Related papers: Reply to "Comment" by A. V. Tsiganov

In this paper we consider the spin 1/2 highest weight representations for the 6-vertex Yang-Baxter algebra on a finite lattice and analyze the integrable quantum models associated to the antiperiodic transfer matrix. For these models, which…

In this article, using only elementary knowledge of complex numbers, we sketch a proof of the celebrated Abel--Ruffini theorem, which states that the general solution to an algebraic equation of degree five or more cannot be written using…

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…

A commutative diagram that connects the basic objects of commutative algebra with the main objects of commutative analysis is constructed. Namely, with the help of five types of canonical embeddings we constructed a diagram between two sets…

Any complex-valued polynomial on $(\mathbb{R}^n)^k$ decomposes into an algebraic combination of $O(n)$-invariant polynomials and harmonic polynomials. This decomposition, separation of variables, is granted to be unique if $n \geq 2k-1$. We…

In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which…

We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal…

We propose a way to separate variables in a rational integrable $\mathfrak{gl}(n)$ spin chain with an arbitrary finite-dimensional irreducible representation at each site and with generic twisted periodic boundary conditions. Firstly, we…

We construct a large family of commutative algebras of partial differential operators invariant under rotations. These algebras are isomorphic extensions of the algebras of ordinary differential operators introduced by Grunbaum and Yakimov…

We establish homogenization for nondegenerate viscous Hamilton-Jacobi equations in one space dimension when the diffusion coefficient $a(x,\omega) > 0$ and the Hamiltonian $H(p,x,\omega)$ are general stationary ergodic processes in $x$. Our…

We consider the unital associative algebra $\mathcal{A}$ with two generators $\mathcal{X}$, $\mathcal{Z}$ obeying the defining relation $[\mathcal{Z},\mathcal{X}]=\mathcal{Z}^2+\Delta$. We construct irreducible tridiagonal representations…

Iterated Geronimus transformations generate Sobolev-type orthogonal polynomials from classical families. We establish a direct equivalence between a Sobolev inner product involving point evaluation and the first derivative at a point a…

The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…

Continuing on from recent results of Brumer-Kramer and of Schoof, we show that there exist non-zero semistable Abelian varieties over Z[1/N], with N squarefree, if and only if N is not in the set {1,2,3,5,6,7,10,13}. Our results are…

We study meromorphic jacobian pairs, i.e., pairs of polynomials in one variable, with coefficients meromorphic series in a second variable, whose jacobian relative to the two variables depends only on the second variable. We pose two…

We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential…

We develop a general framework to describe the cubically nonlinear interaction of a unidirectional degenerate quartet of deep-water gravity waves. Starting from the discretised Zakharov equation, and thus without restriction on spectral…

We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one…

The class of finitely presented algebras A over a field K with a set of generators x_{1},...,x_{n} and defined by homogeneous relations of the form x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{sigma(i_l)}, where l geq 2 is a…

In order to compute with $l$--adic sheaves or crystals on a line over $\mathbb{F} _q$ a low-technology alternative to the traditional computation with the Hecke operators on the automorphic side could be helpful. A program which has evolved…