Bivariate second--order linear partial differential equations and orthogonal polynomial solutions

In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially self--adjoint and of hypergeometric type. General formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation, using vector matrix notation. Moreover, Rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given. Finally, as illustration, these results are applied to specific Appell and Koornwinder orthogonal polynomials, solutions of the same partial differential equation.Comment: 27 page

Linear partial divided-difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices

In this paper, a fourth-order partial divided-difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this equation we obtain explicitly the matrix coefficients appearing in the three-term recurrence relations satisfied by any bivariate orthogonal polynomial solution of the equation. In particular, we provide explicit expressions for the matrices in the three-term recurrence relations satisfied by the bivariate Racah polynomials introduced by Tratnik. Moreover, we present the family of monic bivariate Racah polynomials defined from the three-term recurrence relations they satisfy, and we solve the connection problem between two different families of bivariate Racah polynomials. These results are then applied to other families of bivariate orthogonal polynomials, namely the bivariate Wilson, continuous dual Hahn and continuous Hahn, the latter two through limiting processes. The fourth-order partial divided-difference equations on quadratic lattices are shown to be of hypergeometric type in the sense that the divided-difference derivatives of solutions are themselves solution of the same type of divided-difference equations.Comment: 36 page

On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions

AbstractIn this paper we classify the bivariate second-order linear partial difference equations, which are admissible, potentially self-adjoint, and of hypergeometric type. Using vector matrix notation, explicit expressions for the coefficients of the three-term recurrence relations satisfied by monic orthogonal polynomial solutions are obtained in terms of the coefficients of the partial difference equation. Finally, we make a compilation of the examples existing in the literature belonging to the class analyzed in this paper, namely bivariate Charlier, Meixner, Kravchuk and Hahn orthogonal polynomials

A Case Study of the Suquamish Tribe\u27s Benefits Package

This case study describes the Suquamish Tribe\u27s Contract Health Services (CHS) alternative delivery demonstration project. Services under this project are provided through an administrative services contract with a local third party insurance administrator. Under the terms of this agreement, Suquamish tribal members residing in Kitsap County, Washington receive a predetermined package of health care services. The Tribe administers the plan by engaging the services of an administrator who defines and coordinates benefits, adjudicates claims, and pays vendors for services provided. The Suquamish Tribe\u27s Health Benefit Package was initially an alternative demonstration project. This study provides a delivery and cost analysis of the health package. A point by point comparison is made between the Tribe\u27s program and IHS\u27 Contract Health Service. The continuation of the program was based on the study. Each component of the program including the Suquamish Tribe, health provider, consumer insurance agency, and IHS was included in the study.The large portion of the paper is narrative. That narrative, however, is based on the compilation of comparative graphs, cost analysis data, and statistical information provided by the Suquamish Tribe, the insurance provider, IHS, and tribal members. A plan description and process of application for the user as well as payment forms are included. Administration of the program is discussed at length, included in this section are utilization and cost analysis statistics. Interviews with clients and health providers were an important part of the evaluation. Population description, background and history of both Tribe and program are included in the narrative. The Suquamish Tribe\u27s benefits package is a cost-effective alternative to contract health services. Through this system the Tribe has achieved greater local control over services resulting in a higher use of alternate resources, faster payment of bills, and improved patient knowledge of the system. The program has proven a health benefits package is a viable alternative to Contract Health Services. Many problems that exist with CHS have been resolved including priorities for care, slow payment of bills, and lack of local control. Patient satisfaction with the project is best illustrated by the results of a survey conducted in 1986. The most significant findings were: 1) 96% felt the benefits package was an improvement over CHS; 2) 97% felt their family had received at least adequate health care over the past twelve months; 3) 93% were satisfied with the quality of care provided; and 4) 94% felt that the provider they used had convenient hours that met their needs. In terms of cost-effectiveness, there are several conclusions to be drawn: 1) the plan has significantly lowered hospital costs through better coordination of alternate resources, use of outpatient surgeries, and second opinions; 2) use of outpatient and inpatient services among tribal members is equal to, or greater than, other Indians and the general population, thus, it appears patients are getting the care needed; and 3) administrative costs of the program are higher than CHS administrative costs of IHS but per capita expenditures for services are comparable or equal to that of other tribes in the Portland Area. The Suquamish project exists in an atypical environment where tribal members have access to a multitude of service providers unlike other rural areas in which most tribes live. The Tribe\u27s relationship with the medical and general community has been a positive one. In addition, the Tribe is small enough to allow for very individualized services and is geographically situated so that care is limited to a small number of accessible providers. The success of this program, therefore, cannot imply carry-over value to other reservations.There are no actual recommendations made but there is a conclusive statement made for the benefit of those considering the adoption of similar efforts on other reservations. Whether or not a benefits package can be replicated in other parts of the country cannot be completely answered through the experience of the Suquamish Tribe. The success or failure of using benefits packages as a viable alternative to CHS rests with the IHS and the Federal Government. For such programs to be successful, the following issues need to be addressed and resolved: 1) system for monitoring services and controlling utilization and costs needs to be in place; 2) means of identifying and using all available alternate resources needs to be developed; 3) adequate and ongoing funding support for such programs needs to exist; and 4) initiation of risk sharing arrangements with Insurers and providers must be a goal

Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case

AbstractWe present a simple approach in order to compute recursively the connection coefficients between two families of classical (discrete) orthogonal polynomials (Charlier, Meixner, Kravchuk, Hahn), i.e., the coefficients Cm(n) in the expression Pn(X)=∑nm=0Cm(n)Qm(x), where Pn(x) and Qm(x) belong to the aforementioned class of polynomials. This is SCV2 done by adapting a general and systematic algorithm, recently developed by the authors, to the discrete classical situation. Moreover, extensions of this method allow to give new addition formulae and to estimate Cm(n)-asymptotics in limit relations between some families

Connection problems for polynomial solutions of nonhomogeneous differential and difference equations

AbstractWe consider nonhomogeneous hypergeometric-type differential, difference and q-difference equations whose nonhomogeneity is a polynomial qn(x). The polynomial solution of these problems is expanded in the ∗ Qn(x)∗ basis, and also in a basis ∗Pn(x)∗, related in a natural way with the homogeneous hypergeometric equation. We give an algorithm building a recurrence relation for the expansion coefficients in both bases that we solve explicitly in many cases involving classical orthogonal polynomials. Finally, some concrete applications and extensions are given

Office paper recyclability: fibrous characteristics

Recyclability is the ability of a material to reacquire the same properties it had originally. The aim of this work was to verify the recyclability of three printing and writing papers, from the characteristics of their fibers after two recycles. Three ECF bleached kraft eucalyptus commercial bond papers from Argentina and Brazil were studied (A, B, C). The papers were repulped and refined using different levels and intensities of energy (1st recycle). Laboratory sheets were produced, and they were repulped and refined again (2nd recycle). The microscopic characteristics of repulped papers were obtained by automatic equipment based on image analysis. Differences found in the behavior of the different samples can be explained by fiber parameters. The fiber length was significantly different in the three papers (A > B > C) and globally decreased in the second recycle (about 6%). Sample A had the highest initial fiber length and length/width, but it largely decreased with refining conditions in the 1st recycle (length fall 12%, generating fines by cutting), whereas it fall 9% between the 1st and 2nd recycles, and nothing with refining conditions in the 2nd recycle. Sample B fall by 5% with refining conditions in the 1st recycle, and 9% between the 1st and the 2nd recycle, but suffered few alteration in the second recycle. Fiber length of sample C was unaffected by refining conditions and only decreased 9% between the 1st and 2nd recycles. In all cases, the generated fines increased lightly with refining in the first recycle, but were two-fold higher in the second recycle than in the first one. The fiber coarseness of the 3 samples was similar in the first recycle, but decreases significantly in the 2nd recycleFil: Benitez, Julieta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Materiales de Misiones. Universidad Nacional de Misiones. Facultad de Cs.exactas Químicas y Naturales. Instituto de Materiales de Misiones; ArgentinaFil: Koga, Mariza E. T.. Instituto de Pesquisas Tecnologicas de Sao Paulo; BrasilFil: Otero D'Almeida, Maria L.. Instituto de Pesquisas Tecnologicas de Sao Paulo; BrasilFil: 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 Cs.exactas Químicas y Naturales. Instituto de Materiales de Misiones; ArgentinaFil: Park, Song W.. Universidade de Sao Paulo; BrasilFil: 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 Cs.exactas Químicas y Naturales. Instituto de Materiales de Misiones; Argentin

