The usual attractor coding technique is to partition a given image into a number of non-overlapping range blocks. Each block of the partition is expressed as the contractive transformation of another part of the image. However, the non-overlapping partitioning induces blocking artifacts which is highly disturbing to human visual system. In this work, a novel coding scheme using iterated functio...

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t →∞ to t...

The aim of this paper is to analyze contractivity properties of Wasserstein-type metrics for one-dimensional scalar conservation laws with nonnegative, L∞ and compactly supported initial data and its implications on the long time asymptotics. The flux is assumed to be convex and without any growth condition at the zero state. We propose a time–parameterized family of functions as intermediate a...

Let a smooth family of Riemannian metrics g(τ) satisfy the backwards Ricci flow equation on a compact oriented n-dimensional manifold M . Suppose two families of normalized n-forms ω(τ) ≥ 0 and ω̃(τ) ≥ 0 satisfy the forwards (in τ) heat equation on M generated by the connection Laplacian ∆g(τ). If these n-forms represent two evolving distributions of particles over M , the minimum root-mean-squa...

This paper focuses on the convergence of infor- mation in distributed systems of agents communicating over a network. The information on which the convergence is sought is not represented by real numbers, rather by sets of real numbers, whose possible dynamics are given by the class of so-called Boolean maps, involving only unions, intersections, and complements of sets. Based on a notion of co...

The basic requirement of numerical methods is convergence. However, from the practical point of view, it is generally not sufficient to construct convergent numerical methods for the solutions of partial differential equations. The qualitative adequateness of the methods is also an issue. The numerical solutions should mirror the characteristic properties of the original physical process that i...

This paper studies the celebrated KuramotoSakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets n-torus called winding cells. Second, analyze semicontractivity model, i.e., property that distance between trajectories decreases when measured according to a seminorm. establishes local Kuramoto-Sakaguchi which is equivalent contractiv...

After the appearance of relation-theoretic contraction principle due to Alam and Imdad, domain fixed point theory applied relational metric spaces has attracted much attention. Existence uniqueness fixed/coincidence points satisfying different types contractivity conditions in framework space have been studied recent times. Such results great advantage solve certain matrix equations boundary va...