Related papers: Refined functional relations for the elliptic SOS …
We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They…
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems \begin{equation*}\label{00} \left\{ \begin{array}{l} (-\Delta)^{s}u + u = |u|^{p-2}u\;\;\mbox{in $\Omega$},\\ u \geq 0 \quad \mbox{in}…
This thesis pertains to the study of elliptic and parabolic partial differential equations on "thin" structures. The first main objective is to establish the strong and weak low-dimensional counterparts of the parabolic Neumann problem. The…
In this paper, we show how to get matrix models corresponding to the refined BPS states partition functions of $\mathbb{C}^3$, resolved conifold and $\mathbb{C}^3/\mathbb{Z}_2$ by inserting the identity operator at a proper position in the…
We construct integrable boundary conditions for sl(2) coset models with central charges c=3/2-12/(m(m+2)) and m=3,4,... The associated cylinder partition functions are generating functions for the branching functions but these boundary…
Starting from multidimensional consistency of non-commutative lattice modified Gel'fand-Dikii systems we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the…
We obtain in terms of the Weierstrass elliptic $\wp-$function, sigma function, and zeta function an explicit parametrized solution of a particular nonlinear, ordinary differential equation. This equation includes, in special cases,…
This paper aims to introduce a construction technique of set-theoretic solutions of the Yang-Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new…
The Weierstrassian $\wp, \zeta$ and $\sigma $ functions are generalized to ${\bf R}^{n}$. The $n=3$ and $n=4$ cases have already been used in gravitational and Yang-Mills instanton solutions which may be interpreted as explicit realizations…
Plane partitions naturally appear in many problems of statistical physics and quantum field theory, for instance, in the theory of faceted crystals and of topological strings on Calabi-Yau threefolds. In this paper a connection is made…
Using a rational R-matrix associated with the 4 x 4 defining matrix representation of c_2=sp(4), the Lie algebra of Sp(4), a one-site operator solution of the associated Yang-Baxter algebra acting in the Fock space of two harmonic…
With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we obtain the explicit determinant expression of the partition function of the eight-vertex model with a generic non-diagonal reflecting end and…
A class of exact solutions of the Skyrme model are obtained. They are described by the Weierstrass $\wp$-function or the Jacobi elliptic function. They are not solitonic but of wave character. They supply us with examples of the…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
We obtain identities and relationships between the modular $j$-function, the generating functions for the classical partition function and the Andrews $spt$-function, and two functions related to unimodal sequences and a new partition…
The normalized cochain complex of a simplicial set N^*(Y) is endowed with the structure of an E_{infinity} algebra. More specifically, we prove in a previous article that N^*(Y) is an algebra over the Barratt-Eccles operad. According to M.…
We construct a factorized representation of the $\frak g \frak l _n$-Sklyanin algebra from the vertex-face correspondence. Using this representation, we obtain a new solvable model which gives an $\frak s \frak l _n$-generalization of the…
In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-generated finite differences (RBF-FD) on unfitted node sets…