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We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding,…
From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta…
The non-holonomic deformation of the nonlinear Schr\"odinger equation, uniquely obtained from both the Lax pair and Kupershmidt's bi-Hamiltonian [Phys. Lett. A 372, 2634 (2008)] approaches, is compared with the quasi-integrable deformation…
This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…
We first point out it is conditional to apply the variational approach to the nonlocal nonlinear Schr\"{o}dinger equation (NNLSE), that is, the response function must be an even function. Different from the variational approach, the…
The present paper concentrates on the analogues of Rosenthal's inequalities for ordinary and decoupled bilinear forms in symmetric random variables. More specifically, we prove the exact moment inequalities for these objects in terms of…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
We study the asymptotic behavior of parametrized black hole quasinormal modes (QNMs) in the high-overtone limit. To gain insights into their analytical structure, we apply the exact WKB method, which was recently developed by the same…
We investigate a Riemann-Hilbert problem (RHP), whose solution corresponds to a group of $q$-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the…
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…
We consider the Hamburger, Stieltjes and Hausdorff moment problems, that are problems of the construction of a Borel measure supported on a real line, on a half-line or on an interval $(0,1)$, from a prescribed set of moments. We propose a…
We present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner-Nordstr\"om black holes. We show that QNMs can be…
We study an inverse source problem for a semilinear parabolic equation in a bounded domain, where the nonlinearity depends on the unknown function and its gradient through a quadratic reaction term and a Burgers-type convection term. From…
We study, in this paper, a one parameter deformation of the $q-$Laguerre weight function. An investigation is made on the polynomials orthogonal with respect to such a weight. With the aid of the two compatibility conditions previously…
We study the monic polynomials orthogonal with respect to a symmetric perturbed Gaussian weight $$ w(x;t):=\mathrm{e}^{-x^2}\left(1+t\: x^2\right)^\lambda,\qquad x\in \mathbb{R}, $$ where $t> 0,\;\lambda\in \mathbb{R}$. This weight is…
We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck processes driven by L\'{e}vy motion and their finite and infinite superpositions. We…
The Loewner equation, in its stochastic incarnation introduced by Schramm, is an insightful method for the description of critical random curves and interfaces in two-dimensional statistical mechanics. Two features are crucial, namely…
We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.
We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…
We find an inverse factorial series expansion for the ratio of products of gamma functions whose arguments are linear functions of the variable. We a give recurrence relation for the coefficients in terms of the N{\o}rlund-Bernoulli…