We study codes over a finite field F4. We relate self-dual codes over F4 to real 5-modular lattices and to self-dual codes over F2 via a Gray map. We construct Jacobi forms over Q( √ 5) from the complete weight enumerators of self-dual codes over F4. Furthermore, we relate Hilbert–Siegel forms to the joint weight enumerators of self-dual codes over F4. © 2004 Elsevier Ltd. All rights reserved.

A number of linear programming relaxations have been proposed for finding most likely settings of the variables (MAP) in large probabilistic models. The relaxations are often succinctly expressed in the dual and reduce to different types of reparameterizations of the original model. The dual objectives are typically solved by performing local block coordinate descent steps. In this work, we sho...

In communication systems, specifically wireless mobile communication applications, Size and Speed are dominant factors while meeting the performance requirements. Turbo codes play an important role in such practical applications due to their better error-correcting capability. In Turbo decoders, Maximum A Posterior probability (MAP) algorithm has been widely used for its optimum error correctin...

We developpe a direct sum decomposition for n-dual spaces. Introduction Let X be a Banach space. We will denote π0 : X → X ∗∗ and π1 : X ∗ → X∗∗∗ the canonical maps ofX and its dual space X∗ into their respective bidual spaces. According to [G] we have X∗∗∗ = Ran(π1)⊕Ker(π ∗ 0), where π∗ 0 denotes the adjoint map of π0. 1. Remark. In [G] we also saw as an application that X is reflexive if and ...

Many receptor-linked agents that prime or activate the NADPH oxidase in polymorphonuclear neutrophils (PMNs) elicit changes in cytosolic Ca2+ concentration and activate mitogen-activated protein (MAP) kinases. To investigate the role of Ca2+ in the activation of p38 and p42/44 MAP kinases, we examined the effects of the Ca2+-selective ionophore ionomycin on priming and activation of the PMN oxi...

introduction:  the  advent  of  dual-modality  pet/ct  scanners  has  revolutionized  clinical  oncology  by  improving lesion localization and facilitating treatment planning for radiotherapy. in addition, the use of  ct images for ct-based attenuation correction (ctac) decreases the overall scanning time and creates  a noise-free  attenuation  map  (6map).  ctac  methods  include  scaling,  s...

A polyhedral map is called {p, q}-equivelar if each face has p edges and each vertex belongs to q faces. In [12], it was shown that there exist infinitely many geometrically realizable {p, q}-equivelar polyhedral maps if q > p = 4, p > q = 4 or q − 3 > p = 3. It was shown in [6] that there exist infinitely many {4, 4}and {3, 6}-equivelar polyhedral maps. In [1], it was shown that {5, 5}and {6, ...

We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real valued Lipschitz functions and the resulting bi-Lipschitz nonembedding theorems for finite dimensional vector space targets extend to Banach space targets having what we term a good finite dimensional approximati...

Two unital dual operator algebras A,B are called ∆-equivalent if there exists an equivalence functor F : AM → BM which “extends” to a ∗−functor implementing an equivalence between the categories ADM and BDM. Here AM denotes the category of normal representations of A and ADM denotes the category with the same objects as AM and ∆(A)-module maps as morphisms (∆(A) = A ∩A ). We prove that any such...

The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are ...