begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

We propose a method to axiomatize by equations the least pre$xed point of an order preserving function. We discuss its domain of application and show that the Boolean modal -calculus has a complete equational axiomatization. The method relies on the existence of a “closed structure” and its relationship to the equational axiomatization of Action Logic is made explicit. The implication operation...

for the Dyson{Baker Hierarchical Model Hans Koch 1 Department of Mathematics, University of Texas at Austin Austin, TX 78712 Peter Wittwer 2 D epartement de Physique Th eorique, Universit e de Gen eve Gen eve, CH 1211 Abstract. We prove the existence of a nontrivial Renormalization Group (RG) xed point for the Dyson{Baker hierarchical model in d = 3 dimensions. The single spin distribution of t...

We study the renormalization group evolution up to the xed point of the lattice topological susceptibility in the 2{d O(3) non{linear {model. We start with a discretization of the continuum topological charge by a local charge density, polynomial in the lattice elds. Among the diierent choices we propose also a Symanzik{improved lattice topological charge. We check step by step in the renormali...

Synopsis. In this paper we study the logical aspects of the Smyth powerdomain via clausal theories. The clause-theoretic view leads to an unexpectedly simple, operational, representation of the Smyth powerdomain. At the heart of this representation is a hyperresolution rule, whose completeness hinges upon a combinatorial lemma for the book-keeping of intermediate clauses. These results are moti...

1 Problem Formulation Last two weeks we discussed controller synthesis for: Discrete systems: design characterized by a xed point of a diierence equation. Continuous systems: design characterized by xed point of a partial diierential equation. In either case the solution is characterized as a xed point of an equation, which we refer to as the Hamilton-Jacobi equation. Today, we bring the discre...

Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA-type cryptosystems over elliptic curves. The analysis is more diicult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent fact...

The common numerical problem in Bayesian analysis is the numerical integration of the posterior. In high dimensions, this problem becomes too formidable for xed quadrature methods, and Monte Carlo integration is the usual approach. Through the use of modal standardization and a spherical-radial transformation, we reparameterize in terms of a radius r and point z on the surface of the sphere in ...

Let P be a set of polygonal pseudodiscs in the plane with n edges in total translating with xed velocities in xed directions. We prove that the maximumnumber of combinatorial changes in the union of P is (n (n)). In general, if the pseudodiscs move along curved trajectories, then the maximum number of changes in the union is (n s+2(n)), where s is the maximum number of times any triple of polyg...

We describe an encoding of major parts of domain theory in the PVS extension of the simply typed calculus these encodings consist of Formalizations of basic structures like partial orders and complete partial orders domains Various domain constructions Notions related to monotonic functions and continuous functions Knaster Tarski xed point theorems for monotonic and continuous functions the pro...