Related papers: Hilbert Transforms and Sum Rules of Bessel Moments
We present a framework which unifies a large class of non-commutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the…
Employing Hilbert-Schmidt measure, we explicitly compute and analyze a number of determinantal product (bivariate) moments |rho|^k |rho^{PT}|^n, k,n=0,1,2,3,..., PT denoting partial transpose, for both generic (9-dimensional) two-rebit…
In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma…
We present a model of (double) kinetic theory which paves the way to describe matter in a Double Field Theory background. Generalized diffeomorphisms acting on double phase space tensors are introduced. The generalized covariant derivative…
We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of $L$-functions defined over number fields. Specifically, we give a…
Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let ${\mathrm U}_{2m}(B)$ be the unitary group of rank $2m$ associated to a hermitian or skew hermitian form relative to $*$. When $B$ is finite, we construct a…
We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter…
It is a well-known property of holographic theories that diffeomorphism invariance in the bulk space-time implies Weyl invariance of the dual holographic field theory in the sense that the field theory couples to a conformal class of…
We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
A proof is found for the elliptic integral evaluation of the Bessel moment $$M:=\int_0^\infty t I_0^2(t)K_0^2(t)K_0(2t) {\rm d}t ={1/12} {\bf K}(\sin(\pi/12)){\bf K}(\cos(\pi/12)) =\frac{\Gamma^6(\frac13)}{64\pi^22^{2/3}}$$ resulting from…
In his work on the foundations of geometry, Hilbert observed that a formula which appeared in works by Beltrami, Cayley, and Klein, gives rise to a complete metric on any bounded convex domain. Some decades later, Garrett Birkhoff and Hans…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erd\"os-Moser problem). The main tools are Minkowski's theorem on…
Using the Non-Abelian Batalin-Vilkovisky formalism introduced recently, we present a generalization of the Yang-Mills gauge transformations , to include antisymmetric tensor fields as gauge bosons. The Freedman-Townsend transformation for…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
By combining the telescoping method with an algebraic relation, four classes of binomial moments are examined. Several explicit summation formulae are established.
We show that simple explicit formulas can be obtained for several relevant quantities related to the laws of the uniformly sampled Brownian bridge, Brownian meander and three dimensional Bessel process. To prove such results, we use the…
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…