Search results for " Operator"

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems

2000

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e. the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is finite in at least some directions, and with absorbing boundary conditions, the moving particle escapes the system with probability one. However, there is a set of zero Lebesgue measure of initial phase points for the moving particle, such that escape never occurs. Typically, this set of points forms a fractal repeller, and the Lyapunov spectrum is calculated here for trajectories on this repeller. For this calculation, we need the solution of the recently…

Rational Solutions to the KdV Equation in Terms of Particular Polynomials

2022

Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order n for any positive integer n, and we call these solutions, solutions of the order n. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order 10.

On fractional smoothness and Lp-approximation on the Wiener space

2015

Approximation of Baskakov type Pólya–Durrmeyer operators

2017

In the present paper we propose the Durrmeyer type modification of Baskakov operators based on inverse Polya-Eggenberger distribution. First we estimate a recurrence relation by using hypergeometric series. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem. Some approximation results in weighted space are obtained. Also, we show the rate of convergence of these operators to certain functions by illustrative graphics using the Maple algorithms.

Inequalities for Information Potentials and Entropies

2020

We consider a probability distribution p0(x),p1(x),&hellip

On the intrinsic complexity of learning

1995

A new view of learning is presented. The basis of this view is a natural notion of reduction. We prove completeness and relative difficulty results. An infinite hierarchy of intrinsically more and more difficult to learn concepts is presented. Our results indicate that the complexity notion captured by our new notion of reduction differs dramatically from the traditional studies of the complexity of the algorithms performing learning tasks.

Metodi automatici di analisi e caratterizzazione di esami radiologici del massiccio facciale.

L'obiettivo di questo lavoro è lo sviluppo di algoritmi e procedure di analisi di referti radiografici digitali di tipo CBCT delle strutture della mandibola e dell’apparato dentario. In particolare, mediante un’opportuna campagna di sperimentazione, in collaborazione con i reparti di radiologia ed odontoiatria del Policlinico di Palermo, è stata realizzata un procedura in grado di: • eliminare i problemi di sovrapponibilità dei referti tridimensionali effettuati in tempi successivi; • identificare lo spazio parodontale su indagini CBCT per la valutazione dei possibili difetti nello stesso e prevedere l’insorgenza di parodontiti. • individuare gli elementi di maggiore interesse medico caratt…

Multiple nodal solutions for semilinear robin problems with indefinite linear part and concave terms

2017

We consider a semilinear Robin problem driven by Laplacian plus an indefinite and unbounded potential. The reaction function contains a concave term and a perturbation of arbitrary growth. Using a variant of the symmetric mountain pass theorem, we show the existence of smooth nodal solutions which converge to zero in $C^1(\overline{\Omega})$. If the coefficient of the concave term is sign changing, then again we produce a sequence of smooth solutions converging to zero in $C^1(\overline{\Omega})$, but we cannot claim that they are nodal.

Multiple solutions for strongly resonant Robin problems

2018

We consider nonlinear (driven by the p†Laplacian) and semilinear Robin problems with indefinite potential and strong resonance with respect to the principal eigenvalue. Using variational methods and critical groups, we prove four multiplicity theorems producing up to four nontrivial smooth solutions.

Fractional model of concrete hereditary viscoelastic behaviour

2016

The evaluation of creep effects in concrete structures is addressed in the literature using different predictive models, supplied by specific codes, and applying the concepts of linear viscoelastic theory with ageing. The expressions used in the literature are mainly based on exponential laws, which are introduced in the integral expression of the Boltzmann principle; this approach leads to the need of finding approximated numerical solutions of the viscoelastic response. In this study, the hereditary fractional viscoelastic model is applied to concrete elements, underlining the convenience of using creep or relaxation functions expressed by power laws. The full reciprocal character of cree…