Related papers: A New Method for the Calculation of Functional and…
The Fundamental Theorem of Integral Calculus links the integrand and its antiderivative via a simple first order differential equation. A numerical solution of this ode yields the antiderivative and hence the required integral. This…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of…
One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate…
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
This report (written in French) is devoted to studying special functions the most used in physics. Special functions are a very broad branch of mathematics, theoretical physics, and mathematical physics. They appeared in the nineteenth…
A perturbative approach to quantum field theory involves the computation of loop integrals, as soon as one goes beyond the leading term in the perturbative expansion. First I review standard techniques for the computation of loop integrals.…
We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations.…
This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…