Frequent visitors to the website, Rotten Tomatoes, may be surprised to discover that a movie with a 15% positive rating is not necessarily better reviewed than than one which gets, say, 45% positive. This is because dichotomizing reviews as either just good or bad, period, discards lots of information. A strong consensus that a film is not great (say, mostly C-) will result in a low percentage ...

where |c/(ab)| < 1. Gauss’s name is attached to this theorem, because it is the qanalogue of Gauss’s summation for ordinary or Gaussian hypergeometric series. The theorem (1.1) was however first discovered by E. Heine [8] in 1847. We only know of two proofs of (1.1) up to recent times. The first proof, due to Heine [8], uses what we now call Heine’s transformation, and this proof can be found i...

Abstract In the theory of orthogonal polynomials, as well in its intersection with harmonic analysis, it is an important problem to decide whether a given polynomial sequence $$(P_n(x))_{n\in \mathbb {N}_0}$$ ( P n x ) <...

1. The q-disease A symptom of the q-disease|that scourge since Euler's times|is that those aaicted feel compelled to retrace steps taken long ago by their masters. For instance, when last counted 4], there were 53 proofs of the Rogers{Ramanujan identities. Other popular identities, such as the q-binomial theorem, Euler's pentagonal number theorem, Jacobi's triple product identity, and Ramanujan...

A tutorial introduction is given to q-special functions and to q-analogues of the classical orthogonal polynomials, up to the level of Askey-Wilson polynomials. 0. Introduction It is the purpose of this paper to give a tutorial introduction to q-hypergeometric functions and to orthogonal polynomials expressible in terms of such functions. An earlier version of this paper was written for an inte...

1. Introduction The South China Sea (SCS) is a semi-enclosed tropical and subtropical sea located between the Asian land mass (including Taiwan) to the west and north, the Phillipine Islands to the east and Malaysia and Borneo to the south (Figure 1), a total of 3.5×10 6 km 2 surface area. It includes the shallow Gulf of Thailand and connections to the East China Sea (through the Taiwan Strait)...

Three experiments indicate that affective cues regulate expression of implicitly measured stereotypes and attitudes. In Experiment 1, negative mood led to less stereotypic bias on the weapon-identification task [Payne, B. K. (2001). Prejudice and perception: The role of automatic and controlled processes in misperceiving a weapon. Journal of Personality and Social Psychology, 81, 181–192] than ...

Previous theoretical and empirical research on term limits has focused on the problem of accountability—that is, the possibility that term-limited politicians exert less effort than those who are eligible to run for reelection. We present a model with both accountability and selection effects, in which term limits not only cause incumbents to shirk but also interfere with voters’ ability to ree...

The U.S. Navy is a major investor in ocean model development. The pay-off of such an investment is the value-added ocean nowcast/forecast systems on naval operations and warfare effectiveness. The purpose of this paper is to investigate the value added of the Navy’s nowcast/forecast system to naval antisubmarine warfare (ASW) and anti-surface warfare (ASUW). The nowcast/forecast versus observat...