Related papers: Closed Form for Some Gaussian Convolutions
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper we study the theory of (formal) deformation of…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
This work is devoted in the derivation of novel upper and lower bounds for the Rice $Ie$-function. These bounds are expressed in closed-form and are shown to be quite tight. This is particularly evident by the fact that for a certain range…
We consider a generalized Gauss sum supported on matrices over a number field. We evaluate this Gauss sum and relate it to the number of totally isotropic subspaces of related quadratic spaces. Then we consider a further generalization of…
A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution…
If a student asks for an antiderivative of exp(x^2), there is a standard reply: the answer is not an elementary function. But if a student asks for a closed-form expression for the real root of x = cos(x), there is no standard reply. We…
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are…
We study the functorial and growth properties of closed orbits for maps. By viewing an arbitrary sequence as the orbit-counting function for a map, iterates and Cartesian products of maps define new transformations between integer…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian…
In this note we review the theory of Gaussian functions by exploiting a point of view based on symbolic methods of umbral nature. We introduce quasi-Gaussian functions, which are close to Gaussian distribution but have a longer tail. Their…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.
In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors,…
For nonuniform cofinite Fuchsian groups $\Gamma$ which satisfy a certain additional geometric condition, we show that the Maass cusp forms for $\Gamma$ are isomorphic to 1-eigenfunctions of a finite-term transfer operator. The isomorphism…
Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential forms of n-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are…
We develop a new higher order closed-form model for the dynamics of a hyperelastic isotropic 3D cylindrical body. We derive, for the first time, a simple explicit expression for the fundamental frequency.
We derive the gravitational Lagrangian to all orders of curvature when the canonical constraint algebra is deformed by a phase space function as predicted by some studies into loop quantum cosmology. The deformation function seems to be…