Search results for "calculu"
showing 10 items of 642 documents
Heat Flow on Metric Measure Spaces
2020
In order to develop a second-order differential calculus on spaces with curvature bounds we need to make use of the regularising effects of the heat flow, to which this chapter is dedicated.
Indefinite integrals of some special functions from a new method
2015
A substantial number of indefinite integrals of special functions are presented, which have been obtained using a new method presented in a companion paper [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. The method was originally derived from the Euler–Lagrange equations but an elementary proof is also presented in [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. Sample results are presented here for Bessel functions, Airy functions and hypergeometric functions. More extensive results are given for th…
Pseudo-Abelian integrals along Darboux cycles
2008
We study polynomial perturbations of integrable, non-Hamiltonian system with first integral of Darboux-type with positive exponents. We assume that the unperturbed system admits a period annulus. The linear part of the Poincare return map is given by pseudo-Abelian integrals. In this paper we investigate analytic properties of these integrals. We prove that iterated variations of these integrals vanish identically. Using this relation we prove that the number of zeros of these integrals is locally uniformly bounded under generic hypothesis. This is a generic analog of the Varchenko-Khovanskii theorem for pseudo-Abelian integrals. Finally, under some arithmetic properties of exponents, the p…
On the Convergence of Formal Integrals in Finite Time
1982
Consider a differential system: x = f (x) + e g(x), \(x \in {R^n}.\). Let h(x) = ho(x) + eh1 (x)... a “third” integral. For finite time t, I obtain an eo such that the series h(x) converges if e > eo. When t tends to infinite, eo tends to zero.
Kirkwood-Buff Integrals for Finite Volumes.
2012
Exact expressions for finite-volume Kirkwood−Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.
Drawing and extruding: Theoretical and approximate formulas
1969
The problem of drawing of wires and of strips has been treated in several studies; among these the studies of Sachs seem essential. However, the results deduced according to similar theories are not always in accordance with the experimental results: reduction of area or of thickness are in fact usually smaller than those resulting from the theory. This is in dependance of the fact that Sachs has adopted the Limiting Condition of Yielding by v. Mises, according to which the limit values of stress in traction and compression are equal. More recently other AA. (Alberti, Noto La Diega, Bugini), admitting the Limiting Condition of Yielding by A. (or of the Paraboloid of Revolution) of which we …
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).