Related papers: Electric network and Hirota type $4$-simplex maps
We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube and the Wu-Kadanoff duality between the cube…
Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS)…
A sort of two dimensional linear auxiliary problem for the complex of 3D $R$ -- operators associated with the Zamolodchikov -- Bazhanov -- Baxter statistical model is proposed. This problem resembles the problem of the local Yang -- Baxter…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…
We consider triholomorphic maps from an almost hyper-Hermitian manifold $\mathcal{M}^{4m}$ into a hyperK\"ahler manifold $\mathcal{N}^{4n}$. This means that $u \in W^{1,2}$ satisfies a quaternionic del-bar equation. We work under the…
A set of canonical parahermitian connections on an almost paraHermitian manifold is defined. ParaHermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the…
We study the minimum Manhattan network problem, which is defined as follows. Given a set of points called \emph{terminals} in $\R^d$, find a minimum-length network such that each pair of terminals is connected by a set of axis-parallel line…
A different approach will be presented that aims to scrutinize the phase-space trajectories of a general class of Hamiltonian systems with regard to their regular or irregular behavior. The approach is based on the `energy-second-moment…
The Faddeev-Yakubovsky equations in configuration space have been solved for the four nucleon system with special interest in their scattering states. We present results concerning the structure of the first $^4$He, scattering states in…
Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights,…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
We construct a compactification of the space of circular planar electrical networks studied by Curtis-Ingerman-Morrow and De Verdiere-Gitler-Vertigan, using cactus networks. We embed this compactification as a linear slice of the totally…
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not…
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…
Thurston's equations determine the hyperbolic structure of a 3-manifold with a triangulation. In work by Thistlethwaite and Tsvietkova, an alternative method was developed for link complements in $S^3$ depending on the link diagram, where a…
Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a…
The problem of construction of Barabanov norms for analysis of properties of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In previous papers of the author the method of Barabanov…
A branched covering $f: S^2 \to S^2$ is a nearly Euclidean Thurston (NET) map if each critical point is simple and its postcritical set has exactly four points. We show that up to equivalence, each NET map admits a normal form in terms of…
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix…