Related papers: Beyond the Gaussian II : A Mathematical Experiment
A recent paper by T. Dauxois entitled "Non-Gaussian distributions under scrutiny" is submitted to scrutiny. Several comments on its content are made, which constitute, at the same time, a brief state-of-the-art review of nonextensive…
We compute the Gauss-Manin differential equation for any period of a polynomial in \ $\C[x_{0},\dots, x_{n}]$ \ with \ $(n+2)$ \ monomials. We give two general factorizations theorem in the algebra \ $\C< z, (\frac{\partial}{\partial…
The analogous quaternionic polynomials of a class of bivariate orthogonal polynomials (arXiv: 1502.07256, 2014) introduced. The ladder operators for these quaternionic polynomials also studied. For the quaternionic case, the ladder…
In this paper we will give the calculus, the criterion, and the existence of the arithmetic Galois covers of higher relative dimensions.
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
We study the problem of writing Gaussian primes as the sum of two squares, both of which are interesting arithmetically, in particular, when one is the square of a prime and the other the square of an almost-prime.
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that…
Author presents a study of certain category of the integrals, which might look quite difficult to compute, but in fact are easily computable, because they do not depend on the parameter in the integrand. As simple and elementary the…
We give simple necessary and sufficient conditions for the $\frac{\partial}{\partial t}$-transcendence of the solutions to a parameterized second order linear differential equation of the form \frac{\partial^2 Y}{\partial x^2} - p…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
The present work is concerned with Gaussian integrals on simply connected non-positively curved Riemannian symmetric spaces. It is motivated by the aim of explicitly finding the high-rank limit of these integrals for each of the eleven…
In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
We appeal to a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultra-distributions we are able to show that the q-Gaussian distribution can be…
The crisis in the reproducibility of experiments invites a re-evaluation of methods of inquiry and validation procedures. The text challenges current assumptions of knowledge acquisition and introduces G-complexity for defining decidable…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
This paper is the first part of a two-paper series whose aim is to give a thorough account on Connes' pseudodifferential calculus on noncommutative tori. This pseudodifferential calculus has been used in numerous recent papers, but a…
We define fermionic convolution and demonstrate its utility in characterizing fermionic non-Gaussian components, which are essential to the computational advantage of fermionic systems. Using fermionic convolution, we propose an efficient…