Office paper recyclability: first recycling

Paper recyclability implies in the paper capacity to be recycled maintaining its properties to the maximum. Four commercial papers from Argentina and Brazil were studied, including three eucalyptus kraft (A, B, C) and one sugar cane bagasse soda-AQ (D), all with different bleaching processes. Their physical and chemical properties and a first laboratory recycling were evaluated. A refining of the pulp with a PFI mill, applying two energy levels at two different intensities - measured by number of revolutions and load - was accomplished to reach the same °SR (between 30 and 40, approximately). The refining energy and the yield were registered in each case. The properties of laboratory handsheets, and the aging to 24, 48, 72 and 144 hours were evaluated. The statistical analysis of the results indicates that the properties of the initial eucalyptus papers were similar, whereas they were generally inferior in the case of the bagasse paper. The bagasse and eucalyptus papers presented similar initial whiteness, but the first one had a higher reversion than the others. Once repulped, the eucalyptus papers A, B and C required, respectively, 4, 7 and 10 times greater energy than D, to obtain the same °SR. In all cases, the required energy to achieve the same °SR is slightly greater with the smaller refining intensity. The physical properties of the handsheets from the first recycle of paper D were, in general, lower. Among eucalyptus papers, B showed a slightly higher resistance and C, a slightly lower one. The mechanical properties of pulp sheets A, and D to a lesser extension, were more affected by the refining intensity than the rest, indicating a higher sensitivity of the fibers. The whiteness of the sheets of pulp B is lower than the rest. Opacity and light scattering coefficient of the sheets of pulp C were much higher than those of the other pulps.Fil: Benitez, Julieta Beatriz. Universidad Nacional de Misiones; ArgentinaFil: Koga, Mariza E. T.. Instituto de Pesquisas Tecnológicas de São Paulo (ipt); BrasilFil: Otero D'Almeida, Maria L.. Instituto de Pesquisas Tecnológicas de São Paulo (ipt); BrasilFil: Felissia, Fernando Esteban. Universidad Nacional de Misiones; ArgentinaFil: Park, Song W.. Escola Politecnica, Universidad de Sao Paulo (usp); BrasilFil: Area, Maria Cristina. Universidad Nacional de Misiones; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Three term relations for multivariate Uvarov orthogonal polynomials

Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by a Uvarov modification of a given moment functional are studied. Existence of Uvarov orthogonal polynomials is analyzed, stating conditions to ensure it. The matrices of the three term relations of the Uvarov orthogonal polynomials are explicitly given in terms of the matrices of the three term relations satisfied by the original family. Two examples are presented in order to show that the results are valid for positive definite linear functionals and also for some quasi definite linear functionals which are not positive definite.Agencia Estatal de Investigación | Ref. PID2020-113275GB-I00IMAG-María de Maeztu | Ref. CEX2020-001105-MAgencia Estatal de Investigación | Ref. PGC2018-094932-B-I00Junta de Andalucía | Ref. A-FQM-246-UGR20Universidade de Vigo/CISU

Chemimechanical Pulping of Eucalyptus Grandis

Eucayptus is currently one of the main fibrous raw materials used in the pulp and paper industry in given parts of the world. The objective of the present paper is to optimize the chemimechanical pulping conditions for Eucalyptus grandis. evaluate the pulp quality obtained, and draw conclusions regarding its potential use. The raw material used was Eucalyptus grandis industrial chips obtained at a Celulosa Argentina mill in Puerto Piray, Misiones, Argentina. For all the experiments, the chemical stage was carried out in a stainless steel digester with a liquor recirculation system. The mechanical stage was carried out in an 8-in. atmospheric disk refiner. Sodium sulfite and sodium hydroxide were added as chemical reactives. The central composite experimental design used involved five levels for the two variables studied (LL factorial design + star + central point). Three repetitions of the central point were carried out to check for errors. The variables studied were: initial amount of sodium sulfite in the wood (0.9 to 3.5% oven-dry wood) and reaction temperature (96 to 124 C). Times until maximum temperature and time at maximum temperature were, respectively, 20 and 90 minutes. A constant level of sodium hydroxide was maintained in all the experiments (1.5% oven-dry wood). Pulp evaluation was carried out using the usual characterization techniques. Chemical and physical evaluations, including optical testing, were, for the most part, done in accordance with TAPPI procedures.The results obtained indicate that the central point of the design used in our research (110 C and 2.5% oven-dry wood sulfite), appears to represent the optimal conditions for the variables studied for the chemimechanical pulping of Eucalyptus grandis. The pulps obtained could be used as furnish in printing and writing paper grades. The positive correlation between sulfonate concentration and water retention value (WRV) suggests that by increasing fiber wall swelling, the number of sites accessible to sulfonation is increased. The tensile index correlates positively with the degree of sulfonation and with the water retention value of the pulps. It decreases according to the fraction retained in a 30-mesh screen (due to the presence of numerous shives) and increases according to the fraction of fines passing through a 270-mesh screen