Related papers: On multidimensional consistent systems of asymmetr…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
It is known that there is a duality between the Davey--Stewartson type coupled systems and a class of integrable two--dimensional Toda type lattices. More precisely, the coupled systems are generalized symmetries for the lattices and the…
We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
QCD in $d=4-2\epsilon$ space-time dimensions possesses a nontrivial critical point. Scale invariance usually implies conformal symmetry so that there are good reasons to expect that QCD at the critical point restricted to the gauge…
Upon having presented a bird's eye view of history of integrable systems, we give a brief review of certain earlier advances (arXiv:1401.2122 & arXiv:1812.02263) in the longstanding problem of search for partial differential systems in four…
Extensive and systematic machine computations are carried out to investigate the integral cohomology of the Euclidean Bianchi groups and their congruence subgroups. The collected data give insight on several aspects, including the…
In this work, we prove the existence of solutions for a tripled system of integral equations using some new results of fixed point theory associated with measure of noncompactness. These results extend some previous works in the literature,…
This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations,…
In this paper, we seek analytically checkable necessary and sufficient condition for copositivity of a three-dimensional symmetric tensor. We first show that for a general third order three-dimensional symmetric tensor, this means to solve…
The symmetry classification method is applied to the string-like scalar fields in two-dimensional space-time. When the configurational space is three-dimensional and reducible we present the complete list of the systems admiting higher…
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such…
The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
For a 4th order 3-dimensional symmetric tensor with its some entries $1$ or $-1$, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for…
In this paper, we examine an analogue of the recently solved spectrum conjecture by Fujita in the setting of Fine polyhedral adjunction theory. We present computational results for lower-dimensional polytopes, which lead to a complete…
We construct a weight matrix for the 3D Ising model satisfying the so-called twisted tetrahedron equation. The result is based on the theory of the n-simplicial complex and the invented recursion procedure on the space of n-simplex…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
We first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the complete classification of triharmonic curves in surfaces…