The complex-logarithmic number system (CLNS), which represents each complex point in log/polar coordinates, may be practical to implement the Fast Fourier Transform (FFT). The roots of unity needed by the FFT have exact representations in CLNS and do not require a ROM. We present an error analysis and simulation results for a radix-two FFT that compares a rectangular xed-point representation of...

Synopsis. We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of a coherent algebraic dcpo. The robustness of this approach comes from the agreement bewteen the declarative semantics and the xed-point semantics, as well as the agreement between the xed-point semantics and the semantics...

We investigate circuit complexity under the additional assumption of full combinatorial symmetry with respect to permutations of the input representation. With this approach we derive a very natural and simple characterization of rst-order logic and its innnitary variant with bounded numbers of variables over nite structures. Extending these results to not necessarily acyclic boolean networks, ...

In this paper we summarize a dual-time scale formulation of dynamic user equilibrium with demand growth due to Friesz et al (2008). This formulation belongs to the problem class that Pang and Stewart (2008) refer to as di¤erential variational inequalities. We also present a …xed point algorithm for computing solutions to the dual time-scale model without calculating derivatives, along with a nu...

A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of speci"city of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that speci"c and non-speci"c res...

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...