A (p, ν)-extension of the Appell function F1(·) and its properties

In this paper, we obtain a (p, v)-extension of the Appell hypergeometric functionF1(·), together with its integral representation, by using the extended Beta functionBp,v(x, y) introduced in [9]. Also, we give some of its main properties, namely theMellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, some new integral representations of the extended Appell functionF1,p,v(·) involving Meijer’s G-function are obtained

A (p,q)-extension of Srivastava's triple hypergeometric function H_B and its properties

In this paper, we obtain a (p,q)-extension of Srivastava's triple hypergeometric function HB(⋅), by using the extended Beta function Bp,q(x,y) introduced by Choi et al. (2014). We give some of the main properties of this extended function, which include several integral representations involving Exton's hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, a new integral representation of the extended Srivastava triple hypergeometric function involving Laguerre polynomials is obtained.</p

TeV Scale Quantum Gravity and Mirror Supernovae as Sources of Gamma Ray Bursts

Mirror matter models have been suggested recently as an explanation of neutrino puzzles and microlensing anomalies. We show that mirror supernovae can be a copious source of energetic gamma rays if one assumes that the quantum gravity scale is in the TeV range. We show that under certain assumptions plausible in the mirror models, the gamma energies could be degraded to the 10 MeV range (and perhaps even further) so as to provide an explanation of observed gamma ray bursts. This mechanism for the origin of the gamma ray bursts has the advantage that it neatly avoids the ``baryon load problem''.Comment: Latex 8 pages; no figures; UMD-PP-00-02

The cepheid-like relationship between variability and luminosity explained within the ``cannonball model'' of Gamma-Ray bursts

I show how an empirical variability - luminosity relationship for prompt gamma-ray bursts, first proposed by Fenimore and Ramirez-Ruiz, can be understood as a special-relativistic beaming effect in the ``cannonball model'' of Dar and De R\'ujula. In this scenario the variability is a measure of the direction of propagation and the Lorentz factor of the cannonball on which in turn the apparent luminosity of the prompt GRB depends sensitively. The observed absence of cosmological time dilation in the ``aligned peak test'' - when using redshifts derived with this relation - is also explained. The most direct evidence in favour of the cannonball model presented here is its correct description for the observed relation between narrow-spike width and amplitude within a given GRB. There seems to be an indication for cosmological time dilation in the total duration of GRBs, as expected in the cannonball model. Quantitative predictions for the luminosity function of GRBs and the ``spectral-lag luminosity relation'' are given.Comment: 7 pages, Latex, 2 eps figures, submitted to Astronomy & Astrophysics, improved clarity of exposition in section 1.2 and 2.5 of revised versio

Effectiveness of lending for vocational education and training: lessons from World Bank experience

This paper reviews the Bank involvement in the vocational education and training (VET) sub-sector in the 1990s. The paper aims to do just that, by mainly seeking answers to the following questions: 1) How has the Bank performed in its lending services to its clients in VET? 2) How have VET projects performed in terms of meeting stated objectives? 3) What factors led to the success, or failure of Bank operations? Based on what has been learned, the paper provides suggestions about how the performance of future VET interventions can be improved. This review concerns itself primarily with implementation performance, and proposes measures to improve project outcomes.ICT Policy and Strategies,Health Economics&Finance,Health Monitoring&Evaluation,Teaching and Learning,Banks&Banking Reform