into another in
the least-squares sense, and thus it requires the minimization of the Frobenius matrix norm. We consider, the solution of
this problem for a family of orthogonally invariant norms which includes the Frobenius norm as a special case. 相似文献
19.
S.V. Astashkin F.A. Sukochev 《Journal of Mathematical Analysis and Applications》2007,336(2):1231-1258
We catalogue all Marcinkiewicz function and sequence spaces with the Banach-Saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p-Banach-Saks property, 1<p<∞. We apply our results to several open problems. 相似文献
20.
Djavvat Khadjiev 《Journal of Mathematical Analysis and Applications》2007,326(2):1101-1115
An approach to a definition of an integral, which differs from definitions of Lebesgue and Henstock-Kurzweil integrals, is considered. We use trigonometrical polynomials instead of simple functions. Let V be the space of all complex trigonometrical polynomials without the free term. The definition of a continuous integral on the space V is introduced. All continuous integrals are described in terms of norms on V. The existence of the widest continuous integral is proved, the explicit form of its norm is obtained and it is proved that this norm is equivalent to the Alexiewicz norm. It is shown that the widest continuous integral is wider than the Lebesgue integral. An analog of the fundamental theorem of calculus for the widest continuous integral is given. 相似文献