When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?

7 pages, no figures.-- MSC2000 codes: 33C45; 42C05.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics" (Special issue dedicated to Professor Jesús Sánchez Dehesa on the occasion of his 60th birthday).Given {Pn}n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e.,Qn(x) = Pn(x) + a1Pn-1(x) + ... + akPn-k(x), ak0, n>k.Necessary and sufficient conditions are given for the orthogonality of the sequence {Qn}n≥0. An interesting interpretation in terms of the Jacobi matrices associated with {Pn}n≥0 and {Qn}n≥0 is shown.MA and MLR partially supported by Ministerio de Educación y Ciencia (MEC) of Spain under Grant MTM 2006-13000-C03-03 and Diputación General de Aragón (DGA) project E-64. FM partially supported by MEC of Spain under Grant MTM 2006-13000-C03-02 and INTAS Research Network NeCCA 03-51-6637. AP partially supported by MEC of Spain under Grants MTM 2004-03036 and MTM 2006-13000-C03-03 and DGA project E-64.Publicad

Legal Anarchism: Does Existence Need to Be Regulated by the State

This thesis asks does existence need to be regulated by the State? The answer relies on legal anarchism, an interdisciplinary, particularly criminal law and philosophy, and unconventional research project based on multiple methodologies with a specific language. It critically analyzes and consequently rejects State law because of its unjustified and unnecessary nature founded on unlimited violence and white-collar crime (Chapters 1-4), on the one hand, and suggests some alternatives to the Governmental legal system founded on agreement and peace (Chapter 5), on the other hand. It furthermore takes into account the elements of time and space, which means the ecological, local, national, regional, and international aspects of the legal system, in its analysis, critiques, and models