We are interested in counting integer and rational points in affine algebraic varieties, also under congruence conditions. We introduce the notions of a strongly Hardy-Littlewood variety and a relatively Hardy-Littlewood variety, in terms of counting rational points satisfying congruence conditions. The definition of a strongly Hardy-Littlewood variety is given in such a way that varieties for ...

The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that ...

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...

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...

This article reviews the impact of Carl Rogers' postulate about the necessary and sufficient conditions of therapeutic change on the field of psychotherapy. It is proposed that his article (see record 2007-14630-002) made an impact in two ways; first, by acting as a spur to researchers to identify the active ingredients of therapeutic change; and, second, by providing guidelines for therapeutic...

If a continued fraction K∞ n=1an/bn is known to converge but its limit is not easy to determine, it may be easier to use an extension of K∞ n=1an/bn to find the limit. By an extension of K ∞ n=1an/bn we mean a continued fraction K∞ n=1cn/dn whose odd or even part is K ∞ n=1an/bn. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii...