The semiclassical--Sobolev orthogonal polynomials: a general approach

We say that the polynomial sequence $(Q^{(\lambda)}_n)$ is a semiclassical Sobolev polynomial sequence when it is orthogonal with respect to the inner product $$_S= +\lambda <{{\bf u}}, {{\mathscr D}p \,{\mathscr D}r}>,$$ where ${\bf u}$ is a semiclassical linear functional, ${\mathscr D}$ is the differential, the difference or the $q$--difference operator, and $\lambda$ is a positive constant. In this paper we get algebraic and differential/difference properties for such polynomials as well as algebraic relations between them and the polynomial sequence orthogonal with respect to the semiclassical functional $\bf u$. The main goal of this article is to give a general approach to the study of the polynomials orthogonal with respect to the above nonstandard inner product regardless of the type of operator ${\mathscr D}$ considered. Finally, we illustrate our results by applying them to some known families of Sobolev orthogonal polynomials as well as to some new ones introduced in this paper for the first time.Comment: 23 pages, special issue dedicated to Professor Guillermo Lopez lagomasino on the occasion of his 60th birthday, accepted in Journal of Approximation Theor

On affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures

We consider two positive, normalized measures dA(x) and dB(x) related by the relationship dA(x)=(C/(x+D))dB(x) or by dA(x) = (C/(x^2+E))dB(x) and dB(x) is symmetric. We show that then the polynomial sequences {a_{n}(x)}, {b_{n}(x)} orthogonal with respect to these measures are related by the relationship a_{n}(x)=b_{n}(x)+{\kappa}_{n}b_{n-1}(x) or by a_{n}(x) = b_{n}(x) + {\lambda}_{n}b_{n-2}(x) for some sequences {{\kappa}_{n}} and {{\lambda}_{n}}. We present several examples illustrating this fact and also present some attempts for extensions and generalizations. We also give some universal identities involving polynomials {b_{n}(x)} and the sequence {{\kappa}_{n}} that have a form of Fourier series expansion of the Radon--Nikodym derivative of one measure with respect to the other

News Briefs: Congressional Review of EEO Reorganization Plan, 1979

Report on Presldent Carter\u27s proposed federal Equal Employment Opportunity Commission reorganization plan to consolidate most of the government\u27s enforcement programs into EEOC over the years 1978-1980. April 26, 1978. No 17

Removal of recalcitrant organic compounds from an industrial complex effluent by heterogeneous Fenton-type treatment

Because of their chemical complexity, industrial chemi-mechanical pulping effluents are evaporated and burned, in spite of the high associated cost involved in these processes. The aim of this study was to remove recalcitrant compounds from this kind of wastewater using a Fenton-type treatment. The main parameters involved in the process and their influence on the results were determined. Homemade catalysts based on CuO, Fe2O3, NiO and ZnO, supported on γ-Al2O3 have been tested for catalytic oxidation, and the CuO/γ- Al2O3 catalysts showed the greatest effect on total organic carbon (TOC) reduction (52.7%). A series of twolevel factorial experiments was subsequently applied to evaluate the most favorable range of conditions for CuO/γ-Al2O3 application. The studied variables were hydrogen peroxide concentration ([H2O2], g/L), active phase content (metal oxide supported on alumina, %), mass of catalyst (metal oxide/alumina system, g), and reaction temperature (°C). The highest reduction of all parameters was obtained at the superior level of all variables with CuO/γ-Al2O3, achieving reductions of chemical oxygen demand (COD) and TOC between 40 and 50%. Increasing catalyst mass did not produce additional benefit. This variable has a significant effect only on the reduction of aromatic compounds. At its low level, reduction in aromatic content exceeded 80%. Color reduction was influenced only by temperature (maximum reduction of 90%)Fil: Covinich, Laura Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Materiales de Misiones. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Instituto de Materiales de Misiones; ArgentinaFil: Felissia, Fernando Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Materiales de Misiones. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Instituto de Materiales de Misiones; ArgentinaFil: Fenoglio, Rosa Juana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; ArgentinaFil: Area, Maria Cristina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Materiales de Misiones. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Instituto de Materiales de Misiones; Argentin

BLS Report On Labor Union And Employee Association Membership, 1973

Report about white collar employees belonging to unions and employee associations for the period 1976-1978. October 3, 1979