Related papers: Generalized pentagram maps via Q-nets and refactor…
The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are…
We provide a graphical treatment of SAT and #SAT on equal footing. Instances of #SAT can be represented as tensor networks in a standard way. These tensor networks are interpreted by diagrams of the ZH-calculus: a system to reason about…
In this paper, we study the class of parabolically geometrically finite (PGF) subgroups of mapping class groups, introduced by Dowdall-Durham-Leininger-Sisto. We prove a combination theorem for graphs of PGF groups (and other…
The study of the set-theoretic solutions of the reflection equation, also known as reflection maps, is closely related to that of the Yang-Baxter maps. In this work, we construct reflection maps on various geometrical objects, associated…
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is…
In a recent paper, Belishev and Sharafutdinov consider a compact Riemannian manifold $M$ with boundary $\partial M$. They define a generalized Dirichlet to Neumann (DN) operator $\Lambda$ on all forms on the boundary and they prove that the…
A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),\Delta_z) starting from the Lie bialgebra (g,\delta) that gives the first-order deformation of the coproduct map \Delta_z is presented.…
Some relations between different objects associated with quantum affine algebras are reviewed. It is shown that the Frenkel-Jing bosonization of a new realization of quantum affine algebra $\Uqa$ as well as bosonization of $L$-operators for…
In this paper, we present a theory of Poisson deformation of Hamiltonian quasi-Poisson manifolds to Hamiltonian Poisson manifolds that include degenerate cases. More significantly, this theory extends to singular cases arising from…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
Topological quantum field theory (TQFT) is a powerful tool to describe homologies, which normally involve complexes and a variety of maps/morphisms, what makes a functional integration approach with a sum over a single kind of maps…
We study the partition function Z_{G(nk,k)}(Q,v) of the Q-state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its zeros in the plane (Q,v) for 1<= k <= 7. We also consider two specializations of…
We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of…
Bidimensionality theory is a powerful framework for the development of metaalgorithmic techniques. It was introduced by Demaine et al. as a tool to obtain sub-exponential time parameterized algorithms for problems on H-minor free graphs.…
Inspired by cartographic generalization principles, we present a generalization technique for rendering line charts at different sizes, preserving the important semantics of the data at that display size. The algorithm automatically…
In a previous paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187) we presented a new method for renormalization in Euclidean configuration spaces based on certain renormalization maps. This…
In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…
The theory of Lie point symmetries is applied to study the generalized Zakharov system with two unknown parameters. The system reduces into a three-dimensional real value functions system, where we find that admits five Lie point…
Let $U^-_q = U^-_q(\mathfrak g)$ be the negative part of the quantum group associated to a finite dimensional simple Lie algebra $\mathfrak g$, and $\sigma : \mathfrak g \to \mathfrak g$ be the automorphism obtained from the diagram…
We extend the construction of the relativistic Toda chains as integrable systems on the Poisson submanifolds in Lie groups beyond the case of A-series. For the simply-laced case this is just a direct generalization of the well-known…