Reed-Muller展开系数与谱系数之间的直接转换算法

本文通过引入p-bj系数,提出了实现Reeb-Muller展开系数与谱系数之间直接互相转换的矩阵算法。通过利用bj图与谱系数图,发展了有效实现谱系数转换为bj系数的图形方法。     

Stochastic differential equations with coefficients in Sobolev spaces

We consider the Itô stochastic differential equation on Rd. The diffusion coefficients A₁,…,Am are supposed to be in the Sobolev space with p>d, and to have linear growth. For the drift coefficient A₀, we distinguish two cases: (i) A₀ is a continuous vector field whose distributional divergence δ(A₀) with respect to the Gaussian measure γd exists, (ii) A₀ has Sobolev regularity for some p^′>1. Assume for some λ₀>0. In case (i), if the pathwise uniqueness of solutions holds, then the push-forward #(Xt)γd admits a density with respect to γd. In particular, if the coefficients are bounded Lipschitz continuous, then Xt leaves the Lebesgue measure Lebd quasi-invariant. In case (ii), we develop a method used by G. Crippa and C. De Lellis for ODE and implemented by X. Zhang for SDE, to establish existence and uniqueness of stochastic flow of maps.     

On the lindblad equation with unbounded time-dependent coefficients

We prove newa priori estimates for the resolvent of a minimal quantum dynamical semigroup. These estimates simplify well-known conditions sufficient for conservativity and impose continuity conditions on the time-dependent operator coefficients ensuring the existence of conservative solutions of the Markov evolution equations. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 125–140, January, 1997. Translated by A. M. Chebotarev     

IDENTIFICATION OF PARAMETERS IN SEMILINEAR PARABOLTC EQUATIONS

1IntroductionWeconsiderthefollowingsystem:notu--Z0',(a(x)ox.u)=f(x,t,u),(x,t)EQ,i=1,u(x,t)=0,(x,t)ES,(1)u(x,0)=u000,xEfi,wherefiisaboundeddomaininR"(n21),Q={(x,t):xEfi,tE(0,T)}with0相似文献   

Study of ion–solvent interactions and activation energy of LiBr in DMSO,H<Subscript>2</Subscript>O and DMSO–H<Subscript>2</Subscript>O mixtures at various temperatures

The Jones–Dole B coefficients of the electrolyte Lithium bromide (LiBr), reference salts tetra butyl ammonium tetra phenyl borate (BU₄NBPh₄), tetra butyl ammonium bromide (BU₄NBr), and potassium chloride (KCl) in dimethylsulfoxide (DMSO), water, and DMSO–water mixtures were obtained at different temperatures range from 25 to 45 °C For this, the relative viscosities were measured for Lithium bromide (LiBr) and reference salts in DMSO, water, and DMSO–water mixtures at above-mentioned temperatures. The B coefficients of these electrolytes were behaved as structure makers in DMSO, while in H₂O and DMSO–H₂O mixtures, the B-coefficient values were less positive showing the weak structure-making effect. Ionic viscosity B coefficients allow us to assess the behavior of ions in the solvent mixtures. In this study it was observed that all the values of ionic B coefficient of (Li⁺) were positive and small showing the weak structure-making effects. It was also observed that Br⁻ ions maintain negative B coefficient values in all DMSO–H₂O mixtures, except in 60% DMSO mole fraction. From this it can be concluded that Br⁻ ion behaved as a structure breaker in water and in all DMSO–H₂O mixtures except in 60% DMSO mole fraction mixtures. The low B _± values of alkali metal ions and Br⁻ ions in water are due to the breakdown of the tetrahedral structural of water and the formation of strongly structured solvated ion. It is also observed that the values of the energy of activation of the flow for LiBr are greater in DMSO–water mixtures and in pure water than in DMSO. This may be due the presence of a network of hydrogen bonds which cause the hindrance in the flow of the solution of LiBr in DMSO–water mixtures and in pure water than in DMSO.     

The Fejér-Riesz inequality for the Besov spaces

A Fejér-Riesz inequality for the weighted Besov spaces B _p,q is given. Some characterizations of functions in B _p,q in terms of their Taylor coefficients are obtained.     

Relations between regularity coefficients

For a bounded sequence of matrices defining a nonautonomous dynamics with discrete time, we obtain all possible relations between the regularity coefficients introduced by Lyapunov, Perron and Grobman. This includes considering general inequalities between the coefficients and showing that these inequalities are the best possible, in the sense that for any three nonnegative numbers satisfying them, and for no others, there exists a bounded sequence of matrices having the numbers respectively as Lyapunov, Perron and Grobman coefficients. Moreover, we establish inequalities between the three coefficients and some other regularity coefficients.     

High-order splitting methods for separable non-autonomous parabolic equations

We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative coefficients). We propose to consider a class of methods that allows us to evaluate all time-dependent operators at real values of the time, leading to schemes which are stable and simple to implement. If the system can be considered as the perturbation of an exactly solvable problem and the flow of the dominant part is advanced using real coefficients, it is possible to build highly efficient methods for these problems. We show the performance of this class of methods on several numerical examples and present some new improved schemes.     

On summability of Fourier coefficients of functions from Lebesgue space

In this paper we state new theorems of Hardy–Littlewood type for functions with general monotone Fourier coefficients. Sharpness of stated results is discusses.     

On the robustness of the BPX-preconditioner with respect to jumps in the coefficients

We determine the worst case behavior of the standard BPX-preconditioner for elliptic problems with arbitrary coefficient jumps along the boundaries of the coarsest partition. The counterexamples are also useful for other problems.