Showing papers in "Journal of Mathematical Sciences in 1994"
TL;DR: Tangent spaces of a sub-Riemannian manifold are themselves sub-riemannians as mentioned in this paper, and they come with an algebraic structure: nilpotent Lie groups with dilations.
Abstract: Tangent spaces of a sub-Riemannian manifold are themselves sub-Riemannian manifolds. They can be defined as metric spaces, using Gromov’s definition of tangent spaces to a metric space, and they turn out to be sub-Riemannian manifolds. Moreover, they come with an algebraic structure: nilpotent Lie groups with dilations. In the classical, Riemannian, case, they are indeed vector spaces, that is, abelian groups with dilations. Actually, the above is true only for regular points. At singular points, instead of nilpotent Lie groups one gets quotient spaces G/H of such groups G.
749 citations
TL;DR: In this article, various classes of extensions and generalized resolvents of Hermitian operators acting in Krein spaces are described in terms of abstract boundary conditions and abstract boundary condition.
Abstract: Various classes of extensions and generalized resolvents of Hermitian operators acting in Krein spaces are described in terms of abstract boundary conditions.
75 citations
TL;DR: In this article, generalizations of Sobolev spaces in two directions are considered: instead of LP-norms one makes use of more general norms and, secondly, spaces of functions with values in a Banach space are investigated.
Abstract: Generalizations of Sobolev spaces in two directions are considered: firstly, instead of LP-norms one makes use of more general norms and, secondly, spaces of functions with values in a Banach space are investigated. The problem of the connection between such spaces and spaces of Bessel potentials is solved.
46 citations
TL;DR: In this article, it was shown that many known properties of the spaces W σ p (some imbedding and uniqueness theorems, the Logvinenko-Sereda theorem on equivalent norms, S. N. Bernshtein's differential inequality) remain valid for the spaces K θ p if and only if the derivative θ′ is bounded.
Abstract: Let W σ p be the space of entire fonctions in ℂ of exponential type ≤ σ, whose restrictions to the real line ℝ belong to Lp(ℝ). For an inner function θ in the upper half- plane ℂ+ we denote by K θ p (p ≥ 1) the invariant subspace of the inverse shift operator (the model subspace) in Hp, generated by the function θK θ p =Hp ∩\(\theta \bar H^\beta \), where Hp=Hp(ℂ+) is the Hardy class. In the paper it is shown that many known properties of the spaces W σ p (some imbedding and uniqueness theorems, the Logvinenko-Sereda theorem on equivalent norms, S. N. Bernshtein's differential inequality) remain valid for the spaces K θ p if and only if the derivative θ′ is bounded. The classical results for entire functions are obtained for θ(x)= eiσx.
46 citations
TL;DR: In this article, the authors studied the initial-boundary value problem for the Stokes' system, arising at the investigation of the nonstationary motion of two viscous fluids, separated by a free surface.
Abstract: One studies the initial-boundary value problem for the Stokes' system, arising at the investigation of the nonstationary motion of two viscous fluids, separated by a free surface. Junction conditions are prescribed in the plane ×3=0}. The consideration of the surface tension leads to a noncoercive integral term in the condition for the jump of the normal stresses. The unique solvability and estimates of the solution in Holder classes of functions of the given model problem are proved with the aid of a theorem on Fourier multipliers and a significant part of the paper is devoted to the proof of the required modifications of this theorem.
42 citations
TL;DR: In this paper, the classical global solvability on [0, ∞] is proved for initial-boundary value problems (30), (32), (33), and (31, (32, and 33) which describe two-dimensional motion of Oldroyd fluids and three dimensional motion of Kelvin fluids of orders L = 2, 3, ⋯.
Abstract: Classical global solvability on [0, ∞) is proved for initial-boundary value problems (30), (32), (33), and (31), (32), (33) which describe two-dimensional motion of Oldroyd fluids and three-dimensional motion of Kelvin—Voight fluids of orders L = 2, 3, ⋯ .
35 citations
TL;DR: A survey of results on the theory of deformation and infinitesimal deformation of surfaces in three-dimensional Euclidean space can be found in this paper, with a focus on the last 25-30 years.
Abstract: This article surveys results on the theory of deformation and infinitesimal deformation of surfaces in three-dimensional Euclidean space that have been obtained in the last 25–30 years and do not appear in previous survey articles.
