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91.
证明了由BMO函数与α阶内蕴面积函数S_α和内蕴g_(λ,α)*函数生成的交换子都是由加权弱Hardy空间WH_(b,ω)~1到加权弱L1空间WL_ω~1上的有界算子. 相似文献
92.
Optical vortices as topological objects exist ubiquitously in nature. In this paper, we use the principle of variational method and mountain pass lemma to develop some existence theorems for the stationary vortex wave solution of a coupled nonlinear Schrödinger equations, which describe the possibility of effective waveguiding of a weak probe beam via the cross‐phase modulation‐type interaction. The main goal is to obtain a positive solution, of minimal action if possible, with all vector components not identically zero. Additionally, as demanded by beam confinement, we prove the exponential decay of the soliton amplitude at infinity. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
93.
94.
Let LB be a sequent calculus of the first-order classical temporal logic TB with time gaps. Let, further, LBJ be the intuitionistic counterpart of LB. In this paper, we consider conditions under which a sequent is derivable in the calculus LBJ if and only if it is derivable in the calculus LB. Such conditions are defined for sequents with one formula in the succedent (purely Glivenko -classes) and for sequents with the empty succedent (Glivenko -classes). 相似文献
95.
We prove a uniform bound for the density, p
t
(x), of the solution at time t(0, 1] of a 1-dimensional stochastic differential equation, under hypoellipticity conditions. A similar bound is obtained for an expression involving the distributional derivative (with respect to x) of p
t
(x). These results are applied to extend the Itô formula to the composition of a function (satisfying slight regularity conditions) with a hypoelliptic diffusion process in the spirit of the work of Föllmer et al.
(5) 相似文献
96.
Differential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous
and discrete time-evolution processes respectively. The processes in which time evolution takes place on Cantor-like fractal
subsets of the real line may be termed as fractal-time dynamical systems. Formulation of these systems requires an appropriate
framework. A new calculus calledF
α-calculus, is a natural calculus on subsetsF⊂ R of dimension α,0 < α ≤ 1. It involves integral and derivative of order α, calledF
α-integral andF
α-derivative respectively. TheF
α-integral is suitable for integrating functions with fractal support of dimension α, while theF
α-derivative enables us to differentiate functions like the Cantor staircase. The functions like the Cantor staircase function
occur naturally as solutions ofF
α-differential equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems.
We discuss construction and solutions of some fractal differential equations of the form
whereh is a vector field andD
F,t
α
is a fractal differential operator of order α in timet. We also consider some equations of the form
whereL is an ordinary differential operator in the real variablex, and(t,x) ∈F × Rn whereF is a Cantor-like set of dimension α.
Further, we discuss a method of finding solutions toF
α-differential equations: They can be mapped to ordinary differential equations, and the solutions of the latter can be transformed
back to get those of the former. This is illustrated with a couple of examples. 相似文献
97.
In this paper we show that the Cahn–Hilliard stochastic PDE has a function valued solution in dimension 4 and 5 when the perturbation is driven by a space-correlated Gaussian noise. We study the regularity of the trajectories of the solution and the absolute continuity of its law at some given time and position. This is done by showing a priori estimates which heavily depend on the specific equation, and by proving general results on stochastic and deterministic integrals involving general operators on smooth domains of d which are parabolic in the sense of Petrovskii, and do not necessarily define a semi-group of operators. These last estimates might be used in a more general framework. 相似文献
98.
DING Yong LU Shanzhen & ZHANG PuDepartment of Mathematics Beijing Normal University Beijing China Department of Information Computing Science Zhejiang Institute of Science Technology Hangzhou China 《中国科学A辑(英文版)》2004,47(1):83-95
In this paper the authors give the weighted weak L logL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities for the Marcinkiewicz integral and its commutators with different weight functions are also discussed. 相似文献
99.
In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate
coercivity whose prototype is
where for example, a(x,u)=(1+|u|)−θ with θ ∈ (0,1). We study the same problem for minima of functionals closely related to the previous equation. 相似文献
100.
THE SPACE—FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS 总被引:1,自引:0,他引:1
The space-fractional telegraph equation is analyzed and the Fourier transform of its fundamental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies the space-fractional telegraph equation, is presented. Its limiting behaviour and the connection with symmetric stable processes is also examined. 相似文献