共查询到20条相似文献,搜索用时 687 毫秒
1.
D. D. Tskhakaya 《Theoretical and Mathematical Physics》1993,95(1):378-386
A study is made of the degeneracy of multidimensional dispersion laws (k) that increase unboundedly as k and satisfy some additional conditions. Under the assumption that the corresponding degeneracy functionf(k) satisfies a certain condition [Eq. (4)], it is shown that only two-dimensional dispersion laws of the form (p,q)=p
3(q/p)+cp(q/p)(|p|,|q|1), wherep(q/p)=f(p, q) is the corresponding unique degeneracy function, can be degenerate with respect to a 12 process. Some conditions that the function () must satisfy are obtained. The explicit form of a degenerate dispersion law with functionp
3(q/p) of polynomial form is found.Institute of Physics, Georgian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 20–33, April, 1993. 相似文献
2.
The scattering problem is studied, which is described by the equation (-Δ
x
+q(x,x/ɛ)−E)ψ = f(x), where ψ = ψ (x,ɛ) ∈ ℂ, x ℂ ℝ
d
, ɛ > 0, E > 0, the function q(x,y) is periodic with respect to y, and the function f is compactly supported. The solution satisfying radiation conditions at infinity is considered, and its asymptotic behavior
as ɛ → O is described. The asymptotic behavior of the scattering amplitude of a plane wave is also considered. It is shown
that in principal order both the solution and the scattering amplitude are described by the homogenized equation with potential
$
\hat q(x) = \frac{1}
{{\left| \Omega \right|}}\int_\Omega {q(x,y)dy} .
$
\hat q(x) = \frac{1}
{{\left| \Omega \right|}}\int_\Omega {q(x,y)dy} .
相似文献
3.
A. A. Panov 《Mathematical Notes》1977,21(1):22-28
The number Kp,q, i.e., the number of (p, q) corridors of closed domains which are convex in the vertical direction, consist of elementary
squares of the integral lattice, are situated within a rectangle of the size q × p, and completely cover the side of length
p of this rectangle under projection is computed. The asymptotic (Kp,q/q2)1/p → λ, as p, q → ∞, where λ = 0.3644255… is the maximum root of the equation1F1(-1/2 − 1/(16λ), 1/2, 1/(4λ)) = 0,1F1 being the confluence hypergeometric function, is established. These results allow us to compute the ε entropy of the space
of continuous functions with the Hausdorff metric.
Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 39–50, January, 1977. 相似文献
4.
M. I. Gvaradze 《Mathematical Notes》1977,21(2):79-84
The spacesb (p, q, λ) (0<p<q⩽∞, 0<λ⩽∞) of functions, analytic in the circle |z|< 1, are introduced, and an unimprovable estimate is obtained for the Taylor coefficients
of a functionf∃
b (p, q, λ). It is shown that B(p, q, λ) is the space of fractional derivatives f(α) of order α (−∞<α<1/p−1/q) of a function
f of B(s, q, λ), where s=p/(1−αp).
Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 141–150, February, 1977. 相似文献
5.
A General Comparison Result for Higher Order Nonlinear Difference Equations With Deviating Arguments
John R. Graef Agnes Miciano-Cariño Chuanxi Qian 《Journal of Difference Equations and Applications》2013,19(11):1033-1052
The authors consider m -th order nonlinear difference equations of the form D m p x n + i h j ( n , x s j ( n ) )=0, j =1,2,( E j ) where m S 1, n ] N 0 ={0,1,2,…}, D 0 p x n = x n , D i p x n = p n i j ( D i m 1 p x n ), i =1,2,…, m , j x n = x n +1 m x n , { p n 1 },…,{ p n m } are real sequences, p n i >0, and p n m L 1. In Eq. ( E 1 ) , p = a and p n i = a n i , and in Eq. ( E 2 ) , p = A and p n i = A n i , i =1,2,…, m . Here, { s j ( n )} are sequences of nonnegative integers with s j ( n ) M X as n M X , and h j : N 0 2 R M R is continuous with uh j ( n , u )>0 for u p 0. They prove a comparison result on the oscillation of solutions and the asymptotic behavior of nonoscillatory solutions of Eq. ( E j ) for j =1,2. Examples illustrating the results are also included. 相似文献
6.
JIANG Yanjie 《中国科学A辑(英文版)》2000,43(6):609-615
This paper concerns the problem of average σ-K width and average σ-L width of some anisotropic Besov-Wiener classes Srp q θb(Rd) and Srp q θB(Rd) in Lq(Rd) (1≤q≤p<∞). The weak asymptotic behavior is established for the corresponding quantities. 相似文献
7.
袁荣 《应用数学学报(英文版)》1998,14(1):68-73
Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.[5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot… 相似文献
8.
