We survey recent research on mixed-integer rounding (MIR) inequalities and a generalization, namely the two-step MIR inequalities defined by Dash and Günlük (2006). We discuss the master cyclic group polyhedron of Gomory (1969) and discuss how other subadditive inequalities, similar to MIR inequalities, can be derived from this polyhedron. Recent numerical experiments have shed much light on th...

Polynomial generalizations of all 130 of the identities in Slater’s list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free do...

This study aimed to explore the influence of the therapist’s theoretical orientation on patient’s narrative production. Cathy’s therapeutic narratives with Carl Rogers, Arnold Lazarus and Everett Shostrom were analyzed in terms of three narrative dimensions: structural coherence, process complexity and content multiplicity. Results showed statistically significant differences in scores of Cathy...

Diffusion of innovations is a theory profound by Everett Rogers that seeks to explain how, why, and at what rate new ideas and technology spread. Rogers argues that diffusion is the process by which an innovation is communicated over time among the participants in a social system. For Rogers (2003), adoption is a decision of “full use of an innovation as the best course of action available” and...

In this paper we study the properties of coefficients appearing in the series expansions for zeros of generalized Rogers-Ramanujan series. Our primary purpose is to address several conjectures made by M. E. H Ismail and C. Zhang. We prove that the coefficients in the series expansion of each zero approach rational multiples of π and π as q → 1−. We also show that certain polynomials arising in ...