35 citations
TL;DR: In this article, a survey of variational principles for equations with operators which are nonpotential is presented, with a series of applications in theoretical physics and analytic mechanics, as well as for graduate students of physics.
Abstract: One presents numerous approaches for the construction of variational principles for equations with operators which, in general, are nonpotential One considers separately linear and nonlinear ordinary differential equations, partial and integropartial differential equations One constructs and investigates both extremal and stationary variational principles and one gives applications of these principles in theoretical physics and in analytic mechanics A series of unsolved problems are indicated The survey is intended for mathematicians, physicists, working in both theoretical and applied areas, as well as for graduate students of physics and mathematics
29 citations
24 citations
TL;DR: In this paper, the boundary value problem for a half plane for the elliptic sine-Gordon equation is solved using the inverse scattering method, which is applied to the theory of the stationary Josephson effect.
Abstract: The boundary-value problem for a half plane for the elliptic sine-Gordon equation is solved using the inverse scattering method. The solution is applied to the theory of the stationary Josephson effect.
20 citations
TL;DR: An algorithm is obtained for factoring polynomials in several variables over local fields with complexity which is polynomial in the length of notation of the input data and the characteristic of the residue field of the local field.
Abstract: An algorithm is obtained for factoring polynomials in several variables over local fields with complexity which is polynomial in the length of notation of the input data and the characteristic of the residue field of the local field. Here by definition we assume that an infinite series can be calculated in polynomial time if its i-th partial sum can be calculated in time which is polynomial in the length of notation of the input data and i for any i.
TL;DR: In this paper, the problem of the minimax detection of a signal is considered in a Gaussian white noise of intensity e → 0, where the set of the signals represents an ellipsoid in the lp-metric with lengths of semiaxes α−1 → 0 as k → ∞.
Abstract: The problem of the minimax detection of a signal is considered in a Gaussian white noise of intensity e → 0. The set of the signals represents an ellipsoid in the lp-metric with lengths of semiaxes ak−1 → 0 as k → ∞, from which a ball of radius ρe → 0 as e → 0 in the lp-metric has been removed. Asymptotically minimax tests have been constructed for the cases 1 < p ≤ ∞ and asymptotically sharp estimates of the minimax efficiency have been obtained.
TL;DR: In this paper, the authors investigated the solvability, uniqueness, and regularity of the solution of the evolution variational inequality, arising in the theory of the motion of a two-dimensional Bingham fluid.
Abstract: In this paper one investigates the solvability, uniqueness, and regularity of the solution of the evolution variational inequality, arising in the theory of the motion of a two-dimensional Bingham fluid. It is proved that, under definite conditions, the family of resolving operators forms a semigroup, having a minimal global B-attractorM
λ. It is shown that, for certain values of the parameter λ, the attractorM
λ has a trivial structure. One gives an estimate of “the finite-dimensionality of the dynamics” of the semigroup on the attractorM
λ.
TL;DR: In this article, the authors considered single-server queueing systems with repeated calls and an unreliable server and obtained a central limit theorem and a diffusion approximation for the queue as a time-dependent process in the case of low rate of repeated calls.
Abstract: We consider single-server queueing systems with repeated calls and an unreliable server, which may fail both when free and when busy. A central limit theorem and a diffusion approximation theorem are obtained for the queue as a time-dependent process in the case of a low rate of repeated calls.
TL;DR: For the first time, the problem of arranging three non-overlapping circles of greatest total area in a triangle is solved as mentioned in this paper, which is the same as the problem we are solving here.
Abstract: For the first time Malfatti's old problem about arranging three non-overlapping circles of greatest total area in a triangle is solved.
TL;DR: In this paper, the definitions of homoclinic partitions and transformations are given in situations that are standard for topological dynamics and ergodic theory, and a variant of the central limit theorem is proved.
Abstract: The definitions of homoclinic partitions and transformations are given in situations that are standard for topological dynamics and ergodic theory A variant of the central limit theorem is proved, the formulation of which makes use of homoclinic transformations
TL;DR: In this article, the algebraic theory of rings of continuous functions is studied and the relationship between topological spaces and the corresponding rings of functions is considered, and the ring properties of ring properties are discussed.
Abstract: This survey paper is devoted to the algebraic theory of rings of continuous functions. The author considers the relationship between topological spaces and the corresponding rings of continuous functions. The ring properties of rings of continuous functions are discussed. The general theory of sheaves of rings is considered briefly. The importance of rings of functions in mathematics is demonstrated.
