We give an example of an operator that satisfies the curvature condition as defined in [2], but is not similar to the backward shift S ∗ on the Hardy class H. We conclude therefore that the contraction assumption in the similarity characterization given in [2] is a necessary requirement.

In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic ...

Clinical assessment of myocardial ischemia based on visually-assessed wall motion scoring from echocardiography is semiquantitative, operator dependent, and heavily weighted by operator experience and expertise. Cardiac motion estimation methods such as tissue Doppler imaging, used to assess myocardial muscle velocity, provides quantitative parameters such as the strain-rate and strain derived ...

We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin’s LJT for the implicational fragment. We introduce a variant of lambda calculus with potentially infinitely deep terms and a means of expressing alternatives for the description of the “solution spaces” (called Böhm forests), which are a repre...

The standard (AGM) approach to belief change assumes that the underlying logic is at least as strong as classical propositional logic. This paper investigates an account of belief change, specifically contraction, where the underlying logic is that governing Horn clauses. Thus this work sheds light on the theoretical underpinnings of belief change by weakening a fundamental assumption of the ar...

In many iterative optimization methods, fixed-point theory enables the analysis of convergence rate via contraction factor associated with linear approximation operator. While this characterizes asymptotic convergence, it does not explain non-linear behavior these algorithms in non-asymptotic regime. letter, we take into account effect first-order error and present a closed-form bound on terms ...

Abstract We develop a new formulation of deep learning based on the Mori–Zwanzig (MZ) formalism irreversible statistical mechanics. The is built upon well-known duality between neural networks and discrete dynamical systems, it allows us to directly propagate quantities interest (conditional expectations probability density functions) forward backward through network by means exact linear opera...

In this note we give a computable criterion for a piecewise expanding interval map T to be mixing, which at the same time not only establishes explicit bounds on the spectral gap of the associated Perron Frobenius operator acting on the space of functions of bounded variation, but establishes strict contraction rates for this operator. Of course such a result cannot be completely general, but o...

We give a new proof of the hyperbolicity of the fixed point for the period-doubling renormalization operator using the local dynamics near a semi-attractive fixed point (in a Banach space) and the theory of holomorphic motions. We also give a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the period-doubling fixed point: such proof use...

Correspondence: [email protected]. ir Department of Mathematics, Faculty of Basic Science, Babol University of Technology, Babol 47148-71167, Iran Abstract In this article, we established the existence and uniqueness of the solution for a generalized class of fractional order differential equations involving the RiemannLiouville differential operator on unbounded domain [0, +∞). The contraction ...