We demonstrate fiber nonlinearity mitigation by using multiple optical phase conjugations (OPCs) in the WDM transmission systems of both 8 × 32-Gbaud PDM QPSK channels and 8 × 32-Gbaud PDM 16-QAM channels, showing improved performance over a single mid-span OPC and no OPC in terms of nonlinear threshold and a best achievable Q2 factor after transmission. In addition, after an even nu...

Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the ‘even-dimensional’ case they correspond to the Twisted Canonical Commutation Relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C-algebras and polynomial algebras...

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...

A new class of Embedded Multiple Description Scalar Quantizers (EMDSQ) is proposed. EMDSQ meet the desired features of high redundancy level, fine grain rate adaptation and progressive transmission of each description. Experimental results show that EMDSQ yield better rate-distortion performance in comparison to Multiple Description Uniform Scalar Quantizers (MDUSQ) previously proposed in the l...

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...