Search results for "calculus"

Mauro Picone, Sandro Faedo, and the numerical solution of partial differential equations in Italy (1928-1953)

2013

In this paper we revisit the pioneering work on the numerical analysis of partial differential equations (PDEs) by two Italian mathematicians, Mauro Picone (1885-1977) and Sandro Faedo (1913-2001). We argue that while the development of constructive methods for the solution of PDEs was central to Picone's vision of applied mathematics, his own work in this area had relatively little direct influence on the emerging field of modern numerical analysis. We contrast this with Picone's influence through his students and collaborators, in particular on the work of Faedo which, while not the result of immediate applied concerns, turned out to be of lasting importance for the numerical analysis of …

Hamilton–Jacobi semi-groups in infinite dimensional spaces

2006

AbstractLet (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let d:X×X→[0,+∞] be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton–Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux.

A FailedCassatio: Goldstein on the Liar

2009

The purpose of this note is to express some doubts about Goldstein's cassationist solution to the Liar Paradox. After sketching his theory (§I), we argue that the notions he introduces in order to solve the Strengthened Liar give rise to paradoxes the theory cannot deal with (§II).

Frege, Peano and Russell on Descriptions: a Comparison

2000

Terminology and Definitions

1986

In order to eliminate as much misunderstanding as possible in the evaluation of various forms of vibration stress, it is necessary to define the technical physical concepts used (Table 1). In addition, the special medical terms are explained at the end of the book (p. 158).

Scaling and data collapse for the mean exit time of asset prices

2005

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model …

199 Causal Classes of Space-Time Frames

1992

It is shown that from the causal point of view Minkowskian space-time admits 199, and only 199, different classes of frames.

Closure to “Stage–Discharge Relationship for an Upstream Inclined Grid with Transversal Bars” by C. Di Stefano and V. Ferro

2016

Stationary solutions of aerotaxis equations

2015

Stochastic Response Of Fractionally Damped Beams

2014

Abstract This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system. Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional de…