Related papers: Linear correlations amongst numbers represented by…
We use the embedding formalism to study correlation functions of a d-dimensional Euclidean CFT in the presence of a $q$ co-dimensional defect. The defect breaks the global conformal group $SO(d+1,1)$ into $SO(d-q+1,1) \times SO(q)$. We…
In this paper we consider certain quaternary quadratic forms and octonary quadratic forms and by using the theory of modular forms, we find formulae for the number of representations of a positive integer by these quadratic forms.
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
A rational homogeneous (of degree one) positive real matrix-valued function is presented as the Schur complement of a block of the linear pencil with positive semidefinite matrix coefficients. The partial derivative numerators of a rational…
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic…
In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…
Let f(m,n) denote the number of relatively prime subsets of {m+1,m+2,...,n}, and let Phi(m,n) denote the number of subsets A of {m+1,m+2,...,n} such that gcd(A) is relatively prime to n. Let f_k(m,n) and Phi_k(m,n) be the analogous counting…
In the Frobenius problem we are given a set of coprime, positive integers $a_1, a_2,...,a_k$, and are interested in the set of positive numbers NR that have no representation by the linear form $\sum_i a_ix_i$ in nonnegative integers $x_1,…
Positive and negative quadratic forms are well known and widely used. They are multivariate homogeneous polynomials of degree two taking positive or negative values respectively for any values of their arguments not all zero. In the present…
Let $F_n$ and $L_n$ be the Fibonacci and Lucas numbers, respectively. Four corresponding zeta functions in $s$ are defined by \[\zeta_F(s) \,:=\, \sum_{n=1}^{\infty} \frac{1}{F_n^s}\,,\quad \zeta_F^*(s) \,:=\,\sum_{n=1}^{\infty}…
We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
Given an infinite sequence of positive integers $\cA$, we prove that for every nonnegative integer $k$ the number of solutions of the equation $n=a_1+...+a_k$, $a_1,\,..., a_k\in \cA$, is not constant for $n$ large enough. This result is a…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$…
The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations…
In this paper, under certain restrictions on linear factors of the denominator of a rational function of two variables, the leading term of the asymptotic expansion of the coefficients is found.
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
Let $\beta>1$ be fixed. We consider the $(\frak{b, d})$ numeration system, where the base ${\frak b}=(b_k)_{k\geq 0}$ is a sequence of positive real numbers satisfying $\lim_{k\rightarrow \infty}b_{k+1}/b_k=\beta$, and the set of digits…
The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…