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41.
D. Dryanov 《Constructive Approximation》2009,30(1):137-153
Kolmogorov ε-entropy of a compact set in a metric space measures its metric massivity and thus replaces its dimension which is usually infinite. The notion quantifies the compactness property of sets in metric
spaces, and it is widely applied in pure and applied mathematics. The ε-entropy of a compact set is the most economic quantity of information that permits a recovery of elements of this set with
accuracy ε. In the present article we study the problem of asymptotic behavior of the ε-entropy for uniformly bounded classes of convex functions in L
p
-metric proposed by A.I. Shnirelman. The asymptotic of the Kolmogorov ε-entropy for the compact metric space of convex and uniformly bounded functions equipped with L
p
-metric is ε
−1/2, ε→0+.
相似文献
42.
Martin de Kort Adriaan W. Tuin Hermen S. Overkleeft Rogier C. Buijsman 《Tetrahedron letters》2004,45(10):2171-2175
The synthesis of ionic support 1 and its application in the preparation of a set of amides and sulfonamides is described. The potential of 1 is further exemplified by its use in a one-pot multistep ionic liquid phase assisted synthesis of tirofiban analogue 2. 相似文献
43.
In this paper we present a multistep difference scheme for the problem of miscible displacement of incompressible fluid flow in porous media. The discretization involves a three-level time scheme based on the characteristic method and a five-point finite difference scheme for space discretization. We prove that the convergence is of order O(h2+(Δt)2), which is in contrast to the convergence of order O(h+Δt) proved for a singlestep characteristic with the same space discretization. Numerical experiments demonstrate the stability and second-order convergence of the scheme. 相似文献
44.
45.
In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures. This allows many multistep methods of practical interest to be included in the theory. In a related manner, we also consider contractivity and stability in arbitrary norms.
46.
In the present paper we introduce a new methodology for the development of numerical methods for the numerical solution of
the one-dimensional Schr?dinger equation. The new methodology is based on the requirement of vanishing the phase-lag and its
derivatives. The efficiency of the new methodology is proved via error analysis and numerical applications.
T. E. Simos is Highly Cited Researcher, Active Member of the European Academy of Sciences and Arts.
Corresponding Member of the European Academy of Sciences and European Academy of Arts, Sciences and Humanities. 相似文献
47.
E.O. Ayoola 《随机分析与应用》2013,31(4):525-554
Multistep schemes for computing weak solutions of Lipschitzian quantum stochastic differential equations (QSDE) driven by certain operator-valued stochastic processes associated with the basic field operators of quantum field theory are introduced and studied. This is accomplished within the framework of the Hudson–Parthasarathy formulation of quantum stochastic calculus and subject to matrix element of solution being sufficiently differentiable. Results concerning convergence of explicit schemes of class A in the topology of the locally convex space of solution are presented.Numerical examples are given. 相似文献