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

Signed degree sets in signed graphs

The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph

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

Origin of the ultrahigh-energy cosmic rays and their spectral break

The energy spectrum, composition and arrival directions of ultrahigh energy cosmic rays (UHECRs) with energy above the cosmic ray ankle, measured by the Pierre Auger Observatory, appear to be in conflict if their origin is assumed to be extragalactic. Their spectrum and composition, however, are those expected from Galactic UHECRs accelerated by highly relativistic jets such as those producing short hard gamma ray bursts (SHBs). If this alternative interpretation is correct, then the observed break in the energy spectrum of UHECRs around 50 EeV is the energy threshold for free escape of UHE iron nuclei from the Galaxy and not the Greisen-Zatsepin-Kuzmin (GZK) cutoff for protons, and the arrival directions of UHECR nuclei with energy above their UHE breaks must point back to their Galactic sources rather than to active galactic nuclei (AGN) within the GZK horizon