Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. III. Associated continuous dual q-Hahn polynomials

AbstractExplicit solutions for the three-term recurrence satisfied by associated continuous dual q-Hahn polynomials are obtained. A minimal solution is identified and an explicit expression for the related continued fraction is derived. The absolutely continuous component of the spectral measure is obtained. Eleven limit cases are discussed in some detail. These include associated big q-Laguerre, associated Wall, associated Al-Salam-Chihara, associated Al-Salam-Carlitz I, and associated continuous q-Hermite polynomials

Physics Prospects at the Hadron Colliders

I start with a brief introduction to the elementary particles and their interactions, Higgs mechanism and supersymmetry. The major physics objectives of the Tevatron and LHC colliders are identified. The status and prospects of the top quark, charged Higgs boson and superparticle searches are discussed in detail, while those of the neutral Higgs boson(s) are covered in a parallel talk by R.J.N. Phillips at this workshop.Comment: 16 pages Latex + 15 figures (available on request

The vector-valued big q-Jacobi transform

Big $q$-Jacobi functions are eigenfunctions of a second order $q$-difference operator $L$. We study $L$ as an unbounded self-adjoint operator on an $L^2$-space of functions on $\mathbb R$ with a discrete measure. We describe explicitly the spectral decomposition of $L$ using an integral transform $\mathcal F$ with two different big $q$-Jacobi functions as a kernel, and we construct the inverse of $\mathcal F$.Comment: 35 pages, corrected an error and typo

Rural Entrepreneurship through Vermicomposting – Case Studies

Solid waste management continue to be  a major challenge and permanent problem of urban as well as semi-urban areas of the country. A number of initiatives have been taken  by several public and private sector organizations to overcome this serious problem.  One such initiative taken at the Dev Sanskriti Vishwavidyalaya (DSVV), Haridwar has  successfully  turned the  bio-degradable part of the solid waste  into a thriving and profitable enterprise. DSVV has transferred this technology to a number of entrepreneurs through their on-going capacity development programmes for rural development and organic farming. The paper describes how DSVV continue to manage its solid waste of over 5  MT generated daily in the Campus as  well as that of Shantikunj by converting it into valuable vermicompost and handmade paper, after segregation, and thus helping DSVV as well as Shantikunj to become completely organic in managing their total area of over 200 acres lush green campus.  The paper also describes how rural entrepreneurship training on vermicomposting  at DSVV has helped three entrepreneurs, besides many, to develop large commercial vermicompost units with attractive returns.  The paper also highlight potential of vermicomposting in solid waste management, employment generation and organic farming with least damage to environment

The STAR Photon Multiplicity Detector

Details concerning the design, fabrication and performance of STAR Photon Multiplicity Detector (PMD) are presented. The PMD will cover the forward region, within the pseudorapidity range 2.3--3.5, behind the forward time projection chamber. It will measure the spatial distribution of photons in order to study collective flow, fluctuation and chiral symmetry restoration.Comment: 15 pages, including 11 figures; to appear in a special NIM volume dedicated to the accelerator and detectors at RHI

Charmonium states in QCD-inspired quark potential model using Gaussian expansion method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/\psi$ and $\psi^{\prime}$ are alleviated spontaneously. This work also intends to provide an inspection and suggestion for the possible $c\bar{c}$ among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as $M(2^1D_2)= 4164.9$ MeV and $M(3^3P_2)= 4352.4$ MeV, which strongly favor the $J^{PC}=2^{-+}, 2^{++}$ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.Comment: 16 pages,3 figure

Spin-based quantum information processing with semiconductor quantum dots and cavity QED

A quantum information processing scheme is proposed with semiconductor quantum dots located in a high-Q single mode QED cavity. The spin degrees of freedom of one excess conduction electron of the quantum dots are employed as qubits. Excitonic states, which can be produced ultrafastly with optical operation, are used as auxiliary states in the realization of quantum gates. We show how properly tailored ultrafast laser pulses and Pauli-blocking effects, can be used to achieve a universal encoded quantum computing.Comment: RevTex, 2 figure

Properties of generalized univariate hypergeometric functions

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E_7 (elliptic, hyperbolic) and of type E_6 (trigonometric) using the appropriate versions of the Nassrallah-Rahman beta integral, and we derive contiguous relations using fundamental addition formulas for theta and sine functions. The top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with Ruijsenaars' relativistic hypergeometric function and the Askey-Wilson function, respectively. We show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions. We also describe an intimate connection between the hyperbolic and trigonometric theory, which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions.Comment: 46 page