Related papers: Modified Tetrahedron Equations and Related 3D Inte…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
A matroid is a combinatorial structure that captures and generalizes the algebraic concept of linear independence under a broader and more abstract framework. Matroids are closely related with many other topics in discrete mathematics, such…
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…
We pose the problem to determine explicit defining equations of various elliptic fibrations on a given $K3$ surface, and study the case of the Kummer surfaces of the product of two elliptic curves.
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
An integrable extension of the well known nonlinear Schroedinger (NLS) equation to a higher space-dimension, recently proposed by us, is investigated, exploring its various important aspects. Focusing on the idea of construction its…
Across various scientific and engineering domains, a growing interest in flexible and deployable structures is becoming evident. These structures facilitate seamless transitions between distinct states of shape and find broad applicability…
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures…
The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on…
The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian $H=T+V$ into a geodesic Hamiltonian ${\cal T}$ with one additional degree of freedom, is applied to the four families of quadratically superintegrable…
This paper establishes relationships between elliptic functions and Riordan arrays leading to new classes of Riordan arrays which here are called elliptic Riordan arrays. In particular, the case of Riordan arrays derived from Jacobi…
This work concerns to the studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group ${\cal U}_{q}[X_{n}]$ for the affine Lie algebras $X_{n}$ = $A_{1}^{(1)}$,…
The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local…
In this paper we obtain a set of meta-functional equations as new species of formulas in classical mathematical analysis. Mentioned species are generated by crossbreeding complete hybrid formula as a mother formula. Namely, they are…
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These…
Elliptic K3 admit contraction to plane models, the Weierstrass models. We define a higher dimensional notion of Weierstrass models, show that they are compactification of torsors in a unique form, and propose an application to the kahler…
We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field theory living on a 4d defect is proposed…