‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

One dimensional chiral Hubbard model reduces to the Haldane-Shastry spin chain at half-filling with large but finite on-site energy U . In this talk, we show that the Gutzwiller-Jastrow wavefunctions are the eigen-states of the Hubbard model at U = +∞ at less than half-filling. The full energy spectrum and an infinite set of mutually commuting constants of motion are also given in this limit fo...

Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the dual systems. We demonstrate that the Θ-function coefficients of their expansion can be expressed entirely in terms of the co-ordinates of the Seiberg-Witten integrable system, being, th...

We study a variety of modes (idempotent algebras with mutually commuting term operations), so called differential modes, having a strongly solvable chain 0 ≤ α ≤ 1 in their congruence lattices. We show an explicit description of subdirectly irreducible algebras in this variety, and use it to compute residual bounds of its subvarieties. It follows from our results that all subvarieties with a fi...

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W -orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A ...

We examine a two-parameter (, λ) deformation of the Poincarè algebra which is covariant under the action of SLq(2, C). When λ → 0 it yields the Poincarè algebra, while in the → 0 limit we recover the classical quadratic algebra discussed previously in [1], [2]. The analogues of the Pauli-Lubanski vector w and Casimirs p 2 and w 2 are found and a set of mutually commuting operators is constructed.

Based on a novel point of view on 1-dimensional Gaussian quadrature, we present a new approach to the computation of d-dimensional cubature formulae. It is well known that the nodes of 1-dimensional Gaussian quadrature can be computed as eigenvalues of the so-called Jacobi matrix. The d-dimensional analog is that cubature nodes can be obtained from the eigenvalues of certain mutually commuting ...

Based on a novel point of view on 1-dimensional Gaussian quadrature, we present a new approach to d-dimensional cubature formulae. It is well known that the nodes of 1-dimensional Gaussian quadrature can be computed as eigenvalues of the so-called Jacobi matrix. The d-dimensional analog is that cubature nodes can be obtained from the eigenvalues of certain mutually commuting matrices. These are...

We study the variant of the k-local hamiltonian problem which is a natural generalization of k-CSPs, in which the hamiltonian terms all commute. More specifically, we consider a hamiltonian H = ∑i Hi over n qubits, where each Hi acts non-trivially on O(log n) qubits and all the terms Hi commute, and show the following 1. We show that a specific case of O(log n) local commuting hamiltonians over...