Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies

Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight vectors are represented in terms of Schur's $Q$-functions. The method to get the polynomial solutions to the reduced BKP hierarchies is shown to be equivalent to a certain rule in Maya game.Comment: January 1994, 11 page

Knowledge attitude and practice of haemovigilance among doctors in tertiary care hospital in Nagpur, Maharashtra, India

Background: Haemovigilance program of India was launched on December 2012 and is a comprehensive, and a well-structured approach to collect, collate, and analyse data to address the issues of adverse reactions associated with blood transfusion. The information thus collected would facilitate corrective and preventive actions to be taken to minimize the potential risk associated blood collection processing and transfusion to patients. Considering the deep concern over the under-reporting of transfusion reactions prevailing among the doctors, the present study was done to know the knowledge attitude and practice (KAP) of haemovigilance among doctors.Methods: The present study was a cross sectional questionnaire based study, which included doctors of a tertiary care hospital. The purpose of the questionnaire was to know awareness of doctors regarding haemovigilance programme of India. With this study we also tried to   identify the factors responsible for underreporting of transfusion reactions and to find out the possible ways to improve reporting of transfusion reactions.Results: (38.88%) and (30%) of the responders were aware of the haemovigilance programme and transfusion reaction reporting centre respectively. Reporting of transfusion reaction was poor 22.22% among the respondents. According to respondents creating awareness about haemovigilance by conducting continuing medical education (CMEs), and   training to healthcare professionals would lead to improvement in reporting of transfusion reactions. Complacency and ignorance were the main factors which discouraged transfusion reaction reporting by doctors.Conclusions: Increasing awareness of haemovigilance among doctors and training on reporting transfusion reactions would likely improve spontaneous reporting and help to strengthen the blood transfusion system

Highest weight representations of the quantum algebra U_h(gl_\infty)

A class of highest weight irreducible representations of the quantum algebra U_h(gl_\infty) is constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the Chevalley generators are explicitly written.Comment: 7 pages, PlainTe

Novel classical ground state of a many body system in arbitrary dimensions

The classical ground state of a D- dimensional many body system with two and three body interactions is studied as a function of the strength of the three body interaction. We prove exactly that beyond a critical strength of the three body interaction, the classical ground state of the system is one in which all the particles are on a line. The positions of the particles in this string configuration are uniquely determined by the zeros of the Hermite polynomials.Comment: 4 pages, RevTeX, no figure; version to appear in Physical Review Letter

The Bloch-Okounkov correlation functions of classical type

Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc, and it can also be interpreted as correlation functions on integrable gl_\infty-modules of level one. Such gl_\infty-correlation functions at higher levels were then calculated by Cheng and Wang. In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of gl_\infty of type B,C,D at arbitrary levels. As byproducts, we obtain new q-dimension formulas for integrable modules of type B,C,D and some fermionic type q-identities.Comment: v2, very minor changes, Latex, 41 pages, to appear in Commun. Math. Phy

Weight Vectors of the Basic A_1^(1)-Module and the Littlewood-Richardson Rule

The basic representation of \A is studied. The weight vectors are represented in terms of Schur functions. A suitable base of any weight space is given. Littlewood-Richardson rule appears in the linear relations among weight vectors.Comment: February 1995, 7pages, Using AMS-Te

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty

The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of \hgl_\infty-modules of level one. Recent works have calculated these character functions for higher levels for \hgl_\infty and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.Comment: v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physic

Virasoro constraint for Nekrasov instanton partition function

We show that Nekrasov instanton partition function for SU(N) gauge theories satisfies recursion relations in the form of U(1)+Virasoro constraints when {\beta} = 1. The constraints give a direct support for AGT conjecture for general quiver gauge theories.Comment: 23 pages, 7 figures. v2: typos correcte

Knowledge and perception about generic drugs in patients coming to OPD of tertiary care centre

Background: In an era of rapidly rising health care costs generic medicines provide a less expensive alternative to branded medicines. In addition to reducing the overall health care expenditure, it has been shown to improve adherence. Objective was to study knowledge and perception about generic drugs among patients coming to outpatient department of tertiary care centre.Methods: After ethical approval a cross sectional questionnaire based study was conducted. Patients (n=71) were interviewed according to questionnaire in vernacular language by investigator to fill questionnaire.Results: About 28% people think that price of generic drug is less than a branded drug while nearly 61% of people don’t know of it. Only 18.85% participants had taken generic medicine. Trusting efficacy of generic drugs only 30 participants were in favour it. Even they have not seen or heard publicity of generic drugs (61.97%). They (60.56%) opined that generic drugs never prescribe in our country.Conclusions: Limitation in knowledge and perception about generic medicines has been seen among participants