Search results for "Calculus"
showing 10 items of 617 documents
Logical Sentential Calculi Inspired by the Chrysippean Sentential Calculus
2021
The aim of the present paper is to consider an approach, different from that presented by J. Łukasiewicz, concerning the interpretation of the so-called stoic undemonstrables, which were given by Chrysippus. Stoic undemonstrables have been interpreted in two different ways: using the notion of “negation of a sentence” (Łukasiewicz) and using the notion of “a sentence inconsistent with a given one” (Mates). According to the Stoics, two sentences are inconsistent if one of them is negation of the other. The Mates’ interpretation generates five different inference rules. Based on one of these rules we can consider (with other undemonstrables) four different stoic propositional calculi. Taking …
Linear Regression Analysis
2010
SUMMARY Background: Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. Methods: This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. Results: After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the resul…
Advanced materials modelling via fractional calculus: challenges and perspectives.
2020
Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced mat…
Control zeros and nonminimum phase LTI mimo systems
1999
Abstract The paper presents a new, general, inverse-model/output-zeroing approach to zeros of LTI discrete-time multivariable, possibly nonsquare systems. It is shown on simple examples that the existing definitions of multivariable zeros fail to detect certain important zeros which contribute to zeroing the system output. As a result, a concept of ‘control zeros’ is introduced, followed by a general redefinition of minimum/nonminimum phase systems, both new contributions being based on the notion of (generalized) inverse systems. Output-zeroing/inverse-model/minimum-variance control-related justifications of the new approach are presented.
Statistic moments of the total energy of potential systems and application to equivalent non-linearization
2000
In this paper some properties of the total energy moments of potential systems, subjected to external white noise processes, are shown. Potential systems with a polynomial form of energy-dependent damping have been considered. It is shown that the analytical relations between the statistical moments of the energy associated with such systems can be obtained with the aid of the standard Ito calculus. Furthermore, it is shown that, for the stationary case, these analytical relations are very useful for the application of the equivalent non-linearization technique.
�ber ein Verfahren der Ordnung $$1 + \sqrt 2 $$ zur Nullstellenbestimmung
1979
A new iterative method for solving nonlinear equations is presented which is shown to converge locally withR-order of convergence $$1 + \sqrt 2 $$ at least under suitable differentiability assumptions. The method needs as many function evaluations per step as the classical Newton method.
An Iterative Approach to Dynamic Elastic-Plastic Analysis
1998
The step-by-step analysis of structures constituted by elastic-plastic finite elements, subjected to an assigned loading history, is here considered. The structure may possess dynamic and/or not dynamic degrees-of-freedom. As it is well-known, at each step of analysis the solution of a linear complementarity problem is required. An iterative method devoted to solving the relevant linear complementarity problem is presented. It is based on the recursive solution of a linear complementarity, problem in which the constraint matrix is block-diagonal and deduced from the matrix of the original linear complementarity problem. The convergence of the procedure is also proved. Some particular cases …
Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes
2008
This paper concerns the statistical characterization of the non-Gaussian response of non-linear systems excited by polynomial forms of filtered Gaussian processes. The non-Gaussianity requires the computation of moments of any order. The problem is solved profiting from both the stochastic equivalent linearization (EL), and the moment equation approach of Ito's stochastic differential calculus through a procedure divided into two parts. The first step requires the linearization of the system, while retaining the non-linear excitation; the response statistical moments are calculated exactly, and constitute a first estimate of the moments of the actual non-linear system. In the second step, t…
An Existence Result for Fractional Kirchhoff-Type Equations
2016
The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.
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 …