In order to solve domain equations over 1-bounded compact metric spaces, xed points of functors on categories of 1-bounded compact metric spaces are studied. Two categories of 1-bounded compact metric spaces are considered: KMS and KMS E. In both categories, objects are isomorphic if and only if they are isometric. As a consequence, provided that the operation of a domain equation can be extend...

We present a treatment for mathematical economists of three topics in the theory of xed points: (a) the Lefschetz xed point index; (b) the Lefschetz xed point theorem; (c) the theory of essential sets of xed points. Our treatment is geometric, based on elementary techniques, and largely selfcontained. In particular there is no essential reference to algebraic topology. Within the chosen scope o...

Induction for Horn clauses from data received a major boost from the success of FOIL 1;2;3 as a pioneer clausal learning algorithm. FOIL attempts to explain a target relation (while avoiding a negative set) by incrementally adding clauses that successively increase this explained part. The residue of the target set is obtained by postulating the target set in the antecedents (body) of the gener...

an idea of fuzzy reexivity of felbin's type fuzzy normed linear spaces is introduced and its properties are studied. concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

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 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 at which these are unfolde...

In this paper, we prove some …xed point theorems for two hybrid pairs of mappings in 2-metric spaces by using some weaker conditions. Mathematics subject classi…cation: 47H10, 54H25. Key words and phrases: Coincidence point, common …xed point, compatible maps, weak commutativity of type (KB) :

Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70 iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian xed point. Convergence of the subsequent trajectory to the Gaussian xed point is shown by power decay of the eeective coupling constant. The analysis in the...

In this paper we give a numerical description of the neighbourhood of a xed point of a symplectic map undergoing a transition from linear stability to complex instability i e the so called Hamiltonian Hopf bifurcation We have considered both the direct and inverse cases The study is based on the numerical computation of the Lyapunov families of invariant curves near the xed point We show how th...

We de ne a value-based modal -calculus, built from rst-order formulas, modalities, and xed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over CRL terms de ned by linear process equations. The satisfaction of a temporal formula by a CRL term is translated to the satisfaction of a rst-order formula containing p...

It is critical to have an induction method for reasoning about re-cursive programs expressed as xed points, for otherwise our reasoning ability is severely impaired. The xed point induction rule developed by deBakker and Scott is one such well known principle. Here we propose a new induction method, computational induction , which is an induction on the computation process. Computational induct...