A SIMPLE DERIVATION OF ζ ( 1 − k ) = − Bk / k

Fermionic Basis for Space of Operators in the Xxz Model

In the recent study of correlation functions for the infinite XXZ spin chain, a new pair of anti-commuting operators b(ζ), c(ζ) was introduced. They act on the space of quasi-local operators, which are local operators multiplied by the disorder operator q where S(0) = 1 2 ∑0 j=−∞ σ 3 j . For the inhomogeneous chain with the spectral parameters ξk, these operators have simple poles at ζ 2 = ξ k....

On Jordan generalized k-derivations of semiprime Γ_N-Rings

Epidural Analgesia with Bupivacaine, Ketamine, and the Combination of Bupivacaine and Ketamine in Sheep

Objective- To evaluate the effects of bupivacaine (B), ketamine (K), and a combination of bupivacaine and ketamine (BK) after lumbosacral epidural analgesia in sheep.   Design- Experimental study.   Animals- Nine healthy male and non-pregnant female Iranian Chall sheep with mean body weight of 38.9 ± 15.1 kg.   Procedures- Animals were selected randomly and three treatments administered. The ...

A Duality of a Twisted Group Algebra of the Hyperoctahedral Group and the Queer Lie Superalgebra

We establish a duality relation (Theorem 4.2) between one of the twisted group algebras, of the hyperoctahedral group Hk (or the Weyl group of type Bk) and a Lie superalgebra q(n0)⊕ q(n1) for any integers k ≥ 4 and n0, n1 ≥ 1. Here q(n0) and q(n1) denote the “queer” Liesuperalgebras as called by some authors. The twisted group algebra B′ k in focus in this paper belongs to a different cocycle f...

A sequential Riesz-like criterion for the Riemann hypothesis

Let c k := k j=0 (−1) j k j (1/ζ(2 j + 2)). We prove that the Riemann hypothesis is equivalent to c k k −3/4+ for all > 0; furthermore, we prove that c k k −3/4 implies that the zeros of ζ(s) are simple. This is closely related to M. Riesz's criterion which states that the Riemann hypothesis is equivalent to ∞ k=1 ((−1) k+1 x k /(k − 1)!ζ(2k)) x 1/4+ as x → +∞, for all > 0.