In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

The violation of Bell's inequalities in some EPR-type paired-photon experiments could be as much due to the sensitivity of the coincidence monitoring system to timing variations as to other causes of \enhancement". If there are systematic variations of processing time with polarisation angle, then the \factorability" assumption may not hold if window size and other parameters are not carefully ...

The current record in factoring large RSA keys is the factorization of a 465 bit (140 digit) number achieved in February 1999 by running the Number Field Sieve on hundreds of workstations for several months. This paper describes a novel factoring technique which is several orders of magnitude more e cient. It is based on a very simple handheld optoelectronic device which can analyse 100,000,000...

We report on the generation of an indistinguishable heralded single-photon state, using highly nondegenerate spontaneous parametric downconversion (SPDC). Spectrally factorable photon pairs can be generated by incorporating a broadband pump pulse and a group-velocity matching (GVM) condition in a periodically-poled potassium titanyl phosphate (PPKTP) crystal. The heralding photon is in the near...

In the course of developing a distributed logistics command and control application based on the Cougaar agent architecture@ttp://www.cougaar.org/). we were faced with a Iorge knowledge representation problem. The logistics agents needed to reason about many thousands of different types of logistics assets, where each asset had hundreds of attribuies. The problem is factorable, however, in that...

Edge (5, 3)-colorings of a (5, 3)-regular bipartite graph relating 5cycles and vertices of the Petersen graph lead to solutions of the Great Circle Challenge. This takes, for odd n = 2k + 1 > 1, to a canonical 1-1 correspondence from the family of n-cycles of the complete graph Kn onto the family Ck of n-cycles of the odd graph Ok+1 and onto the family of their pullback 2n-cycles in the middle-...

We have designed and implemented a photon-pair source, based on the spontaneous four wave mixing (SFWM) process in a few-mode fiber, in a geometry which permits multiple, simultaneous SFWM processes, each associated with a distinct combination of transverse modes for the four participating waves. In our source: i) each process is group-velocity-matched so that it is, by design, nearly-factorabl...

We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations of the form yI = ∏ i∈I xi over the 0−1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained binary polynomial optimization problem. We def...

The current record in factoring large RSA keys is the factorization of a 465 bit (140 digit) number achieved in February 1999 by running the Number Field Sieve on hundreds of workstations for several months. This paper describes a novel factoring technique which is several orders of magnitude more e cient. It is based on a very simple handheld optoelectronic device which can analyse 100,000,000...