ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.

Multiparameter twisted Weyl algebras

We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras. (C) 2011 Elsevier Inc. All rights reserved.

COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

DXA, bioelectrical impedance, ultrasonography and biometry for the estimation of fat and lean mass in cats during weight loss

Background: Few equations have been developed in veterinary medicine compared to human medicine to predict body composition. The present study was done to evaluate the influence of weight loss on biometry (BIO), bioimpedance analysis (BIA) and ultrasonography (US) in cats, proposing equations to estimate fat (FM) and lean (LM) body mass, as compared to dual energy x-ray absorptiometry (DXA) as the referenced method. For this were used 16 gonadectomized obese cats (8 males and 8 females) in a weight loss program. DXA, BIO, BIA and US were performed in the obese state (T0; obese animals), after 10% of weight loss (T1) and after 20% of weight loss (T2). Stepwise regression was used to analyze the relationship between the dependent variables (FM, LM) determined by DXA and the independent variables obtained by BIO, BIA and US. The better models chosen were evaluated by a simple regression analysis and means predicted vs. determined by DXA were compared to verify the accuracy of the equations. Results: The independent variables determined by BIO, BIA and US that best correlated (p < 0.005) with the dependent variables (FM and LM) were BW (body weight), TC (thoracic circumference), PC (pelvic circumference), R (resistance) and SFLT (subcutaneous fat layer thickness). Using Mallows'Cp statistics, p value and r(2), 19 equations were selected (12 for FM, 7 for LM); however, only 7 equations accurately predicted FM and one LM of cats. Conclusions: The equations with two variables are better to use because they are effective and will be an alternative method to estimate body composition in the clinical routine. For estimated lean mass the equations using body weight associated with biometrics measures can be proposed. For estimated fat mass the equations using body weight associated with bioimpedance analysis can be proposed.

Monsplasty for Women After Massive Weight Loss

Ptosis with excess skin in the pubic area is a very common deformity in patients after massive weight loss. This deformity requires adequate surgical treatment whether combined with abdominoplasty or not. The enlarged pubogenital area may lead to psychosocial distress and impaired quality of life. A series of 23 women with a mean age of 39.5 years who previously underwent bariatric surgeries and later presented with pubogenital ptosis underwent monsplasty. The preoperative surgical markings and the surgical technique presented are easily reproducible. In this prospective study, the surgical outcomes were assessed by questionnaires applied to the patients, who scored the following parameters: movement dynamics, aesthetic appearance, sexual performance, improved hygiene, and use of clothing items. Four of the parameters assessed (movement dynamics, aesthetic appearance, hygiene, and use of clothing items) showed clear improvement, with scores ranging from good to very good. A small percentage of the patients (13%) reported fair improvement in sexual performance. The findings showed monsplasty to be a simple and reproducible technique with favorable outcomes and low morbidity rates.