G. A. Martynov 《Theoretical and Mathematical Physics》2006,146(2):285-294
We study the propagation of small-amplitude acoustic waves in liquids and gases and use the hydrodynamic equations to obtain
an exact dispersion equation. This equation in dimensionless variables contains only two material constants p and q. We solve
the dispersion equation, obtaining an exact solution that holds for all values of the parameters and all frequencies up to
hypersonic, and thus analytically establish exactly how the speed of sound c, the wave vector k, and the damping factor x
depend on the frequency ω and the dimensionless material constants p and q. Studying the behavior of the solution in the sonic
and ultrasonic frequency bands for ω < 107 sec-1 results in an expression for the damping factor, which differs from the Kirchhoff formula. The speed of sound c and the wave
vector k are shown to have finite nonzero values for all hypersonic frequencies. At the same time, there exists a certain
maximum frequency value, ωmax ≈ 1011-1012 sec-1, at which the damping factor x is zero. This frequency determines the boundary of the applicability domain for the hydrodynamic
equations.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 340–352, February, 2006. 相似文献
9.
A canonically defined mod 2 linear dependency current is associated to each collection v of sections, v1,…,vm, of a real rank n vector bundle. This current is supported on the linear dependency set of v. It is defined whenever the
collection v satisfies a weak measure theoretic condition called “atomicity.” Essentially any reasonable collection of sections
satisfies this condition, vastly extending the usual general position hypothesis. This current is a mod 2 d-closed locally
integrally flat current of degree q = n −m + 1 and hence determines a ℤ2-cohomology class. This class is shown to be well defined independent of the collection of sections. Moreover, it is the qth
Stiefel-Whitney class of the vector bundle.
More is true if q is odd or q = n. In this case a linear dependency current which is twisted by the orientation of the bundle
can be associated to the collection v. The mod 2 reduction of this current is the mod 2 linear dependency current. The cohomology
class of the linear dependency current is 2-torsion and is the qth twisted integral Stiefel-Whitney class of the bundle.
In addition, higher dependency and general degeneracy currents of bundle maps are studied, together with applications to singularities
of projections and maps.
These results rely on a theorem of Federer which states that the complex of integrally flat currents mod p computes cohomology
mod p. An alternate approach to Federer’s theorem is offered in an appendix. This approach is simpler and is via sheaf theory. 相似文献
10.
Bartosz Trojan 《Monatshefte für Mathematik》2020,191(2):349-376
We consider an irreducible finite range random walk on the d-dimensional integer lattice and study asymptotic behavior of its transition function p(n; x) close to the boundary of Cramér’s zone. 相似文献
11.
Summary In addition to obtaining sufficient conditions for continuability of solutions of x″ + q(t)f(x)=r(t), some sufficient conditions
and some necessary and sufficient conditions for boundedness are obtained. The asymptotic behavior of solutions is studied
through examination of r(t)/q(t) as t → ∞.
Supported by Mississippi State University Biological and Physical Sciences Research Institute.
Entrata in Redazione il 6 febbraio 1973. 相似文献
12.
Affine Systems: Asymptotics at Infinity for Fractal Measures 总被引:2,自引:0,他引:2
We study measures on ℝ
d
which are induced by a class of infinite and recursive iterations in symbolic dynamics. Beginning with a finite set of data,
we analyze prescribed recursive iteration systems, each involving subdivisions. The construction includes measures arising
from affine and contractive iterated function systems with and without overlap (IFSs), i.e., limit measures μ induced by a finite family of affine mappings in ℝ
d
(the focus of our paper), as well as equilibrium measures in complex dynamics.
By a systematic analysis of the Fourier transform of the measure μ at hand (frequency domain), we identify asymptotic laws, spectral types, dichotomy, and chaos laws. In particular we show
that the cases when μ is singular carry a gradation, ranging from Cantor-like fractal measures to measures exhibiting chaos, i.e., a situation
when small changes in the initial data produce large fluctuations in the outcome, or rather, the iteration limit (in this
case the measures). Our method depends on asymptotic estimates on the Fourier transform of μ for paths at infinity in ℝ
d
. We show how properties of μ depend on perturbations of the initial data, e.g., variations in a prescribed finite set of affine mappings in ℝ
d
, in parameters of a rational function in one complex variable (Julia sets and equilibrium measures), or in the entries of
a given infinite positive definite matrix.
相似文献
13.
Amnon Rosenmann 《Israel Journal of Mathematics》1997,99(1):285-313
Given a presentation of ann-generated group, we define the normalized cyclomatic quotient (NCQ) of it, which gives a number between 1−n and 1. It is computed through an investigation of the asymptotic behavior of a kind of an “average rank”, or more precisely
the quotient of the rank of the fundamental group of a finite subgraph of the corresponding Cayley graph by the size of the
subgraph. In many ways (but not always) the NCQ behaves similarly to the behavior of the spectral radius of a symmetric random
walk on the graph. In particular, it characterizes amenable groups. For some types of groups, like finite, amenable or free
groups, its value equals that of the Euler characteristic of the group. We give bounds for the value of the NCQ for factor
groups and subgroups, and formulas for its value on direct and free products. Some other asymptotic invariants are also discussed. 相似文献
14.
Global asymptotics for Laguerre polynomials with large negative parameter—a Riemann-Hilbert approach 总被引:1,自引:0,他引:1
In this paper, we study the asymptotic behavior of the Laguerre polynomials
as n→∞. Here α
n
is a sequence of negative numbers and −α
n
/n tends to a limit A>1 as n→∞. An asymptotic expansion is obtained, which is uniformly valid in the upper half plane ℂ+={z:Im z≥0}. A corresponding expansion is also given for the lower half plane ℂ−={z:Im z≤0}. The two expansions hold, in particular, in regions containing the curve Γ in the complex plane, on which these polynomials
are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou.
The work of R. Wong is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative
Region, China (Project No. CityU 102504). 相似文献
15.
G. A. Martynov 《Theoretical and Mathematical Physics》2008,156(3):1356-1364
Using the Ornstein.Zernike equation, we obtain two asymptotic equations, one describing the exponential asymptotic behavior
and the other describing the power asymptotic behavior of the total correlation function h(r). We show that the exponential
asymptotic form is applicable only on a bounded distance interval l < r < L. The power asymptotic form is always applicable
for r > L and reproduces the form of the interaction potential. In this case, as the density of a rarified gas decreases,
L → l, the exponential asymptotic form vanishes, and only the power asymptotic form remains. Conversely, as the critical point
is approached, L → ℞, and the applicability domain of the exponential asymptotic form increases without bound.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 454–464, September, 2008. 相似文献
16.
Consider the parameter space Θ which is an open subset of ℝ
k
,k≧1, and for each θ∈Θ, let the r.v.′sY
n
,n=0, 1, ... be defined on the probability space (X,A,P
θ) and take values in a Borel setS of a Euclidean space. It is assumed that the process {Y
n
},n≧0, is Markovian satisfying certain suitable regularity conditions. For eachn≧1, let υ
n
be a stopping time defined on this process and have some desirable properties. For 0 < τ
n
→ ∞ asn→∞, set
h
n
→h ∈R
k
, and consider the log-likelihood function
of the probability measure
with respect to the probability measure
. Here
is the restriction ofP
θ to the σ-field induced by the r.v.′sY
0,Y
1, ...,
. The main purpose of this paper is to obtain an asymptotic expansion of
in the probability sense. The asymptotic distribution of
, as well as that of another r.v. closely related to it, is obtained under both
and
.
This research was supported by the National Science Foundation, Grant MCS77-09574.
Research supported by the National Science Foundation, Grant MCS76-11620. 相似文献
17.
Asymptotic Behavior of Solutions to a Class of Semilinear Parabolic Equations with Boundary Degeneracy
![]() This paper concerns the asymptotic behavior of solutions to one-dimensional semilinear parabolic equations with boundary degeneracy both
in bounded and unbounded intervals. For the problem in a bounded interval, it is shown that there exist both nontrivial global solutions for small initial
data and blowing-up solutions for large one if the degeneracy is not strong.
Whereas in the case that the degeneracy is strong enough, the nontrivial solution must blow up in a finite time. For the problem in an unbounded interval,
blowing-up theorems of Fujita type are established. It is shown that the critical
Fujita exponent depends on the degeneracy of the equation and the asymptotic
behavior of the diffusion coefficient at infinity, and it may be equal to one or
infinity. Furthermore, the critical case is proved to belong to the blowing-up
case. 相似文献
18.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):81-90
Summary It is desired to estimate a parameter
with the loss function of the formL(θ, a)=W(‖θ−a‖), where
is convex, differentiable, and non-decreasing. With this structure a characterization of Bayes estimators is given. Also
it is noted that if the sample space,
, for the observation,X, is a complete separable metric space then a Bayes estimator exists. 相似文献
19.
Tai Shan YI Li Hong HUANG 《数学学报(英文版)》2007,23(8):1375-1384
The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→∞. Our results improve and extend some corresponding ones already known. 相似文献
20.
S. A. Gritsenko 《Journal of Mathematical Sciences》2006,137(2):4634-4644
Let C be a class of ideals of the ring of algebraic numbers of an imaginary quadratic field. Let l and q be relatively prime
integers,
, and A1 τ; 1. An asymptotic formula for the number π1(x, q, l, C) of prime ideals belonging to the class C whose norms do not exceed x and lie in an arithmetic progression is
obtained in this paper. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 45–62. 相似文献
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