共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we consider a super-Brownian motion X with branching mechanism k(x)zα, where k(x) > 0 is a bounded Holder continuous function on Rd and infx∈Rd k(x) = 0. We prove that if k(x) ≥ //x// -l(0 ≤l < ∞) for sufficiently large x, then X has compact support property, and for dimension d = 1, if k(x) ≥exp(-l‖x‖)(0≤l < ∞) for sufficiently large x, then X also has compact support property. The maximal order of k(x) for finite time extinction is different between d = 1, d = 2 and d ≥ 3: it is O(‖x‖-(α+1)) in one dimension, O(‖x‖-2(log‖x‖)-(α+1) ) in two dimensions, and O(‖x‖2) in higher dimensions. These growth orders also turn out to be the maximum order for the nonexistence of a positive solution for 1/2Δu =k(x)uα. 相似文献
2.
The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (-Δ) -α/2 are extended to the generalised fractional integrals L-α/2 for 0 < α < n, where L =-div A is a uniformly complex elliptic operator with bounded measurable coefficients in Rn. 相似文献
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Yunxia WEI Yanping CHEN Xiulian SHI Yuanyuan ZHANG 《Frontiers of Mathematics in China》2019,14(2):435-448
This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function ω(x)=∏di=1(1-xi)^α(1+xi)^β,-1<α,β<1/d-1/2 (d denotes the space dimensions) as the collocation points. We demonstrate that the errors of approxima te solution decay exponentially. Numerical results are presen ted to demonstrate the effectiveness of the Jacobi spectral collocation method. 相似文献
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LI QiuYue & REN YanXia College of Science China Agricultural University Beijing China LMAM School of Mathematical Sciences Center for Statistical Science Peking University Beijing 《中国科学 数学(英文版)》2011,(7)
In this paper we establish a large deviation principle for the occupation times of critical branching α-stable processes for large dimensions d > 2α, by investigating two related nonlinear differential equations. Our result is an extension of Cox and Griffeath’s (in 1985) for branching Brownian motion for d > 4. 相似文献
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This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers(BBM-Burgers) equation to the corresponding degenerate boundary layer solutions in the half-space.It is shown that the convergence rate is t-(α/4) as t →∞ provided that the initial perturbation lies in H α 1 for α < α(q):= 3 +(2/q),where q is the degeneracy exponent of the flux function.Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1]. 相似文献
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In the paper, for the contamination distribution model F(x) = (1-α)F1(x)+αF2(x), the estimates of α and F1 (x) are studied using two different ways when F2 (x) is known and the strong consistency of the two estimates is proved. At the same time the consistency rate of estimate α is also given. 相似文献
8.
We discuss the integral test for a moving sum of an iid symmetric stable sequence with exponent α (0 < α < 2), and the Chover-type LIL is given as a corollary. We also obtain the law of a single logarithm for moving sums of a normal sequence. 相似文献
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In this paper,we consider the defocusing nonlinear Schrodinger equation in space dimensions d≥4.We prove that if u is a radial solution which is priori bounded inthe critical Sobolev space,that is,u L∈Lt^∞Hx^Sc,then u is global and scatters.In practise,we use weighted Strichartz space adapted for our setting which ultimately helps us solve the problems in cases d≥4 and 0相似文献
10.
The optimal filter π = {π t,t ∈ [0,T ]} of a stochastic signal is approximated by a sequence {π n t } of measure-valued processes defined by branching particle systems in a random environment(given by the observation process).The location and weight of each particle are governed by stochastic differential equations driven by the observation process,which is common for all particles,as well as by an individual Brownian motion,which applies to this specific particle only.The branching mechanism of each particle depends on the observation process and the path of this particle itself during its short lifetime δ = n 2α,where n is the number of initial particles and α is a fixed parameter to be optimized.As n →∞,we prove the convergence of π n t to π t uniformly for t ∈ [0,T ].Compared with the available results in the literature,the main contribution of this article is that the approximation is free of any stochastic integral which makes the numerical implementation readily available. 相似文献
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LI YuQiang 《中国科学 数学(英文版)》2014,(10)
We consider a kind of site-dependent branching Brownian motions whose branching laws depend on the site-branching factorσ(·).We focus on the functional ergodic limits for the occupation time processes of the models in R.It is proved that the limiting process has the form ofλξ(·),where A is the Lebesgue measure on IE andξ(·)is a real-valued process which is non-degenerate if and only ifσis integrable.Whenξ(·)is non-degenerate,it is strictly positive for t0.Moreover,ξconverges to O in finite-dimensional distributions if the integral ofσtends to infinity. 相似文献
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In this paper, we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set S of suitable weak solutions and the parameter α in the nonlinear term in the following parabolic equation■ It is shown that when 5/3 ≤ α < 7/3, the ■-dimensional parabolic Hausdorff measure of S is zero,which generalizes the recent corresponding work of Ozánski and Robinson in [SIAM J. Math. Anal.,51, 228–255(2019)] for α = 2 and f = 0. The same result is valid for a 3... 相似文献
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In [1], Lu discussed the existence of positive solution for the BVPwhere f: [0, 1] × [0, ∞) → R is continuous and satisfies the following conditions(H1) There exists an M > 0 such that(H2) limx→∞ f(t, x)/x =∞uniformly for t [α,β] (0, 1) for some α < β and λ > 0 is a parameter.In this paper, the result of [1] is generalized to the following 2n-th-order BVPThe result of this paper isTheorem 1 Assume (H1) and (H2) hold. Then the BVP (3)-(4) has a positive solutionifλ > 0 is sm… 相似文献
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Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q~n) such that α + α~(-1)is also primitive or α + α~(-1)is primitive and α is a normal element of F_(q~n) over F_q. 相似文献
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In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if C α (X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if C α (X) is an AP-space which has countable tightness, then C α (X) is discretely generated. 相似文献
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The classical risk process that is perturbed by diffusion is studied .The explicit expressions for the runi probability and the surplus distribution of the risk process at the time of runi are obtained when the claim amount distribution is a finite mixture of exponential distributions of a Gamma (2,α) distribution. 相似文献
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LetΩbe a bounded balanced pseudoconvex domain in Cn that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a spiral-like mapping of typeαonΩ, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of typeαare obtained. As a direct application, the growth theorem for spiral-like mappings of typeαis set up. 相似文献
18.
Projectively flat Matsumoto metric and its approximation 总被引:1,自引:0,他引:1
李本伶 《数学物理学报(B辑英文版)》2007,27(4):781-789
In this article, the author studies the projectively flat Matsumoto metric F=α2/(α - β), where α=√aijyiyj is a Riemannian metric and β=biyi is a 1-form. They conclude that α is locally projectively flat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric. 相似文献
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This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process.The uniqueness of the periodic solution is also given. 相似文献
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Cheng Jun Hou 《数学学报(英文版)》2008,24(6):983-996
We introduce two notions of the pressure in operator algebras, one is the pressure Pα(π, T) for an automorphism α of a unital exact C^*-algebra A at a self-adjoint element T in A with respect to a faithful unital *-representation π the other is the pressure Pτ,α(T) for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T. 相似文献