We review the W N algebra and its quantum deformation, based on free eld re-alizations. The (quantum deformed) W N algebra is deened through the (quantum deformed) Miura transformation, and its singular vectors realize the Jack (Macdon-ald) polynomials.

Let ∆̂n,q = ∑n i=1 wi`i andWn = ∑n i=1 wi with wi = p(xi) q(xi) and `i = `(f1(xi), yi)−`(f2(xi), yi). We note that for examples drawn according to q(x), E[∆̂n,q] = n∆ and E[Wn] = n. The random variables w1, . . . , wn and w1`1, . . . , wn`n are iid, therefore the central limit theorem implies that 1 n∆̂ 0 n,q and 1 nWn are asymptotically normally distributed with √ n ( 1 n ∆̂n,q −∆ ) n→∞ −→ N (0,Va...

Formal biomedical ontologies offer the capability to retrieve domain-specific knowledge. Particularly for grievous diseases like Alzheimer’s where latency of onset to clinical symptoms takes many years, automated structured mining approaches can generate great value. No single system is currently capable of covering a complete domain of Alzheimer’s disease (AD) by itself and manual effort will ...

and Applied Analysis 3 From the ideas of Theorem D to Theorem F, it is natural to ask whether the values a, b in Theorem C can be replaced by two polynomials Q1, Q2. The main purpose of this paper is to investigate this problem. We prove the following result. Theorem 1.2. Let Q1 z a1z a1,p−1zp−1 · · · a1,0 and Q2 z a2z a2,p−1zp−1 · · · a2,0 be two polynomials such that degQ1 z degQ2 z p (where ...

During 1999 and 2000, a disease outbreak of West Nile (WN) virus occurred in humans, horses, and wild and zoological birds in the northeastern USA. In our experiments, WN virus infection of young domestic geese (Anser anser domesticus) caused depression, weight loss, torticollis, opisthotonus, and death with accompanying encephalitis and myocarditis. Based on this experimental study and a field...

Fourteen isolations of West Nile (WN) virus were obtained from four mosquito species (Culex pipiens [5], Cx. restuans [4], Cx. salinarius [2], and Culiseta melanura [3]) in statewide surveillance conducted from June through October 2000. Most isolates were obtained from mosquitoes collected in densely populated residential locales in Fairfield and New Haven counties, where the highest rates of ...

1Department of Computer Science, Soft Computing and Intelligent Systems Research Group, University of the Western Cape, Private Bag X17, Bellville, Cape Town, South Africa 2Department of Mathematical Sciences (Computer Science Option), Ekiti State University, Ado-Ekiti, PMB 5363, Ado-Ekiti, Ekiti State, Nigeria 3College of Information and Communication Technology, Crescent University, Abeokuta,...

A review of observational evidence in favour of a metallicity dependence of WN and WC stars is presented. New near-IR studies of Milky Way, LMC and SMC early-type WN stars are presented, with weaker winds amongst WN stars containing hydrogen. A metallicity dependence is supported for WN stars with hydrogen, with dM/dt ∝ Zα with α ∼ 0.8±0.2 The influence of CNO content upon WN subtypes is discus...

Here and in the sequel we maintain the convention of [Bad] that all series which appear are supposed to be convergent. Moreover, (an) and (bn), n ≥ 1, always denote sequences of positive integers. Also, for the sake of brevity, we simply say “the series ∑∞ n=1 bn/an is irrational” instead of “the sum of the series ∑∞ n=1 bn/an is an irrational number”. We note that Theorem A is, in a certain se...