Fundamental Weights, Permutation Weights and Weyl Character Formula

For a finite Lie algebra $G_N$ of rank N, the Weyl orbits $W(\Lambda^{++})$ of strictly dominant weights $\Lambda^{++}$ contain $dimW(G_N)$ number of weights where $dimW(G_N)$ is the dimension of its Weyl group $W(G_N)$. For any $W(\Lambda^{++})$, there is a very peculiar subset $\wp(\Lambda^{++})$ for which we always have $$dim\wp(\Lambda^{++})=dimW(G_N)/dimW(A_{N-1}) .$$ For any dominant weight $\Lambda^+$, the elements of $\wp(\Lambda^+)$ are called {\bf Permutation Weights}. It is shown that there is a one-to-one correspondence between elements of $\wp(\Lambda^{++})$ and $\wp(\rho)$ where $\rho$ is the Weyl vector of $G_N$. The concept of signature factor which enters in Weyl character formula can be relaxed in such a way that signatures are preserved under this one-to-one correspondence in the sense that corresponding permutation weights have the same signature. Once the permutation weights and their signatures are specified for a dominant $\Lambda^+$, calculation of the character $ChR(\Lambda^+)$ for irreducible representation $R(\Lambda^+)$ will then be provided by $A_N$ multiplicity rules governing generalized Schur functions. The main idea is again to express everything in terms of the so-called {\bf Fundamental Weights} with which we obtain a quite relevant specialization in applications of Weyl character formula.Comment: 6 pages, no figures, TeX, as will appear in Journal of Physics A:Mathematical and Genera

An Explicit Construction of Casimir Operators and Eigenvalues : I

We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients $g^{A_1,A_2,.. A_p}$. It is seen that these coefficients can be descibed by some rational polinomials of rank N. These polinomials are also multilinear in Cartan sub-algebra indices taking values from the set $I_0 = {1,2,.. N}$. The crucial point here is that for each degree one needs, in general, more than one polinomials. This in fact is related with an observation that the whole set of symmetric coefficients $g^{A_1,A_2,.. A_p}$ is decomposed into sum subsets which are in one to one correspondence with these polinomials. We call these subsets clusters and introduce some indicators with which we specify different clusters. These indicators determine all the clusters whatever the numerical values of coefficients $g^{A_1,A_2,.. A_p}$ are. For any degree p, the number of clusters is independent of rank N. This hence allows us to generalize our results to any value of rank N. To specify the general framework explicit constructions of 4th and 5th order Casimir operators of $A_N$ Lie algebras are studied and all the polinomials which specify the numerical value of their coefficients are given explicitly.Comment: 14 pages, no figures, revised version, to appear in Jour.Math.Phy

Mutagenic and antimutagenic properties of some lichen species grown in the Eastern Anatolia Region of Turkey

All the methanol extracts did not show mutagenic activity in Ames/Salmonella and Z. mays MI test systems. Furthermore, some extracts showed significant antimutagenic activity against 9-AA in Ames test system. Inhibition rates for 9-AA mutagenicity ranged from 25.51 % (P. furfuracea – 0.05 μg/plate) to 66.14 % (C. islandica – 0.05 μg/plate). In addition, all of the extracts showed significant antimutagenic activity against sodium azide (NaN₃) mutagenicity on MI values of Z. mays.Целью работы было изучить мутагенный и антимутагенный потенциал метанольных экстрактов Cetraria islandica (L.) Ach. (Parmeliaceae), Pseudevernia furfuracea (L.) Zopf (Parmeliaceae) и Xanthoparmelia somloënsis (Gyeln.) Hale (Parmeliaceae) – лишайников из восточной части Турции. Ни один из экстрактов не показал мутагенной активности в тестах Эймса и Z. mays MI. Более того, некоторые экстракты проявляли заметную антимутагенную активность против 9-амино-акридина в тесте Эймса. Уровень ингибирования варьировал от 25,51 % (P. furfuracea) до 66,14 % (C. islandica). Кроме того, все экстракты проявляли значительную антимутагенную активность против азида натрия в Z. mays MI тесте. Все экстракты могут считаться генотоксично безопасными в исследованных концентрациях

