摘要 :
We derive from Motzkin's Theorem that a point can be strongly separated by a hyperplane from a convex polytope and a finitely-generated convex cone. We state a similar result for Tucker's Theorem of the alternative. A generalisati...
展开
We derive from Motzkin's Theorem that a point can be strongly separated by a hyperplane from a convex polytope and a finitely-generated convex cone. We state a similar result for Tucker's Theorem of the alternative. A generalisation of the residual existence theorem for linear equations which has recently been proved by Rohn [8] is a corollary. We state all the results in the setting of a general vector space over a linearly ordered (possibly skew) field.
收起
摘要 :
Two recent results of Zhang and Zhou in [1] are shown to be special cases of previously established oscillation theorems for second-order linear difference equations. (C) 2003 Elsevier Science Ltd. All rights reserved. [References: 4]
摘要 :
We present a library of PVS meta-theories that can be used to verify a class of distributed systems in which agent communication is via message-passing. The theoretical work, as outlined in Chandy et al. (Form Aspect Comput 2011, ...
展开
We present a library of PVS meta-theories that can be used to verify a class of distributed systems in which agent communication is via message-passing. The theoretical work, as outlined in Chandy et al. (Form Aspect Comput 2011, to appear) consists of iterative schemes for solving systems of linear equations, such as message-passing extensions of the Gauss and Gauss-Seidel methods. We briefly review that work and discuss the challenges in formally verifying it.
收起
摘要 :
In this paper, on the basis of some recent works of Fan, Jiang and Jia, we establish a representation theorem in the space of processes for generators of BSDEs with continuous linear-growth generators, which generalizes the corres...
展开
In this paper, on the basis of some recent works of Fan, Jiang and Jia, we establish a representation theorem in the space of processes for generators of BSDEs with continuous linear-growth generators, which generalizes the corresponding results in Fan (2006, 2007) [10,11] and Fan and Hu (2008) [9].
收起
摘要 :
We prove new bounds for sums of multiplicative characters over sums of set with small doubling, and applying this result, we break the square-root barrier in a problem of Balog concerning products of differences in a field of prime order.
摘要 :
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem (P){u(t) + A(t)u(t) = f(t) t-a.e. on [0, τ ],u(0) = 0,} where A: [0, τ ] →φ(X,D) is a bounded and strongly measurable function and X, D ...
展开
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem (P){u(t) + A(t)u(t) = f(t) t-a.e. on [0, τ ],u(0) = 0,} where A: [0, τ ] →φ(X,D) is a bounded and strongly measurable function and X, D are Banach spaces such that D →d X. Our main concern is to characterize Lp-maximal regularity and to give an explicit approximation of the problem (P).
收起
摘要 :
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem $$(P),\left\{ \begin{gathered} \dot u(t) + A(t)u(t) = f(t) t - a.e. on [0,\tau ] \hfill \\ u(0) = 0, \hfill \\ ...
展开
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem $$(P),\left\{ \begin{gathered} \dot u(t) + A(t)u(t) = f(t) t - a.e. on [0,\tau ] \hfill \\ u(0) = 0, \hfill \\ \end{gathered} \right.$$ where A: [0, τ] → L(X,D) is a bounded and strongly measurable function and X, D are Banach spaces such that . Our main concern is to characterize L p -maximal regularity and to give an explicit approximation of the problem (P). Keywords maximal regularity on-autonomous evolution equation stability for linear evolution equation integrability for linear evolution equation MSC 2010 35K90 47D06 This work was financially supported by the Deutscher Akademischer Austauschdienst (DAAD).
收起
摘要 :
In this work we prove a C-1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As ail intermediate step, we prove a specific result of existence of invariant mani...
展开
In this work we prove a C-1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As ail intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations. (C) 2004 Elsevier Inc. All rights reserved.
收起
摘要 :
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations ...
展开
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are well-behaved, we do not assume any asymptotic behaviour of the linear system. Moreover, the control on the nonlinear perturbations may differ along finitely many mutually complementary directions. We consider both the cases of one-sided discrete and continuous dynamics.
收起
摘要 :
Integrating factors and adjoint equations are determined for linear and non-linear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary diff...
展开
Integrating factors and adjoint equations are determined for linear and non-linear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables. The method is illustrated by considering several equations traditionally regarded as equations without Lagrangians. Noether's theorem is applied to the Maxwell equations. (c) 2005 Elsevier Inc. All rights reserved.
收起
原文获取