In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

We have applied the method of integration of the Heisenberg equation of motion proposed by Bender and Dunne, and M. Kamella and M. Razavy to the potential V(q) = v q - µ q with linear and nonlinear dissipation. We concentrate our calculations on the evolution of basis set of Weyl Ordered Operators and calculate the mean position , velocity , the commutation relation [q, p], and the energ...

we have applied the method of integration of the heisenberg equation of motion proposed by bender and dunne, and m. kamella and m. razavy to the potential v(q) = v q - µ q with linear and nonlinear dissipation. we concentrate our calculations on the evolution of basis set of weyl ordered operators and calculate the mean position , velocity , the commutation relation [q, p], and the energy of pa...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand Fuchs 3-cocycle on periodic vector fields. A nontrivial embedding of th...

Introducing an H-Hopf algebroid structure into Uq,p(ŝl2), we investigate the vertex operators of the elliptic quantum group Uq,p(ŝl2) defined as intertwining operators of infinite dimensional Uq,p(ŝl2)-modules. We show that the vertex operators coincide with the previous results obtained indirectly by using the quasi-Hopf algebra Bq,λ(ŝl2). This shows a consistency of our H-Hopf algebroid struc...

In this paper, we show the second part of Schur-Weyl duality for mixed tensor space. The quantum group U = U(gln) of the general linear group and a q-deformation Br,s(q) of the walled Brauer algebra act on V ⊗r ⊗V ∗⊗s where V = R is the natural U-module. We show that EndBnr,s(q)(V ⊗r ⊗ V ∗) is the image of the representation of U, which we call the rational q-Schur algebra. As a byproduct, we o...

An extra term generally appears in the q-deformed su(2) algebra for the deformation parameter q = exp 2πiθ, if one combines the Biedenharn-Macfarlane construction of q-deformed su(2), which is a generalization of Schwinger’s construction of conventional su(2), with the representation of the q-deformed oscillator algebra which is manifestly free of negative norm. This extra term introduced by th...

in this paper we study the notions of cogenerator and subdirectlyirreducible in the category of s-poset. first we give somenecessary and sufficient conditions for a cogenerator $s$-posets.then we see that under some conditions, regular injectivityimplies generator and cogenerator. recalling birkhoff'srepresentation theorem for algebra, we study subdirectlyirreducible s-posets and give this theo...

In this paper we first present the construction of the new 2-variable classical link invariants arising from the Yokonuma-Hecke algebras Yd,n(q), which are not topologically equivalent to the Homflypt polynomial. We then present the algebra FTLd,n(q) which is the appropriate Temperley-Lieb analogue of Yd,n(q), as well as the related 1-variable classical link invariants, which in turn are not to...