TL;DR: A priori C2+α estimates for the solutions of a fully nonlinear second-order parabolic equation satisfying a nondegenerate, nonlinear, first-order boundary condition were established in this paper.
Abstract: A prioriC2+α estimates are established for the solutions of a fully nonlinear second-order parabolic equation, satisfying a nondegenerate, nonlinear, first-order boundary condition.
TL;DR: Some estimates for the mean curvature of nonparametric surfaces defined over domains in R^n$ are given in this paper, where the curvature is defined as a function of the dimension of the domain.
Abstract: Some estimates for the mean curvature of nonparametric surfaces defined over domains in $R^n$
TL;DR: The unique global solvability of the initial-boundary value problem for phase field equations (1, 2) was shown in this paper, for which there exists a minimal global B-attractor.
Abstract: The unique global solvability of the initial-boundary value problem (1)–(3) is proved for the system of phase field equations (1), (2). It is shown that the problem (1)–(3) generates a continuous compact semigroup Vt, t>0, for which there exists a minimal global B-attractor.
TL;DR: In this paper, an algebra of functions on a quantum group and corresponding quantum algebra are defined, using a constant solution of the Yang-Baxter equation depending on two parameters, and a quantum algebra is defined.
Abstract: An algebra of functions on a quantum group and the corresponding quantum algebra are defined, using a constant solution of the Yang—Baxter equation depending on two parameters.
TL;DR: In this article, the authors proved that the probability of the form |F(X) − G(X), ≤ c(k)eβ(F, G, X) for a convex polyhedron X is small in a definite sense.
Abstract: Quantities of the form | F(X) — G(X) | are estimated, where F and G are the convolutions of certain k-dimensional probability distributions, while X is a convex polyhedron in Rk. Estimates of the form | F(X) — G(X) | ≤ c(k)eβ(F, G, X) are proved, differing from the known ones by the presence of the factor β(F, G, X) in the right-hand side, which may turn out to be small if the polyhedron X is small in a definite sense.
TL;DR: Collins' previously known method has a bound which is polynomial inM (kd)ro(1), and an algorithm is constructed which finds the connected components of the semialgebraic set in a time that is Poole's inequality.
Abstract: Let a semialgebraic set be defined by a quantifier-free formula with atomic subformulas of the form fi>0, 0,1 ≦ i ≦ where the polynomials fieℤ[X1,..., Xn] of degree deg (fi)
TL;DR: In this article, it was shown that these integrals satisfy nontrivial algebraic relations, which makes possible the construction of polynomial algorithms for certain polyhedra, and examples are given of the application of exponential integrals to the calculation of volume and nonlinear programming.
Abstract: Let P⊂ ℝdbe a convex polyhedron and f: ℝd→ℝ a linear function. One studies the computational complexity of the integral ∫pexp f(xdx. It is shown that these integrals satisfy nontrivial algebraic relations, which makes possible the construction of polynomial algorithms for certain polyhedra. Examples are given of the application of exponential integrals to the calculation of volume and nonlinear programming.
TL;DR: In this paper, a survey of results obtained on various classes of submanifolds with the interior geometry of Riccisemisymmetric spaces is presented. But the results are restricted to the case where the interior is convex.
Abstract: This article surveys results obtained on various classes of submanifolds with the interior geometry of Riccisemisymmetric spaces.
TL;DR: In this paper, a boundary value problem for the Stokes equations is examined in an exterior domain Ω ⊂ℝn with a uniform Dirichlet condition on the boundary and a homogeneous condition at infinity.
Abstract: A boundary value problem for the Stokes equations is examined in an exterior domain Ω ⊂ℝnwith a uniform Dirichlet condition on the boundary and a homogeneous condition at infinity. It is shown that estimating the norm Lp(Ω) of the second derivatives of the velocity vector field by the same norm of the exterior forces vector field is correct for p < n/2, but not for p ≥ n/2. This estimate is valid also for p ≥ n/2 if the boundary conditions are modified at infinity.
TL;DR: In this paper, Menelaus and Ceva analogies of the classic theorems for a hyperbolic surface, a sphere, and for three-dimensional hyper-bolic and spherical spaces are considered.
Abstract: Certain analogs of the classic theorems of Menelaus and Ceva are considered for a hyperbolic surface, a sphere, and for three-dimensional hyperbolic and spherical spaces.