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S2 Open Access 2011
Q Methodology and Its Position in the Mixed-Methods Continuum

S. Ramlo, I. Newman

In volume 32 of this journal, Paul Stenner suggests that Stephenson was resistant to Q methodology being placed within other theoretical frameworks. Yet in this same piece, Stenner states that it is time for Q methodology to be brought into a greater dialogue with contemporary social theory and research practice. This article seeks to demonstrate how Qfits into the contemporaryresearch practice ofmixed methods and argues that this perspective is not in conflict with Stephenson's positiQns on Q as a methodology. Further, our position reflects recent calls for the developmentofnew techniques and procedures to be used in mixed-methods research. Those making the call will find interest in what Q has to offer the social and behavioral sciences now, 75 years after it emerged in Stephenson's 1935 letter to Nature, and even though the term mixed-methodsresearch has only emerged in last couple of decades. Q methodology is shown to fit well methodologically into the mixed-methods continuum as described by prominent mixed-methods scholars, which further supports a position that Q represents a mixed research methodology.

136 sitasi en Sociology
S2 Open Access 1995
A q-analog of the sixth Painlevé equation

M. Jimbo, H. Sakai

A q-difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear q-difference equations, in close analogy with the monodromy-preserving deformation of linear differential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed.

246 sitasi en Physics, Mathematics
S2 Open Access 2003
The colored Jones function is q-holonomic

S. Garoufalidis, Thang T. Q. Lê

A function of several variables is called holonomic if, roughly speaking, it is determined from finitely many of its values via finitely many linear recursion relations with polynomial coefficients. Zeilberger was the first to notice that the abstract notion of holonomicity can be applied to verify, in a systematic and computerized way, combinatorial identities among special functions. Using a general state sum definition of the colored Jones function of a link in 3-space, we prove from first principles that the colored Jones function is a multisum of a q-proper-hypergeometric function, and thus it is q-holonomic. We demonstrate our results by computer calculations.

239 sitasi en Mathematics
S2 Open Access 2006
q-Euler numbers and polynomials associated with p-adic q-integrals

Taekyun Kim, S. Rim

Abstract The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on ℤp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function.

233 sitasi en Mathematics, Computer Science

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