Related papers: Moments for generalized Farey-Brocot partitions

This paper concerns the relationships between continued fractions and the geometry of the Stern-Brocot diagram. Each rational number can be expressed as a continued fraction $[a_0; a_1, \ldots, a_n]$ whose terms $a_i$ are integers and are…

We present a family of explicit formulae for evaluating absolute moments of probability measures on $\mathbb{R}^d$ in terms of Fourier transforms. As to the space of probability measures possessing finite absolute moments of an arbitrary…

We introduce a new, large class of continued fraction algorithms producing what are called contracted Farey expansions. These algorithms are defined by coupling two acceleration techniques -- induced transformations and contraction -- in…

We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…

We present a Floquet scheme for the ab-initio calculation of nonlinear optical properties in extended systems. This entails a reformulation of the real-time approach based on the dynamical Berry-phase polarisation [Attaccalite & Gr\"uning,…

This paper presents a novel method that allows to generalise the use of the Adam-Bashforth to Partial Differential Equations with local and non local operator. The Method derives a two step Adam-Bashforth numerical scheme in Laplace space…

It is well known that phase function methods allow for the numerical solution of a large class of oscillatory second order linear ordinary differential equations in time independent of frequency. Unfortunately, these methods break down in…

Many asymptotic formulas exist for unrestricted integer partitions as well as for distinct partitions of integers into a finite number of parts. Szekeres and Canfield have derived an asymptotic formula for the number of partitions that is…

We show that if a permutation statistic can be written as a linear combination of bivincular patterns, then its moments can be expressed as a linear combination of factorials with constant coefficients. This generalizes a result of…

Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…

In this paper, we consider fractional parabolic equation of the form $ \frac{\partial u}{\partial t}=-(-\Delta)^{\frac{\alpha}{2}}u+u\dot W(t,x)$, where $-(-\Delta)^{\frac{\alpha}{2}}$ with $\alpha\in(0,2]$ is a fractional Laplacian and…

A Lagrange Theorem in dimension 2 is proved, for a particular two-dimensional algorithm, with a very natural geometrical definition. Dirichlet-type properties for the convergence of the algorithm are also proved. These properties procced…

We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…

In this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. We do this through both theoretical analysis (multivariate delta method)…

A fractional generalization of the Floquet theorem is suggested for fractional Schr\"odinger equations (FTSE)s with the time-dependent periodic Hamiltonians. The obtained result, called the fractional Floquet theorem (fFT), is formulated in…

We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…

We introduce the notion of (co-)filtered sheaves on quotients of moment graphs by a group action. We then introduce a (co-)filtered version of the canonical sheaves of Braden and MacPherson and show that their global sections are the…

This paper continues investigations on the integral transforms of the Minkowski question mark function. In this work we finally establish the long-sought formula for the moments, which does not explicitly involve regular continued…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

We present a method for the numerical computation of Fourier-Bessel transforms on a finite or infinite interval. The function to be transformed needs to be evaluated on a grid of points that is independent of the argument of the Bessel…