Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for ŝl(2) satisfy certain classical recursion formulas of Rogers and Selberg. These recursions were exploited by Andrews in connection with Gordon’s generalization of the Rogers–Ramanujan identities and with Andrews’ related ide...

Effective counselors employ an array of skills. Carl Rogers (1975) believed that the counselor’s ability to be congruent, accepting, and empathic is necessary for clients to be able to change, and these skills are routinely taught in counselor education. Later in his life, Rogers also articulated the need for a quality of presence that is an essential aspect of client-centered therapy. In an in...

A systematic approach is adopted to review the literature, followed by a meta-analysis of articles on Rogers’ innovationattributes. All publications from 1996-2011 are extracted; 226 relevant innovation articles are studied to showcase the informative trends pertaining to Rogers’ five attributes eight features of ideal innovation-attribute study (approach, dependent variable, study type, instru...

Euler's identity and the Rogers-Ramanujan identities are perhaps most famous results in theory of partitions. According to them, 1-distinct 2-distinct partitions n equinumerous with into parts congruent ±1 modulo 4 5, respectively. Furthermore, their generating functions modular up multiplication by rational powers q. For d ≥ 3, however, there is neither same type partition nor modularity for d...

A new crossing symmetric unitarization scheme conveniently applied to meson-meson and meson-baryon scattering amplitudes is shortly proposed which can be not only used by theoreticians to unitarize arbitrary theoretical reaction amplitudes resulting from phenomenological Lagrangeans for mesons and baryons, yet also by experimentalists to generate realistic unitary fitting formulae for meson-mes...

We contrast e¤ects of taxing non-renewable resources with the e¤ects of traditional capital taxes and investment subsidies in an endogenous growth model. In a simple framework we demonstrate that when non-renewable resources are a necessary input in the sector where growth is ultimately generated, interest income taxes and investment subsidies can no longer a¤ect the long-run growth rate, where...

Address: 1Universitätsklinik Tübingen, Kinderklinik I, Hoppe-Seyler-Straße 1, Tübingen, Germany, 2Medizinische Klinik 5, Im Neuenheimer Feld 410, Heidelberg, Germany, 3Univ.-Klinikum Carl-Gustav-Carus, Kinderklinik, Fetscherstraße 74, Dresden, Germany, 4Servicio de Pediatria, Hospital Central de Asturias, C/Julian Claveria, s/n, Oviedo, Spain and 5Novartis Pharma AG, Basel, Switzerland * Corres...