Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

We describe an encoding of major parts of domain theory in the PVS extension of the simply typed calculus these encodings consist of Formalizations of basic structures like partial orders and complete partial orders domains Various domain constructions Notions related to monotonic functions and continuous functions Knaster Tarski xed point theorems for monotonic and continuous functions the pro...

Consider the minimal weights of paths between two points in a complete graph K n with random weights on the edges, the weights being e.g. uniformly distributed. It is shown that, asymptotically, this is log n=n for two given points, that the maximum if one point is xed and the other varies is 2 log n=n, and that the maximum over all pairs of points is 3 log n=n. Some further related results are...

We consider 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 Such proof systems 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...

This paper is a study of the error in approximating the global maximum of a Brownian motion on the unit interval by observing the value at randomly chosen points. One point of view is to look at the error from random sampling for a given xed Brownian sample path; another is to look at the error with both the path and observations random. In the rst case we show that for almost all Brownian path...

A procedure for testing equality across nonparametric regressions is proposed The proce dure allows for any dimension of the explanatory variables and for any number of subsamples We consider the case of random explanatory variables and allow the designs of the regressors and the number of observations to di er across subsamples The division into subsamples is de ned through a variable C which ...

A procedure for testing equality across nonparametric regressions is proposed The proce dure allows for any dimension of the explanatory variables and for any number of subsamples We consider the case of random explanatory variables and allow the designs of the regressors and the number of observations to di er across subsamples The division into subsamples is de ned through a variable C which ...

We show that for any xed dense graph G and bounded-degree tree T on the same number of vertices, a modest random perturbation of G will typically contain a copy of T . This combines the viewpoints of the well-studied problems of embedding trees into xed dense graphs and into random graphs, and extends a sizeable body of existing research on randomly perturbed graphs. Speci cally, we show that t...

A nonlinear generalization of the S-transform known in Gaussian analysis is introduced. It is deened as a nonlinear operator on topolog-ical spaces of entire functions of innnitely many variables with growth of at most second order and nite type restricted to a certain value. This nonlinear S-transform (NLST) has xed points a certain family of which is found and analyzed. In particular, their s...

We study the limiting distribution of the height in a generalized trie in which external nodes are capable to store up to b items (the so called b-tries). We assume that such a tree is built from n random strings (items) generated by an unbiased memoryless source. In this paper, we discuss the case when b and n are both large. We shall identify six natural regions of the height distribution tha...