共查询到20条相似文献,搜索用时 15 毫秒
1.
Mario Lamberger 《Indagationes Mathematicae》2006,17(1):45-63
In the present paper we are investigating a certain point measure of a distribution function arising in a paper by Grabner et al. [Combinatorica 22 (2002) 245-267]. This distribution function is defined by means of the subtractive Euclidean algorithm and bears a striking resemblance to the singular?(x)-function of H. Minkowski. Beyond it, we will also consider a whole family of distribution functions arising in a natural way from the above ones. Nevertheless we will prove that all of the corresponding measures of the mentioned functions are mutually singular by using dynamical systems and the ergodic theorem. 相似文献
2.
Asymptotic behavior of the solutions of the p-Laplacian equation 总被引:1,自引:0,他引:1
ZHANG Liqin & ZHAO Junning Department of Mathematics Xiamen University Xiamen China 《中国科学A辑(英文版)》2006,49(6)
The asymptotic behavior of the solutions for p-Laplacian equations as p→∞ is studied. 相似文献
3.
Let X = {X(t), t ?? T} be a stationary centered Gaussian process with values in ? d , where the parameter set T equals ? or ?+. Let ?? t = Cov(X 0 ,X t ) be the covariance function of X, and (??,?, P) be the underlying probability space. We consider the asymptotic behavior of convex hulls W t = conv{X u , u ?? T ?? [0, t]} as t ?? +?? and show that under the condition ??t ?? 0, t????, the rescaled convex hull (2 ln t) ?1/2 W t converges almost surely (in the sense of Hausdorff distance) to an ellipsoid ? associated to the covariance matrix ?? 0. The asymptotic behavior of the mathematical expectations E f(W t ), where f is a homogeneous function, is also studied. These results complement and generalize in some sense the results of Davydov [Y. Davydov, On convex hull of Gaussian samples, Lith. Math. J., 51(2): 171?C179, 2011]. 相似文献
4.
Jianglong Wu 《Ukrainian Mathematical Journal》2009,61(10):1684-1693
A boundedness result is established for multilinear singular integral operators on the homogeneous Morrey–Herz spaces. As
applications, two corollaries about interesting cases of the boundedness of the considered operators on the homogeneous Morrey–Herz
spaces are obtained. 相似文献
5.
We find the asymptotic behavior of the Jost function(Z,) of a two-dimensional Schrödinger operator for arbitrary and Z/|Z|S1 as |Z| We discuss consequences of the asymptotic formulas for the inverse scattering problem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 173, pp. 96—103, 1988. 相似文献
6.
Abel Klein 《偏微分方程通讯》2016,41(7):1040-1055
We study the local behavior of solutions of the stationary Schrödinger equation with singular potentials, establishing a local decomposition into a homogeneous harmonic polynomial and a lower order term. Combining a corollary to this result with a quantitative unique continuation principle for singular potentials, we obtain log-Hölder continuity for the density of states outer-measure in one, two, and three dimensions for Schrödinger operators with singular potentials, results that hold for the density of states measure when it exists. 相似文献
7.
We prove the existence of a global attractor for the Newton–Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also establish the regularity of the global attractor. 相似文献
8.
For self-adjoint second-order elliptic differential operators that satisfy the non-trapping condition on the n-dimensional hyperbolic space
H
n
and coincide with the operator
in a neighborhood of infinity, where is the Laplace-Beltrami operator on
H
n
,we obtain the complete asymptotic expansion of the spectral function as +.For self-adjoint operators of the form (–)
+Q
m–r,where Q
m–r is a pseudodifferential operator of order m–r that is automorphic with respect to a discrete group of isometries of the spaceH
n
whose fundamental domain has finite volume, we introduce the spectral distribution function N(),which is the analog of the integrated state density, and we find its asymptotics up to order O((n–r)/m)as +.Bibliography: 49 titles.Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 4–32, 1991. 相似文献
9.
Frédéric Serier 《Comptes Rendus Mathematique》2005,340(9):671-676
We consider an inverse spectral problem for singular Sturm–Liouville equations on the unit interval with explicit singularity , . This problem arises by splitting of the Schrödinger operator with radial potential acting on the unit ball of . Our goal is the global parametrization of potentials by spectral data noted by , and some norming constants noted by . For and 1, was already known to be a global coordinate system on . We extend this to any non-negative integer a. Similar result is obtained for singular AKNS operator. To cite this article: F. Serier, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
10.
According to the classical theory of Weiss, Landau, and Lifshitz, on a microscopic scale a ferromagnetic body is magnetically saturated (i.e., |M| =: constant) and consists of regions in which the magnetization is uniform, separated by thin transition layers. Any stationary configuration corresponds to a minimum point of an energy functional in which a small parameter is present. The asymptotic behavior as 0 is studied here. It is easy to see that any sequence of minimizers contains a subsequenceM
j
that converges to a fieldM. By means of a -limit procedure it is shown that this fieldM is a minimizer of a new functional containing a term proportional to the area of the surfaces separating different domains of uniform magnetization. TheC
1,
-regularity of these surfaces, for < 1/2, is also proved under suitable assumptions for the external magnetic field. 相似文献
11.
A simple explicit bound on the absolute values of the non-real eigenvalues of a singular indefinite Sturm-Liouville operator on the real line with the weight function sgn(·) and an integrable, continuous potential q is obtained. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(9):1145-1150
We use the method of the conjugate operator to prove a limiting absorption principle and the absence of the singular continuous spectrum for discrete Schrödinger operators. We also obtain local decay estimates. Our results apply to a large class of perturbating potentials V decaying arbitrarily slowly to zero at infinity. 相似文献
13.
14.
This article studies the asymptotic behavior of a stochastic Chemostat model with Lotka–Volterra food chain in which the dilution rate was influenced by white noise. The long-time behavior of the model is studied. Using Lyapunov function and Itô's formula, we show that there is a unique positive solution to the system. Moreover, the sufficient conditions for some population dynamical properties including the boundedness in mean and the stochastically asymptotic stability of the washout equilibrium were obtained. Furthermore, we show how the solutions spiral around the predator-free equilibrium and the positive equilibrium of deterministic system. Besides, the existence of the stationary distribution is proved for the considered model. Numerical simulations are introduced finally to support the obtained results. 相似文献
15.
The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation −Δu = |x|
α
u
p−1, u > 0, x ∈ B
R
(0) ⊂ ℝ
n
(n ⩾ 3), u = 0, x ∈ ∂B
R
(0), where $
p \to p(\alpha ) = \frac{{2(n + \alpha )}}
{{n - 2}}
$
p \to p(\alpha ) = \frac{{2(n + \alpha )}}
{{n - 2}}
from left side, α > 0. 相似文献
16.
Traub and Werschulz [Complexity and Information, Cambridge University Press, New York, 1999] ask whether every linear operator S:⊆X→Y is “computable on the average” w.r.t. a Gaussian measure on X. The question is inspired by an analogous result in information-based complexity on the average-case solvability of linear approximation problems. We give several interpretations of Traub and Werschulz’ question within the framework of type-2 theory of effectivity. We have negative answers to all of these interpretations but the one with minimal requirements on the algorithm's uniformness. On our way to these results, we give an effective version of the Mourier–Prokhorov characterization of Gaussian measures on separable Hilbert spaces. 相似文献
17.
We consider two-particle Schrödinger operator H(k) on a three-dimensional lattice ? 3 (here k is the total quasimomentum of a two-particle system, $k \in \mathbb{T}^3 : = \left( { - \pi ,\pi ]^3 } \right)$ . We show that for any $k \in S = \mathbb{T}^3 \backslash ( - \pi ,\pi )^3$ , there is a potential $\hat v$ such that the two-particle operator H(k) has infinitely many eigenvalues zn(k) accumulating near the left boundary m(k) of the continuous spectrum. We describe classes of potentials W(j) and W(ij) and manifolds S(j) ? S, i, j ∈ {1, 2, 3}, such that if k ∈ S(3), (k 2 , k 3 ) ∈ (?π,π) 2 , and $\hat v \in W(3)$ , then the operator H(k) has infinitely many eigenvalues zn(k) with an asymptotic exponential form as n → ∞ and if k ∈ S(i) ∩ S(j) and $\hat v \in W(ij)$ , then the eigenvalues znm(k) of H(k) can be calculated exactly. In both cases, we present the explicit form of the eigenfunctions. 相似文献
18.
Mathematical Programming - The paper provides a connection between Commutative Algebra and Integer Programming and contains two parts. The first one is devoted to the asymptotic behavior of integer... 相似文献
19.
We consider a Markov-modulated fluid queue with a finite buffer. It is assumed that the fluid flow is modulated by a background
Markov chain which may have different transitions when the buffer content is empty or full. In Sakuma and Miyazawa (Asymptotic
Behavior of Loss Rate for Feedback Finite Fluid Queue with Downward Jumps. Advances in Queueing Theory and Network Applications,
pp. 195–211, Springer, Cambridge, 2009), we have studied asymptotic loss rate for this type of fluid queue when the mean drift of the fluid flow is negative. However,
the null drift case is not studied. Our major interest is in asymptotic loss rate of the fluid queue with a finite buffer
including the null drift case. We consider the density of the stationary buffer content distribution and derive it in matrix
exponential forms from an occupation measure. This result is not only useful to get the asymptotic loss rate especially for
the null drift case, but also it is interesting in its own light. 相似文献
20.
Hussein Fakih 《Applicable analysis》2017,96(2):324-348
We consider in this article a generalized Cahn–Hilliard equation with mass source (nonlinear reaction term) which has applications in biology. We are interested in the well-posedness and the study of the asymptotic behavior of the solutions (and, more precisely, the existence of finite-dimensional attractors). We first consider the usual Dirichlet boundary conditions and then Neumann boundary conditions. The latter require additional assumptions on the mass source term to obtain the dissipativity. Indeed, otherwise, the order parameter u can blow up in finite time. We also give numerical simulations which confirm the theoretical results. 相似文献