Abstract This paper studies hamiltonization of nonholonomic systems using geometric tools, building on [1] , [5] . The main novelty in this is the use symmetries and suitable first integrals system to explicitly define a new bracket reduced space that codifies dynamics carries, additionally, an almost symplectic foliation (determined by common level sets integrals); particular cases interest, P...

‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

Apéry’s proof [13] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significant new results (although further progress has been made on the irrationality of zeta values [1, 14]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and Lege...

Apéry’s proof [11] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significantly new results (although further progress has been made on the irrationality of zeta values [1], [12]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and ...

New examples of the theory recently proposed by Ricca [PRA(1991)] on the generalization of Da RiosBetchov intrinsic equations on curvature and torsion of classical non-Riemannian vortex higher-dimensional string are given. In particular we consider applications to 3-dimesional fluid dynamics, including the case of a twisted flux tube and the fluid rotation. In this case use is made of Da Rios e...

This paper investigates the use of low-discrepancy sequences for computing volume integrals in geometric modelling. An introduction to low-discrepancy point sequences is presented which explains how they can be used to replace random points in Monte Carlo methods. The relative advantages of using low-discrepancy methods compared to random point sequences are discussed theoretically, and then pr...

This talk reviews Feynman integrals, which are associated to elliptic curves. The will give an introduction into the mathematics behind them, covering topics of curves, modular forms and moduli space $n$ marked points on a genus one curve. latter be important, as integrals can expressed iterated ${\mathcal M}_{1,n}$, in same way evaluate multiple polylogarithms M}_{0,n}$. With right language, m...