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51.
§ 1 IntroductionIn this note we are concerned with the asymptotically periodic second order equation-u″+α( x) u =β( x) uq +γ( x) up, x∈ R,( 1 )where1
相似文献
52.
The structure and optical properties of the films of ternary compounds AgInSe2, CuInSe2 and Cu
x
Ag1–x
InSe2 solid solutions obtained by pulsed laser evaporation are investigated. It has been established that the films like bulk crystals have the structure of chalcopyrite. By the transmission and reflection spectra near the edge of natural absorption the refractive index and coefficient of optical absorption are calculated and the energies of interband transitions and the crystalline and spinorbit splitting are determined. 相似文献
53.
A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed. 相似文献
54.
Liénard系统的同宿轨族与闭轨族 总被引:5,自引:1,他引:4
本文讨论Lienard系统解的一些定性性质,得到了存在同宿轨族、闭轨族、双曲扇形和椭圆扇形、正负半轨有界及其与等倾线相交的充要条件或充分条件. 相似文献
55.
JianHuaSUN 《数学学报(英文版)》2005,21(1):65-80
In this paper we study the singularity at the origin with three-fold zero eigenvalue forsymmetric vector fields with nilpotent linear part and 3-jet C^∞-equivalent to y δ/δx zδ/δy ax^2yδ/δz with a≠0. We first obtain several subfamilies of the symmetric versal unfoldings of this singularityby using the normal form and blow-up methods under some conditions, and derive the local and global bifurcation behavior, then prove analytically the existence of the Sil‘nikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of this singularity, by using the generalized Mel‘nikov methods of a homoclinic orbit to a hyperbolic or non-hyperbolic equilibrium in a highdimensional space. 相似文献
56.
Quantum systems with quadratic Hamiltonians are considered. Some results about the time evolution of homogeneous polynomials and of quantum correlation functions are given. The image of arbitrary orbit of Weyl–Heisenberg group under this time evolution is shown to be again an orbit of this group. For quantum free particle it is shown that its time evolution intersects arbitrary such orbit at most once. A result about existence of more orbits having the same dispersion of some quantum position is presented.PACS: 02.20.Qs, 02.30.Sa 相似文献
57.
The flow of the Riemann zeta function, , is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases the zero is a sink. To produce these portraits, the zeta function was evaluated numerically to 12 decimal places, in the region of interest, using the Chebyshev method and using Mathematica.
The phase diagrams suggest new analytic properties of zeta, of which some are proved and others are given in the form of conjectures.
58.
While approaching the target body, the deep-space probe is orbiting hyperbolically before the maneuver. We discuss the variation of perturbed hyperbolic orbit using the method similar to that used in elliptic orbit. Ephemeris calculating and orbit control will benefit from the given analytical solution. 相似文献
59.
B. P. Paneah 《Functional Analysis and Its Applications》2003,37(1):46-60
In this paper, some solvability problems for functional equations of the form
are studied. Here I is a finite closed interval in , F is an unknown continuous function,
and
are given continuous maps of I into itself, and
, and
are real-valued continuous functions on I. Such equations are of interest not only by themselves as an object of analysis, but they are also a necessary link in solving various problems in such diverse fields as integral and functional equations, measure theory, and boundary problems for hyperbolic differential equations. The major part of the proofs is based on the new results in the theory of dynamical systems generated by a noncommutative semigroup with two generators. 相似文献
60.
Alvaro Bustinduy 《Proceedings of the American Mathematical Society》2003,131(12):3767-3775
We prove that a complete polynomial vector field on has at most one zero, and analyze the possible cases of those with exactly one which is not of Poincaré-Dulac type. We also obtain the possible nonzero first jet singularities of the foliation at infinity and the nongenericity of completeness. Connections with the Jacobian Conjecture are established.