Related papers: Some Useful Integral Representations for Informati…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…
We present a Feynman integral representation for the general momentum-space scalar $n$-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of $n(n-3)/2$…
This paper is devoted to derive integral representation formulae for the solution of an inhomogeneous linear wave equation with time-dependent damping and mass terms, that are scale-invariant with respect to the so-called hyperbolic…
Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…
In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other…
Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…
Two-phase design can reduce the cost of epidemiological studies by limiting the ascertainment of expensive covariates or/and exposures to an efficiently selected subset (phase-II) of a larger (phase-I) study. Efficient analysis of the…
In this article we describe the construction of logarithmic models in both real and complex cases. A logarithmic model is a germ of closed meromorphic 1-form with simple poles - and the analytic foliation defined by it - produced upon some…
For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
Compositional data analysis is concerned with multivariate data that have a constant sum, usually 1 or 100\%. These are data often found in biochemistry and geochemistry, but also in the social sciences, when relative values are of interest…
A transformation on homogeneous polynomials is proposed, which is further applied to parametric Feynman integrals. The two representations related through this transformation are dual to each other. It naturally leads to dualities of Landau…
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite…
This paper introduces inter-order formulas for partial and complete moments of a Student $t$ distribution with $n$ degrees of freedom. We show how the partial moment of order $n - j$ about any real value $m$ can be expressed in terms of the…
We present an algorithm for the efficient numerical evaluation of integrals of the form \[ I(\omega) = \int_0^1 F( x,\mathrm e^{\mathrm i \omega x}; \omega) \, \mathrm d x \] for sufficiently smooth but otherwise arbitrary $F$ and $\omega…
We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises…
In this paper, we give a short elementary proof of the well known Euler's recurrence formula for the Riemann zeta function at positive even integers and integral representations of the Riemann zeta function at positive integers and at…