In fractal image compression, the code is given by a contractive aane mapping whose xed point is an approximation to the original image. Usually, the mapping is found by the collage coding method. We propose an algorithm that starts from an initial mapping obtained by collage coding and iteratively provides a sequence of contractive mappings whose xed points are monotonically approaching the or...

The deenition of concepts is a central problem in commonsense reasoning. Many themes in nonmonotonic reasoning concern implicit and explicit deenability. Implicit deenability in nonmonotonic logic is always relative to the context-the current theory of the world. We show that xed point equations provide a generalization of explicit deenability, which correctly captures the relativized context. ...

The existence of stationary solutions to the Povzner equation is established for a class of problems in bounded domains with smooth boundaries. The result holds for general type collision kernels under assumptions of angular cutoo. The boundary conditions with xed in-data and with a linear operator of diiuse reeection type are considered. The method is based on constructing approximate solution...

We analyze a renormalization group transformation R for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable xed points. Under certain assumptions, which are supported by numerical data in the golden mean case, we prove that such a xed point has a critical invariant torus. The proof is constructive and can be used for numerical computa...

We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic xed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori ((xed lines) is worked out. This allows one to give an analytical estimate of the stability ...

This paper presents an e cient hardware algorithm for variable precision division The algorithm is based on a well known convergence algorithm however modi cations are made to allow it to e ciently handle variable precision operands The proposed al gorithm reduces the number of xed precision operation by only computing signi cant words in intermediate results Compared to previous variable preci...

Symplectic Geometry has seen a rapid development since the 80's with the discovery of rigidity phenomena like the non-squeezing theorem based on Gromov's seminal theory of pseudo-holomorphic curves. A directly related development was Floer's method of using Morse theory in a new way, known as Floer homology, in order to solve the Arnold conjecture. In the 60's Arnold formulated his conjecture b...

in HOL Behzad Akbarpour, So ene Tahar, Abdelkader Dekdouk Ele tri al and Computer Engineering Department Con ordia University, Montreal, Canada Email: fbehzad, tahar, adekdoukg e e. on ordia. a Te hni al Report Abstra t In this report we propose the formalization in higher-order logi of xed-point arithmeti based on the SPW (Signal Pro essing WorkSystem) tool. We en oded the xedpoint number syst...

A wide range of problems such as static program analysis and symbolic verii-cation induces the need for an evaluation mechanism of xed point, and thus, a certain form of quantiication over relations. Many specialized tools (MVL 7], MEC 1], .. .) exist, mainly based upon the mu-calculus formalism 9]. On the one hand, while generally ooering good performances, these tools use their own syntaxes, ...

*Correspondence: [email protected] 1School of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing, 210044, China Full list of author information is available at the end of the article Abstract This work is devoted to studying the application of fixed point theory to the stability analysis of complex neural networks. We employ the new method of contraction m...