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

Bid Optimization in Broad-Match Ad auctions

Ad auctions in sponsored search support ``broad match'' that allows an advertiser to target a large number of queries while bidding only on a limited number. While giving more expressiveness to advertisers, this feature makes it challenging to optimize bids to maximize their returns: choosing to bid on a query as a broad match because it provides high profit results in one bidding for related queries which may yield low or even negative profits. We abstract and study the complexity of the {\em bid optimization problem} which is to determine an advertiser's bids on a subset of keywords (possibly using broad match) so that her profit is maximized. In the query language model when the advertiser is allowed to bid on all queries as broad match, we present an linear programming (LP)-based polynomial-time algorithm that gets the optimal profit. In the model in which an advertiser can only bid on keywords, ie., a subset of keywords as an exact or broad match, we show that this problem is not approximable within any reasonable approximation factor unless P=NP. To deal with this hardness result, we present a constant-factor approximation when the optimal profit significantly exceeds the cost. This algorithm is based on rounding a natural LP formulation of the problem. Finally, we study a budgeted variant of the problem, and show that in the query language model, one can find two budget constrained ad campaigns in polynomial time that implement the optimal bidding strategy. Our results are the first to address bid optimization under the broad match feature which is common in ad auctions.Comment: World Wide Web Conference (WWW09), 10 pages, 2 figure