相关论文: A short note about Morozov's formula
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
In the present work we explore relationships between multiplicative functions defined in \cite{Garonzi_2018}, \cite{Lazorec}. To do so, we use other important quotients defined and studied in \cite{ndeg}, \cite{Marius}, thus establishing…
Correlation testing provides a quick method of discriminating amongst potential terms to include in a nuclear mass formula or functional and is a necessary tool for further nuclear mass models; however a firm mathematical foundation of the…
This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…
In this paper, we aim to provide an accessible survey to various formulae for calculating single Hurwitz numbers. Single Hurwitz numbers count certain classes of meromorphic functions on complex algebraic curves and have a rich geometric…
We establish an explicit formula for the n-point correlation functions in the sense of Bloch-Okounkov for the irreducible representations of $\hat{gl}_\infty$ and $W_{1+\infty}$ of arbitrary positive integral levels.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The purpose of this note is to prove an Euler-type formula for partitions of the M\"obius strip. This formula was introduced in our joint paper with R.~Kiwan, "Courant-sharp property for Dirichlet eigenfunctions on the M\"obius strip"…
The purpose of this note is to state some definitions that may be useful in the study of knots, manifolds and the like. They apply to anything for which the concept of a regional change can be defined, such as a product of elements in a…
We rewrite Riemann Zeta function as a sum over the primes. Each term of the sum is a product that depends only on the summation index (a prime) and the primes following it.
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a…
Correction terms generated in the correlator analysis due to multiplicity-dependent observable mean are investigated. A procedure for subtraction of such terms from calculated correlator estimates is suggested and the obtained results are…
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
This article present a new, direct and simple formula for constructing Mignotte sequences.
We give a short proof -- not relying on ideal classes or the geometry of numbers -- of a known criterion for quadratic orders to possess unique factorization.
The aim of this note is to compare work of Formanek \cite{formanek2} on a certain construction of central polynomials with that of Collins \cite{Coll} on integration on unitary groups. These two quite disjoint topics share the construction…
It is well known that a Wilson action reduces to the generating functional of connected correlation functions as we take the momentum cutoff to zero. For a fixed point Wilson action, this implies that for momenta large compared with the…
The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on $\mathbb R$. We formulate here the analogue for functions that are just of…
A generalization of a well-known relation between the Riemann zeta function $\zeta(s)$ and Bernoulli numbers $B_n$ is obtained. The formula is a new representation of the Riemann zeta function in terms of a nested series of Bernoulli…