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61.
We consider the problem of analytic continuation of a solution to the system of Maxwell equations in a bounded spatial domain from data on part of the boundary of the domain. We construct an approximate solution to the problem using the Carleman matrix method. 相似文献
62.
Varghese Mathai 《Geometriae Dedicata》2003,99(1):1-15
We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C*
r
(, )-bundle and connection, which can be used to construct a C*
r
(, )-index that lies in the Grothendieck group of C*
r
(, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem. 相似文献
63.
Conditions for the uniform continuity of a family of weakly regular set functions defined on an algebra of subsets of a -topological space (T,) and taking values in an arbitrary topological space are found. 相似文献
64.
We obtain sufficient conditions for the set of roots of an entire function of order zero of strongly regular growth to possess an angular density. 相似文献
65.
In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved. 相似文献
66.
设G是2-连通图,c(G)是图G的最长诱导圈的长度,c′(G)是图G的最长诱导2-正则子图的长度。本文我们用图的特征值给出了c(G)和c′(G)的几个上界。 相似文献
67.
68.
ShiJun Liao 《中国科学:物理学 力学 天文学(英文版)》2020,(3):70-81
A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum mechanics.It is based on the homotopy analysis method(HAM)that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many fields.Unlike perturbative methods,this HAM-based approach has nothing to do with small/large physical parameters.Besides,convergent series solution can be obtained even if the disturbance is far from the known status.A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative approach.This HAM-based approach could provide us rigorous theoretical results in quantum mechanics,which can be directly compared with experimental data.Obviously,this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories. 相似文献
69.
提出了一种基于几何特征的正六边形检测方法。在简述Hough变换原理和正六边形特点的基础上,把正六边形的检测分解成直线和圆的检测,以及线段长度和直线夹角的计算。利用检测到的直线,在图像平面内建立直线方程,依据直线方程,计算相邻两条直线的夹角和交点,求出每条边的长度,同时检测6个交点是否均匀分布在同一圆周上。在螺栓头部正六边形检测实验中,角度测量误差为0.38%,边长测量误差为0.85%。结果表明,该方法是有效的,能准确地检测出图像中的正六边形。 相似文献
70.
The class of quantum languages Q() over an alphabet is the class of languages accepted by quantum automata. We study properties of Q() and compare Q() with the class of regular languages R(). It is shown that Q() is closed under union, intersection, and reversal but is not closed under complementation, concatenation, or Kleene star. It is also shown that Q() and R() are incomparable. Finally, we prove that L Q() if and only if L admits a transition amplitude function satisfying a certain property and a similar characterization is given for R(). 相似文献