Related papers: Counting partial Hadamard matrices in the cubic re…

This paper presents analytical-approximate solutions of the time-fractional Cahn-Hilliard (TFCH) equations of fourth and sixth-order using the new iterative method (NIM) and q-homotopy analysis method (q-HAM). We obtained convergent series…

The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional…

Let $K$ be a number field, $k\geq 2$ an integer, $(K^*)^k$ the $k$-fold direct product of $K^*$ with coordinatewise multiplication, and $\Gamma$ a finitely generated subgroup of rank $r$ of $(K^*)^k$. Further, let $H(\alpha )$ denote the…

We extend the notion of convexity of functions defined on global nonpositive curvature spaces by introducing (geodesically) $h$-convex functions. We prove estimates of Hermite-Hadamard type via Katugampola's fractional integrals. We obtain…

Based on the work of Green, Tao and Ziegler, we give asymptotics when $N \to \infty$ for the number of $n \times n$ magic squares with their entries being prime numbers in $[0,N]$. For every $n \ge 3$ we give appropriate systems of linear…

It is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian H=\half p^2+\half\mu^2x^2-\lambda x^4 in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C…

In this paper we study the asymptotics (as $n\to \infty$) of the sequences of Laguerre polynomials with varying complex parameters $\alpha$ depending on the degree $n$. More precisely, we assume that $\alpha_n = n A_n, $ and $ \lim_n A_n=A…

We study the asymptotic stability for large times of homogeneous stationary states for the nonlinear Hartree equation for density matrices in Rd for d\geq3. We can reach both the optimal Sobolev and Schatten exponents for the initial data,…

Several misprints and small mistakes were in the initial version. They have been corrected. Following the recent experimental realization of synthetic gauge magnetic forces, Jean Dalibard adressed the question whether the adiabatic ansatz…

We construct almost holomorphic and holomorphic modular forms by considering theta series for quadratic forms of signature $(n-1,1)$. We include homogeneous and spherical polynomials in the definition of the theta series (generalizing a…

We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…

In this paper we obtain the precise description of the asymptotic behavior of the solution $u$ of $$ \partial_t u+(-\Delta)^{\frac{\theta}{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty), \qquad u(x,0)=\varphi(x)\quad\mbox{in}\quad{\bf…

A new effective method for factorization of a class of nonrational $n\times n$ matrix-functions with \emph{stable partial indices} is proposed. The method is a generalization of the one recently proposed by the authors which was valid for…

Andrews-Dyson-Hickerson, Cohen build a striking relation between q-hypergeometric series, real quadratic fields, and Maass forms. Thanks to the works of Lewis-Zagier and Zwegers we have a complete understanding on the part of these…

Hamiltonian matrices appear in a variety or problems in physics and engineering, mostly related to the time evolution of linear dynamical systems as for instance in ion beam optics. The time evolution is given by symplectic transfer…

This short note reports a master theorem on tight asymptotic solutions to divide-and-conquer recurrences with more than one recursive term: for example, T(n) = 1/4 T(n/16) + 1/3 T(3n/5) + 4 T(n/100) + 10 T(n/300) + n^2.

This is the full and extended version of the brief note arXiv:1908.00938. A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The…

We derive the asymptotic formula for $p_n(N,M)$, the number of partitions of integer $n$ with part size at most $N$ and length at most $M$. We consider both $N$ and $M$ are comparable to $\sqrt{n}$. This is an extension of the classical…

This is a continuation of [arXiv:2309.16550] in which we computed the asymptotics near $x = \infty$ of all solutions of the radial Toda equation. In this article, we compute the asymptotics near $x = \infty$ of all solutions of a "partner"…

Two aspects of TDDFT, the linear response approach and the adiabatic local density approximation, are examined from the perspective of lattice models. To this end, we review the DFT formulations on the lattice and give a concise…