Search results for "calculu"

Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation

2004

This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Ito-type stochastic differential equations and Ito's rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown …

Unbounded Linear Operators in Hilbert Spaces

2002

In order to make this monograph self-contained, we summarize in this chapter some basic definitions and results for unbounded linear operators in a Hilbert space. In Section 1.1, we recall the definitions of C*-algebras and von Neumann algebras. In Section 1.2, we define and investigate the notion of closedness, the closure and the adjoint of an unbounded linear operator in a Hilbert space. Section 1.3 is devoted to the Cayley transform approach to the self-adjointness of a symmetric operator. Section 1.4 deals with the self-adjoint extendability of a symmetric operator with help of the deficiency spaces. In Section 1.5, we extend to unbounded self-adjoint operators the spectral theorem and…

Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee

2020

In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted wi…

Probabilistic analysis of non-local random media

2008

Computational stochastic methods have been devoted over the last years to analysis and quantification of the mechanical response of engineering systems involving random media. Specifically analysis of random, heterogeneous media is getting more and more important with the emergence of new complex materials requiring reliable methods to provide accurate probabilistic response. Advanced materials, often used at nano or meso-levels possess strong non-local characters showing that long-range forces between non-adjacent volume elements play an important role in mechanical response. Moreover long and short-range molecular interactions may have random nature due to unpredictable fabrication proces…

Materials Science Forum

2010

This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…

MECHANICAL RESPONSE OF BERNULLI EULER BEAMS ON FRACTIONAL ORDER ELASTIC FOUNDATION

2014

Ludwik Silberstein and the operator calculus

2015

W artykukle przedstawiamy zarys życiorysu Ludwika Silbersteina (1872‒1948). Omawiamy podejście do rachunku macierzowego i jego zastosowanie do podania operatorowej postaci teorii względności. Prezentujemy również listę książek i tłumaczeń z różnych języków dotyczących tej tematyki.

Automatic segmentation and 3D reconstruction of intravascular ultrasound images for a fast preliminar evaluation of vessel pathologies.

2007

Abstract Intravascular ultrasound (IVUS) imaging is used along with X-ray coronary angiography to detect vessel pathologies. Manual analysis of IVUS images is slow and time-consuming and it is not feasible for clinical purposes. A semi-automated method is proposed to generate 3D reconstructions from IVUS video sequences, so that a fast diagnose can be easily done, quantifying plaque length and severity as well as plaque volume of the vessels under study. The methodology described in this work has four steps: a pre-processing of IVUS images, a segmentation of media–adventitia contour, a detection of intima and plaque and a 3D reconstruction of the vessel. Preprocessing is intended to remove …

Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps

2014

This paper is concerned with stochastic finite-time boundedness analysis for a class of uncertain discrete-time neural networks with Markovian jump parameters and time-delays. The concepts of stochastic finite-time stability and stochastic finite-time boundedness are first given for neural networks. Then, applying the Lyapunov approach and the linear matrix inequality technique, sufficient criteria on stochastic finite-time boundedness are provided for the class of nominal or uncertain discrete-time neural networks with Markovian jump parameters and time-delays. It is shown that the derived conditions are characterized in terms of the solution to these linear matrix inequalities. Finally, n…

Malliavin smoothness on the Lévy space with Hölder continuous or BV functionals

2020

We consider Malliavin smoothness of random variables f(X1), where X is a purejump Lévy process and the functionfis either bounded and Hölder continuousor of bounded variation. We show that Malliavin differentiability and fractional differentiability off (X1) depend both on the regularity offand the Blumenthal-Getoor index of the Lévy measure. peerReviewed