Related papers: Closed-Form Expressions for the n-Queens Problem a…
The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the $n^2$ dimensional subspace corresponding to the $n$-th…
In this paper we present a method to derive classical solutions of the Navier-Stokes equations for non-stationary initial value problems in domain $\mathbb{R}^n$ ($n=2,3$ or higher). Exact solutions in $\mathbb{R}^2$ and $\mathbb{R}^3$ in…
In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain (2005) on the quintic NLS, we propose a novel…
This paper studies the solution existence of the continuous-time algebraic Riccati equation (CARE). We formulate the CARE as two constrained polynomial optimization problems, and then use Lasserre's hierarchy of semi-definite relaxations to…
This paper studies a problem of Erd\"{o}s concerning lattice cubes. Given an $N \times N \times N$ lattice cube, we want to find the maximum number of vertices one can select so that no eight corners of a rectangular box are chosen…
It is classically known that the circle method produces an asymptotic for the number of representations of a tuple of integers $(n_1,\ldots,n_R)$ by a system of quadratic forms $Q_1,\ldots, Q_R$ in $k$ variables, as long as $k$ is…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We investigate the structure of solutions of boundary value problems for a one-dimensional nonlinear system of pseudodifferential equations describing the dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar…
We investigate the problem of the maximum number of cubic subwords (of the form $www$) in a given word. We also consider square subwords (of the form $ww$). The problem of the maximum number of squares in a word is not well understood.…
In this work, we introduce a novel variant of the multivariate quadratic problem, which is at the core of one of the most promising post-quantum alternatives: multivariate cryptography. In this variant, the solution of a given multivariate…
We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order $n$ is equivalent to a proper edge-coloring of $K_{n,n}$. A transversal corresponds to a multicolored perfect…
In this work we study weighted total least squares problems on infinite dimensional spaces. We show that in most cases this problem does not admit a solution (except in the trivial case) and then, we consider a regularization on the…
We focus on computing certified upper bounds for the positive maximal singular value (PMSV) of a given matrix. The PMSV problem boils down to maximizing a quadratic polynomial on the intersection of the unit sphere and the nonnegative…
A latin square of order $n$ is an $n\times n$ array of $n$ symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of $n$ entries such that no two entries share the same row, column…
In this paper, we study quantum query complexity of the following rather natural tripartite generalisations (in the spirit of the 3-sum problem) of the hidden shift and the set equality problems, which we call the 3-shift-sum and the…
Solving quadratic equations over finite fields is a fundamental task in algebraic coding theory and serves as a key subroutine for computing the roots of cubic and quartic polynomials. Notably, any quadratic polynomial over binary extension…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
In this paper we address the problem of representing solutions of a system of scalar linear partial difference equations akin to state space equations of 1-D systems theory. We first obtain a representation formula for a special class of…
We prove a closed character formula for the symmetric powers $S^N V(\lambda)$ of a fixed irreducible representation $V(\lambda)$ of a complex semi-simple Lie algebra $\mathfrak{g}$ by means of partial fraction decomposition. The formula…
In 1967, Klarner proposed a problem concerning the existence of reflecting $n$-queens configurations. The problem considers the feasibility of placing $n$ mutually non-attacking queens on the reflecting chessboard, an $n\times n$ chessboard…