A multi-targeted approach to suppress tumor-promoting inflammation

Cancers harbor significant genetic heterogeneity and patterns of relapse following many therapies are due to evolved resistance to treatment. While efforts have been made to combine targeted therapies, significant levels of toxicity have stymied efforts to effectively treat cancer with multi-drug combinations using currently approved therapeutics. We discuss the relationship between tumor-promoting inflammation and cancer as part of a larger effort to develop a broad-spectrum therapeutic approach aimed at a wide range of targets to address this heterogeneity. Specifically, macrophage migration inhibitory factor, cyclooxygenase-2, transcription factor nuclear factor-κB, tumor necrosis factor alpha, inducible nitric oxide synthase, protein kinase B, and CXC chemokines are reviewed as important antiinflammatory targets while curcumin, resveratrol, epigallocatechin gallate, genistein, lycopene, and anthocyanins are reviewed as low-cost, low toxicity means by which these targets might all be reached simultaneously. Future translational work will need to assess the resulting synergies of rationally designed antiinflammatory mixtures (employing low-toxicity constituents), and then combine this with similar approaches targeting the most important pathways across the range of cancer hallmark phenotypes

Laparoscopic versus conventional appendectomy - a meta-analysis of randomized controlled trials

<p>Abstract</p> <p>Background</p> <p>Although laparoscopic surgery has been available for a long time and laparoscopic cholecystectomy has been performed universally, it is still not clear whether open appendectomy (OA) or laparoscopic appendectomy (LA) is the most appropriate surgical approach to acute appendicitis. The purpose of this work is to compare the therapeutic effects and safety of laparoscopic and conventional "open" appendectomy by means of a meta-analysis.</p> <p>Methods</p> <p>A meta-analysis was performed of all randomized controlled trials published in English that compared LA and OA in adults and children between 1990 and 2009. Calculations were made of the effect sizes of: operating time, postoperative length of hospital stay, postoperative pain, return to normal activity, resumption of diet, complications rates, and conversion to open surgery. The effect sizes were then pooled by a fixed or random-effects model.</p> <p>Results</p> <p>Forty-four randomized controlled trials with 5292 patients were included in the meta-analysis. Operating time was 12.35 min longer for LA (95% CI: 7.99 to 16.72, p < 0.00001). Hospital stay after LA was 0.60 days shorter (95% CI: -0.85 to -0.36, p < 0.00001). Patients returned to their normal activity 4.52 days earlier after LA (95% CI: -5.95 to -3.10, p < 0.00001), and resumed their diet 0.34 days earlier(95% CI: -0.46 to -0.21, p < 0.00001). Pain after LA on the first postoperative day was significantly less (p = 0.008). The overall conversion rate from LA to OA was 9.51%. With regard to the rate of complications, wound infection after LA was definitely reduced (OR = 0.45, 95% CI: 0.34 to 0.59, p < 0.00001), while postoperative ileus was not significantly reduced(OR = 0.91, 95% CI: 0.57 to 1.47, p = 0.71). However, intra-abdominal abscess (IAA), intraoperative bleeding and urinary tract infection (UIT) after LA, occurred slightly more frequently(OR = 1.56, 95% CI: 1.01 to 2.43, p = 0.05; OR = 1.56, 95% CI: 0.54 to 4.48, p = 0.41; OR = 1.76, 95% CI: 0.58 to 5.29, p = 0.32).</p> <p>Conclusion</p> <p>LA provides considerable benefits over OA, including a shorter length of hospital stay, less postoperative pain, earlier postoperative recovery, and a lower complication rate. Furthermore, over the study period it was obvious that there had been a trend toward fewer differences in operating time for the two procedures. Although LA was associated with a slight increase in the incidence of IAA, intraoperative bleeding and UIT, it is a safe procedure. It may be that the widespread use of LA is due to its better therapeutic effect.</p

Tourism Planning and Marketing to Generation Y Prospects

https://nsuworks.nova.edu/hcbe_facbooks/1086/thumbnail.jp

Employment and its relationship with functionality and quality of life in patients with schizophrenia: EGOFORS Study

The aim of this study is to investigate the relationship between work/study status and symptom severity, functionality and quality of life (QoL) in schizophrenia patients

Mutagenic and antimutagenic properties of some lichen species grown in the eastern Anatolia region of Turkey

All the methanol extracts did not show mutagenic activity in Ames/Salmonella and Z. mays MI test systems. Furthermore, some extracts showed significant antimutagenic activity against 9-AA in Ames test system. Inhibition rates for 9-AA mutagenicity ranged from 25.51% (P. furfuracea-0.05 ?g/plate) to 66.14% (C. islandica-0.05 ?g/plate). In addition, all of the extracts showed significant antimutagenic activity against sodium azide (NaN3) mutagenicity on MI values of Z. mays. © 2012 Allerton Press, Inc