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31.
A. I. Panasyuk 《Journal of Optimization Theory and Applications》1990,64(2):349-366
In control theory, there is growing interest in the evolution of sets, especially attainable sets at timet. This is caused due to their applications to control under uncertainty, optimal control, and differential games. Recently, a new mathematical theory for attainable set evolution was developed. It is based on the concept of approximate localization, instead of differentiation. Here, we give a generalization of this theory. 相似文献
32.
Luc Devroye 《Random Structures and Algorithms》1990,1(2):191-203
A random m-ary seach tree is constructed from a random permutation of 1,…, n. A law of large numbers is obtained for the height Hn of these trees by applying the theory of branching random walks. in particular, it is shown that Hn/log n→γ in probability as n→∞ where γ = γ(m) is a constant depending upon m only. Interestingly, as m→∞, γ(m) is asymptotic to 1/log m, the coefficient of log n in the asymptotic expression for the height of the complete m-ary search tree. This proves that for large m, random m-ary search trees behave virtually like complete m-ary trees. 相似文献
33.
We construct classical point symmetry groups for joint pairs of evolution equations (systems of equations) of integrable hierarchies related to the auxiliary equation of the method of the inverse problem of second order. For the two cases: the hierarchy of Korteweg--de Vries (KdV) equations and of the systems of Kaup equations, we construct simultaneous solutions invariant with respect to the symmetry group. The problem of the construction of these solutions can be reduced, respectively, to the first and second Painlevé equations depending on a parameter. The Painlevé equations are supplemented by the linear evolution equations defining the deformation of the solution of the corresponding Painlevé equation. 相似文献
34.
We study a system of quasilinear equations describing one-dimensional flow of a viscous compressible heat-conducting medium with a nonmonotone state function and mass force. The large-time behavior of solutions is considered for arbitrarily large initial data. In spite of possible nonuniqueness and discontinuity of the stationary solution, we prove L2-stabilization for the stress and heat flux as t → ∞ along with corresponding global energy estimates for them. The new method of proof utilizes a combination of energy type equalities for the stress and heat flux. Consequently, H1-stabilization of the velocity and temperature along with global estimates for their derivatives are valid as well. 相似文献
35.
36.
We discuss integral transformations of the QCD renormalization-invariant coupling (running coupling constant). Special attention is paid to the Fourier transformation, i.e., to the transition from the space–time to the energy–momentum representation. Our first conclusion is that the condition for the possibility of such a transition provides one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second conclusion relates to a way to translate some singular long-wave asymptotic behaviors to the infrared region of transferred momenta. Such a transition must be performed with the Tauberian theorem taken into account. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by numerical lattice simulation. 相似文献
37.
Mathematical Notes - 相似文献
38.
Toshio Matsushima 《Journal of Mathematical Analysis and Applications》2003,285(2):691-707
Let Ω be a domain of . As a study of boundary behavior of functions and maps in Ω, we consider “the linear cluster set,” which is the cluster set along segment terminating at a boundary point of Ω. We prove that there exist bounded holomorphic functions and maps defined in Ω which have the linear cluster sets of positive measure at every point of a discrete subset of the boundary of Ω under some conditions. 相似文献
39.
Belinda B. King Oliver Stein Michael Winkler 《Journal of Mathematical Analysis and Applications》2003,286(2):459-490
We study the continuum model for epitaxial thin film growth from Phys. D 132 (1999) 520-542, which is known to simulate experimentally observed dynamics very well. We show existence, uniqueness and regularity of solutions in an appropriate function space, and we characterize the existence of nontrivial equilibria in terms of the size of the underlying domain. In an investigation of asymptotical behavior, we give a weak assumption under which the ω-limit set of the dynamical system consists only of steady states. In the one-dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element. The article closes with some illustrative numerical examples. 相似文献
40.
We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line. 相似文献