Related papers: A short note about Morozov's formula
The purpose of this note is to extend in a simple and unified way some results on orthogonal polynomials with respect to the weight function $$\frac{|T_m(x)|^p}{\sqrt{1-x^2}}\;,\quad-1<x<1\;,$$ where $T_m$ is the Chebyshev polynomial of the…
In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.
Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…
We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a…
In the heavy quark limit of QCD, using the Operator Product Expansion and the non-forward amplitude, as proposed by Nikolai Uraltsev, we formulate sum rules that generalize Bjorken and Uraltsev sum rules. We recover the Uraltsev lower bound…
In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools. Both $L^{p}$ and weighted $L^{p}$ estimates can…
These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.
Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict non-exponential correlation functions to be observed by…
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.
Some simple (namely, single-channel) correlation functions involving an arbitrary number of fields are computed by means of a direct application of the residue calculus, through partial fraction expansions. Examples are presented in minimal…
We present formulas for the homogenous multivariate resultant as a quotient of two determinants. They extend classical Macaulay formulas, and involve matrices of considerably smaller size, whose non zero entries include coefficients of the…
A technical point regarding the invariance of Polyakov's nonlocal form of the effective action under uniform rescalings is briefly addressed.
The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
Muchnik's theorem about simple conditional descriprion states that for all words $a$ and $b$ there exists a short program $p$ transforming $a$ to $b$ that has the least possible length and is simple conditional on $b$. This paper presents a…
In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…
The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.