Meromorphic Jost functions and asymptotic expansions for Jacobi parameters

We show that the parameters a _n , b _n of a Jacobi matrix have a complete asymptotic expansion

$a_n^2 - 1 = \sum\limits_{k = 1}^{K(R)} {p_k (n)\mu _k^{ - 2n} + O(R^{ - 2n} ),} b_n = \sum\limits_{k = 1}^{K(R)} {p_k (n)\mu _k^{ - 2n + 1} + O(R^{ - 2n} )} $

, where 1 < |µ_j| < R for j ? K(R) and all R, if and only if the Jost function, u, written in terms of z (where E = z + z ^?1) is an entire meromorphic function. We relate the poles of u to the µ_j’s.

     

Strong spatial mixing of list coloring of graphs

The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise known to be #P hard. In the context of coloring, strong spatial mixing has been established for Kelly trees in (Ge and Stefankovic, arXiv:1102.2886v3 (2011)) when where q the number of colors, Δ is the degree and .. is the unique solution to . It has also been established in (Goldberg et al., SICOMP 35 (2005) 486–517) for bounded degree lattice graphs whenever for some constant β, where Δ is the maximum vertex degree of the graph. We establish strong spatial mixing for a more general problem, namely list coloring, for arbitrary bounded degree triangle‐free graphs. Our results hold for any whenever the size of the list of each vertex v is at least where is the degree of vertex v and β is a constant that only depends on α. The result is obtained by proving the decay of correlations of marginal probabilities associated with graph nodes measured using a suitably chosen error function. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,599–613, 2015     

THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS

This article consider, for the following heat equation ut/|x|s-△pu=uq,(x,t)∈Ω×(0,T), u(x,t)=0,(x,t)∈(?)Ω×(0,T), u(x,0)=u0(x),u0(x)≥0,u0(x)(?)0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, whereΩis a smooth bounded domain in RN(N>p),0∈Ω,△pu=div(|▽u|p-2▽u),0≤s≤2,p≥2,p-1相似文献   

Large time behavior of solutions to 3D compressible Navier-Stokes-Poisson system

We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.     

Exponential decay of the solutions for nonlinear multiharmonic equations

The purpose of this paper is to establish the exponential decay properties of the solutions for the nonlinear multiharmonic equation

where the condition plays the role of a boundary value condition.     

General decay of solutions of a viscoelastic equation

In this paper we consider the following viscoelastic equation:

     

A Note on Time-Decay Estimates for the Compressible Navier–Stokes Equations

In the recent work, we have developed a decay framework in general L~p critical spaces and established optimal time-decay estimates for barotropic compressible Navier–Stokes equations. Those decay rates of L~q-L~r type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.     

具有代数衰减的边界层问题

本文研究了不满足Tikhnov定理中稳定性要求的一类常微分方程奇摄动边值问题.利用边界层函数法以及微分不等式理论,分别构造了渐进解的形式和证明了解的存在性和渐近解一致有效性并进行了余项估计,得出了该类问题边界层代数式衰减的结论.     

Smooth orthonormal wavelets with exponential decay in both time and frequency domains

This article presents the existence of a non-trivial smooth orthonormal wavelet with exponential decay in both time and frequency domains. Meanwhile, we also show that the Meyer wavelets are not in the Schwartz class.     

General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity

This work deals with the study of a new class of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity. A decay result of the energy of solutions for the problem without imposing the usual relation between a certain relaxation function and its derivative is established. This result generalizes earlier ones to an arbitrary rate of decay, which is not necessarily of exponential or polynomial decay.     

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In this paper, we discuss tail asymptoticsproperties for a class of infinite phase type distributions based onprobability generating function or Laplace-Stieltjes transform. The results show that, unlike finite phase cases, the tail asymptotics for the infinite phase type distributions we considered do not decay geometrically or exponentially.     

Uniform decay in a Timoshenko-type system with past history

Fernández Sare and Rivera [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502] considered the following Timoshenko-type system

ρ₁φ_tt−K(φ_x+ψ)_x=0,