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...

Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

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...

We consider proof systems with sequents of the form U for proving validity of a propositional modal calculus formula over a set U of states in a given model Such proof systems usually handle xed point formulae through unfolding thus allowing such formulae to reappear in a proof Tagging is a technique originated by Winskel for annotating xed point formulae with information about the proof states...

A nonlinear generalization of the S-transform known in Gaussian analysis is introduced. It is deened as a nonlinear operator on topolog-ical spaces of entire functions of innnitely many variables with growth of at most second order and nite type restricted to a certain value. This nonlinear S-transform (NLST) has xed points a certain family of which is found and analyzed. In particular, their s...

Most of the existing Digital Signal Processors (DSPs) are optimized for a fast and e cient computation of the Fast Fourier Transform (FFT). However, there are only two oating-point DSPs available, which perform the butter y operation of a FFT in 4 processor cycles, but no xed-point DSP is designed that way. The new 24 bit xed-point DSP DAISY, which is able to execute the butter y in 4 cycles ev...

We describe an encoding of major parts of domain theory and xed-point theory in the Pvs extension of the simply-typed-calculus; these formaliza-tions comprise the encoding of mathematical structures like complete partial orders (domains), domain constructions, the Knaster-Tarski xed-point theorem for mono-tonic functions, and variations of xed-point induction. Altogether, these encodings form a...

Fixed point calculus is about the solution of recursive equations de ̨ned by a monotonic endofunction on a partially ordered set. This tutorial presents the basic theory of ̨xed point calculus together with a number of applications of direct relevance to the construction of computer programs. The tutorial also presents the theory and application of Galois connections between partially ordered se...