We propose a stochastic Forward Douglas-Rachford Splitting framework for finding a zero point of the sum of three maximally monotone operators in real separable Hilbert space, where one of them is cocoercive. We first prove the weak almost sure convergence of the proposed method. We then characterize the rate of convergence in expectation in the case of strongly monotone operators. Finally, we ...

We study explicit solutions for orientifolds of Matrix theory compactified on noncommutative torus. As quotients of torus, cylinder, Klein bottle and Möbius strip are applicable as orientifolds. We calculate the solutions using Connes, Douglas and Schwarz’s projective module solution, and investigate twisted gauge bundle on quotient spaces as well. They are Yang-Mills theory on noncommutative t...

Thomas Bristow, Robert Downs, Marc Gailhanou, Franck Marchis, Douglas Ming, Richard Morris, Vicente Armando Solé, Kathleen Thompson, Philippe Walter, Michael Wilson, Albert Yen and Samuel Webb, NASA Ames Research Center, Moffett Field, CA [email protected], SETI Institute, Mountain View, CA, Univ. of Arizona, Tucson AZ, IM2NP, Université Paul Cézanne, Marseille, France, NASA Johnson Space Ce...

In this paper, we study a special class of generalized Douglas-Weyl metrics whose Douglas curvature is constant along any Finslerian geodesic. We prove that for every Landsberg metric in this class of Finsler metrics, ? = 0 if and only if H = 0. Then we show that every Finsler metric of non-zero isotropic flag curvature in this class of metrics is a Riemannian if and only if ? = 0.

An optimal consumption problem is studied in a growth model for the Cobb-Douglas production function in a finite horizon. The problem is transfered into a stochastic Ramsey problem so as to reduce the dimension of the state space. The corresponding state equation is a stochastic differential ∗The second author is supported in part by a start-up fund at University of Oxford, and RGC Earmarked Gr...

We analyse the behaviour of the newly introduced cyclic Douglas–Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty. 1. Preliminaries and Notation Throughout we assume H is a (real) Hilbert space with inner product 〈·, ·〉 and induced norm ‖ · ‖. We use → (resp. w....

We present a numerical method for the computat ion of discrete solutions of the Plateau Problem. This problem consists of the investigation of minimal surfaces bounded by a prescribed Jordan curve in space. The numerical method allows to compute unstable minimal surfaces with prescribed boundary . It is based on a Boundary Element Method for which asymptotic convergence was proved and which use...

In this paper we analyze and extend a class of adaptive networks for second order blind decorrelation of instantaneous signal mixtures Firstly we compare the performance of the decorrelation neural network employing global knowledge of the adaptive coe cients with a similar structure whose coe cients are adapted via lo cal output connections Through statistical analyses the convergence behavior...