Elastic line deformed on a pseudo-hypersurface by an external field in pseudo-Euclidean spaces

We derive intrinsic formulation for elastic line deformed on a pseudo-hypersurface by an external field in the pseudo-Euclidean spaces E_v~n.This formulation determines elastic line deformed on a pseudo-hypersurface.     

Minkowski空间中定向曲面上的第二类松弛弹性线

在Minkowski空间中,定义了定向曲面上的第二类松弛弹性线,推导了在定向曲面上的第二类松弛弹性线的Euler-Lagrange方程．进一步阐明了,这些曲线是否落在曲率线上,最后给出相关的实例．     

Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the galilean space

In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G₃. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G₃.     

Some properties of cones in normed spaces and their application to investigating extremal problems

In the present paper, the notions of cones of the same sense and cones of the opposite sense are introduced. The basic properties of these cones are examined. The most essential property is the following: ifX is a Banach space, then, in the dual spaceX*, the algebraic sum of a finite number of weakly * closed convex cones of the same sense is weakly * closed. On the basis of the properties of these cones, some necessary conditions for the existence of extrema in extremal problems are given.     

On the first stationary boundary-value problem of elasticity in weighted Sobolev spaces in exterior domains of R3

This paper solves the first boundary-value problem of elasticity both in interior and exterior domains ofR ³. The equations are set in weighted Sobolev spaces for exterior domains that describe the decay of the functions at infinity. The results established include existence, regularity, and convergence of iterations of the solution.This research was supported by the Rashi Foundation.     

Some remarks on the geodesics in infinite dimensional Teichmüller spaces

LetB denote the set of those pointsp in an infinite dimensional Teichmüller space such that a geodesic between the zero point andp is not unique. Some properties of the setB are given.     

A second-order Cauchy problem in a scale of Banach spaces and application to Kirchhoff equations

In a scale of Banach spaces we study the Cauchy problem for the equation u^′′=A(Bu(t),u), where A is a bilinear operator and B is a completely continuous operator. Obtained results are applied to prove existence of solutions in the Gevrey class for Kirchhoff equations.     

Some results on semilinear stochastic differential equations in hilbert spaces

We study a semilinear stochastic equation by reducing it to a deterministic problem     

An operator model for the oscillation problem of liquids on an elastic bottom

This paper deals with the problem of small oscillations in a liquid layer of finite depth under the assumption that the bottom is an elastic medium. The system of equations corresponding to the problem is written out and explained. The main aim of the paper is to recast these equations in the form

Constant mean curvature graphs in a class of warped product spaces

We introduce a new existence result for compact normal geodesic graphs with constant mean curvature and boundary in a class of warped product spaces. In particular, our result includes that of normal geodesic graphs with constant mean curvature in hyperbolic space over a bounded domain in a totally geodesic .      

Algebraic splines in locally convex spaces

In a vector space of continuous functions, a variational solution of a finite system of linear functional equations is found. The locally convex topology on the vector space and the properties of the objective functional required for obtaining the solution in the form of a decomposition in the basis dual to the family of functionals of the system are determined. The basis elements are calculated exactly and called basis algebraic splines; their linear span is called the space of algebraic splines in the corresponding locally convex space.Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 339–353.Original Russian Text Copyright © 2005 by A. P. Kolesnikov.This revised version was published online in April 2005 with a corrected issue number.     

Compact embedding in Besov spaces and B-separable elleptic operators

Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are two Banach spaces and E 0  E.The most regular class of interpolation space E α,between E 0 and E are found such that the mixed differential operator D α is bounded and compact from B p,q l,s (Ω;E 0,E) to B p,q s (Ω;E α) and Ehrling-Nirenberg-Gagliardo type sharp estimates established.By using these results the separability of differential operators with variable coefficients and the maximal B-regularity of parabolic Cauchy problem are obtained.In applications,the infinite systems of the elliptic partial differential equations and parabolic Cauchy problems are studied.     

A duality principle in weighted Sobolev spaces on the real line

An embedding inequality of Sobolev type is characterized in the paper with help of a duality principle and boundedness criteria for the Hardy–Steklov integral operator in weighted Lebesgue spaces.     

Gradient estimates for parabolic equations in generalized weighted Morrey spaces

We consider the Cauchy–Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain.The coefficients supposed to be only measurable in one of the space variables and small BMO with respect to the others.We obtain Calderón–Zygmund type estimate for the gradient of the solution in generalized weighted Morrey spaces with Muckenhoupt weight.     

Transit passenger origin-destination estimation in congested transit networks with elastic line frequencies

This paper deals with the transit passenger origin-destination (O-D) estimation problem by using updated passenger counts in congested transit networks and outdated prior O-D matrix. A bilevel programming approach is extended for the transit passenger O-D updating problem where the upper-level problem seeks to minimize the sum of error measurements in passenger counts and O-D matrices, while the lower level is the stochastic user equilibrium assignment problem for congested transit networks. The transit assignment framework is based on a frequency-adaptive transit network model in this paper, which can help determine transit line frequencies and the network flow pattern simultaneously in congested transit networks. A heuristic solution algorithm is adapted for solving the transit passenger O-D estimation problem. Finally, a numerical example is used to illustrate the applications of the proposed model and solution algorithm. The work described in this paper was mainly supported by two research grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU 5143/03E and PolyU 5040/02E).     

Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line

Consider an evolution family U=(U(t,s))_t?s?0 on a half-line R₊ and an integral equation . We characterize the exponential dichotomy of the evolution family through solvability of this integral equation in admissible function spaces which contain wide classes of function spaces like function spaces of Lp type, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory. We then apply our results to study the robustness of the exponential dichotomy of evolution families on a half-line under small perturbations.     

Hardy spaces for the conjugated Beltrami equation in a doubly connected domain

We consider Hardy spaces associated to the conjugated Beltrami equation on doubly connected planar domains. There are two main differences with previous studies (Baratchart et al., 2010 [2]). First, while the simple connectivity plays an important role in Baratchart et al. (2010) [2], the multiple connectivity of the domain leads to unexpected difficulties. In particular, we make strong use of a suitable parametrization of an analytic function in a ring by its real part on one part of the boundary and by its imaginary part on the other. Then, we allow the coefficient in the conjugated Beltrami equation to belong to W1,q for some q∈(2,+∞], while it was supposed to be Lipschitz in Baratchart et al. (2010) [2]. We define Hardy spaces associated with the conjugated Beltrami equation and solve the corresponding Dirichlet problem. The same problems for generalized analytic function are also solved.