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Moment evaluations are important for the study of non-classical orthogonal polynomial systems for which explicit representations are not known. In this paper we compute, in terms of the hypergeometric function, the moments associated with a…
The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's ${}_1\psi_1$-summation we complement the orthogonal q-Laguerre polynomials into an explicit…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal…
Pick n points independently at random in R^2, according to a prescribed probability measure mu, and let D^n_1 <= D^n_2 <= ... be the areas of the binomial n choose 3 triangles thus formed, in non-decreasing order. If mu is absolutely…
Let $F$ be a Hecke--Maass cusp form for $\mathrm{SL}_3(\mathbb{Z})$ with the Langlands parameter $\mu_{F}=\big(\mu_{F,1},\mu_{F,2},\mu_{F,3}\big)$ and the associated $L$-function $L(s, F)$. Define $S_F(t)=\pi^{-1}\arg L(1/2+\mathrm{i}t,…
In this paper, we prove the smooth cubic moments vanish for the Hecke--Maass cusp forms, which gives a new case of the random wave conjecture. In fact, we can prove a polynomial decay for the smooth cubic moments, while for the smooth…
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…
Measurements of b-hadron masses are performed with the exclusive decay modes B+ -> J/psi K+, B0 -> J/psi K*0, B0 -> J/psi K0S, B0_s -> J/psi phi and Lambda_b -> J/psi Lambda using an integrated luminosity of 35 pb-1 collected in pp…
The kinetics of irreversible annihilation of charged particles performing overdamped motion induced by long-range interaction force, $F(r)\sim r^{-\lambda}$, is investigated. The system exhibits rich kinetic behaviors depending on the force…
Using data collected with the LHCb detector in proton-proton collisions at a centre-of-mass energy of 7 TeV, the semileptonic decays Bs -> Ds+ X mu nu and Bs -> D0 K+ X mu nu are detected. Two structures are observed in the D0 K+ mass…
Extended Thermodynamics is the natural framework in which to study the physics of fluids, because it leads to symmetric hyperbolic systems of field laws, thus assuming important properties such as finite propagation speeds of shock waves…
We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an…
We consider the reconstruction problem in compressed sensing in which the observations are recorded in a finite number of bits. They may thus contain quantization errors (from being rounded to the nearest representable value) and saturation…
Let $\lambda\in (1,\sqrt{2}]$ be an algebraic integer with Mahler measure $2.$ A classical result of Garsia shows that the Bernoulli convolution $\mu_\lambda$ is absolutely continuous with respect to the Lebesgue measure with a density…
The strength of the nonlinearity is measured in decaying two-dimensional turbulence, by comparing its value to that found in a Gaussian field. It is shown how the nonlinearity drops following a two-step process. First a fast relaxation is…
An atomic random complex measure defined on the unit disk with Normally distributed moments is considered. An approximation to the distribution of the zeros of its Cauchy transform is computed. Implications of this result for solving…
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…
Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized…