Extensions of discrete classical orthogonal polynomials beyond the orthogonality

It is well known that the family of Hahn polynomials $\{h_n^{\alpha,\beta}(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $\Delta$-Sobolev orthogonality. We also present an analogous result for dual-Hahn, Krawtchouk, and Racah polynomials and give the limit relations between them for all n\in \XX N_0. Furthermore, in order to get this results for the Krawtchouk polynomials we will get a more general property of orthogonality for Meixner polynomials.Comment: 2 figures, 20 page

A Survey on q-Polynomials and their Orthogonality Properties

In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson polynomials (AW)) for almost any complex value of the parameters and for all non-negative integers degrees. We state the degenerate version of Favard's theorem, which is one of the keys of the paper, that allow us to extend the orthogonality properties valid up to some integer degree N to Sobolev type orthogonality properties. We also present, following an analogous process that applied in [16], tables with the factorization and the discrete Sobolev-type orthogonality property for those families which satisfy a finite orthogonality property, i.e. it consists in sum of finite number of masspoints, such as q-Racah (qR), q-Hahn (qH), dual q-Hahn (dqH), and q-Krawtchouk polynomials (qK), among others. -- [16] R. S. Costas-Santos and J. F. Sanchez-Lara. Extensions of discrete classical orthogonal polynomials beyond the orthogonality. J. Comp. Appl. Math., 225(2) (2009), 440-451Comment: 3 Figures, 3 tables, in a 22 pages manuscrip

Do primordial Lithium abundances imply there's no Dark Energy?

Explaining the well established observation that the expansion rate of the universe is apparently accelerating is one of the defining scientific problems of our age. Within the standard model of cosmology, the repulsive 'dark energy' supposedly responsible has no explanation at a fundamental level, despite many varied attempts. A further important dilemma in the standard model is the Lithium problem, which is the substantial mismatch between the theoretical prediction for 7-Li from Big Bang Nucleosynthesis and the value that we observe today. This observation is one of the very few we have from along our past worldline as opposed to our past lightcone. By releasing the untested assumption that the universe is homogeneous on very large scales, both apparent acceleration and the Lithium problem can be easily accounted for as different aspects of cosmic inhomogeneity, without causing problems for other cosmological phenomena such as the cosmic microwave background. We illustrate this in the context of a void model.Comment: 14 pages, 4 figures. v2: minor rearrangements in the text, comments and references expanded, results unchange

Reconsidering the roots, structure, and implications of gambling motives: An integrative approach.

Accurately identifying motives to gamble is crucial in the functional analysis of gambling behavior. In this study, a data-driven approach was followed to clarify the factor structure underlying a pool of motives for gambling, selected from the Gambling Motives Questionnaire-Financial (GMQ-F), and the Reasons for Gambling Questionnaire (RGQ), in a sample of regular problem and non-problem gamblers. Additionally, the role of gambling motives in the relationship between root behavioral activation/inhibition systems (BIS/BAS) and gambling severity, frequency, and preferences was explored using structural equation modelling (SEM). The present study identified Social, Financial, and Fun/thrill-related gambling motives factors, but also a fourth factor in which some positive and negative reinforcement-based motives were grouped into a single and broader Affect regulation factor. This Affect regulation factor shared variance both with BIS and BAS-related measures, and was the only direct predictor of disordered gambling symptoms. The Fun/thrill factor was directly related to frequency of participation in high-arousal, skill-based games, and all factors were related to participation in lower-arousal, chance games (with Social motives negatively predicting both participation in the latter and total severity). In the SEM model, measures of BIS/BAS sensitivity were connected to gambling behavior only through gambling motives. Based on measures of items' specificity, a shortened Spanish scale (the brief Gambling Motives Inventory, bGMI) is proposed to assess gambling motives in accordance with the observed 4-factor structure

Clauser-Horne inequality for electron counting statistics in multiterminal mesoscopic conductors

In this paper we derive the Clauser-Horne (CH) inequality for the full electron counting statistics in a mesoscopic multiterminal conductor and we discuss its properties. We first consider the idealized situation in which a flux of entangled electrons is generated by an entangler. Given a certain average number of incoming entangled electrons, the CH inequality can be evaluated for different numbers of transmitted particles. Strong violations occur when the number of transmitted charges on the two terminals is the same ($Q_1=Q_2$), whereas no violation is found for $Q_1\ne Q_2$. We then consider two actual setups that can be realized experimentally. The first one consists of a three terminal normal beam splitter and the second one of a hybrid superconducting structure. Interestingly, we find that the CH inequality is violated for the three terminal normal device. The maximum violation scales as 1/M and $1/M^2$ for the entangler and normal beam splitter, respectively, 2$M$ being the average number of injected electrons. As expected, we find full violation of the CH inequality in the case of the superconducting system.Comment: 26 pages, 9 figures. Ref. adde

Plantas daninhas na pós-colheita de milho nas várzeas do rio São Francisco, em Minas Gerais.

Realizou-se um estudo na região do Alto São Francisco, Minas Gerais, no final da safra agrícola 1997/1998, visando identificar as plantas daninhas que permanecem nas áreas após a colheita do milho e sua distribuição ao longo da área estudada, destacando-se as mais importantes. As observações foram realizadas em 12 municípios. Em cada local foi lançado, por cem vezes, um quadrado de 0,50 x 0,50 m, a espaços de 10 m. Dentro do quadrado foram contadas as espécies e registrado o número de indivíduos de cada uma delas. Foram encontradas 151 espécies em 35 famílias, sendo Asteraceae a mais bem representada, com 25 espécies. As espécies com maior Índice de Valor de mportância (IVI) foram: Ageratum conyzoides, Sida glaziovii, Conyza bonariensis, Gaya sp., Sida rhombifolia e Blainvillea biaristata. As plantas daninhas remanescentes nas áreas recém-colhidas são fonte de alimento para insetos polinizadores e inimigos naturais das pragas; adequadamente manejadas, elas podem favorecer a manutenção do equilíbrio nos agroecossistemas

1873-1874, End of a Century?: Time and Space in Valera's Pepita Jiménez, Ros de Olano's Jornadas de retorno, and Alarcón's El sombrero de tres picos and La Alpujarra

This article argues for the existence of a literature of the first Spanish Republic in the early 1870s. Valera's Pepita Jimenez makes sense in relation to this literature, rather than in comparison with 'Realism'. The literature of the first republic is distinguished by two facets: an ongoing dialogue with Ros de Olano's experiments in simultaneous compression and extension of form; and a belief that the nineteenth-century revolutionary spirit of the age has reached a critical end point, and needs reinvention that leads to Restoration politics

Bortezomib maintenance after R-CHOP, cytarabine and autologous stem cell transplantation in newly diagnosed patients with mantle cell lymphoma, results of a randomised phase II HOVON trial

Rituximab-containing induction followed by autologous stem cell transplantation (ASCT) is the standard first-line treatment for young mantle cell lymphoma patients. However, most patients relapse after ASCT. We investigated in a randomised phase II study the outcome of a chemo-immuno regimen and ASCT with or without maintenance therapy with bortezomib. Induction consisted of three cycles R-CHOP (rituximab, cyclophosphamide, doxorubicin, vincristine, prednisone), two cycles high-dose cytarabine, BEAM (carmustine, etoposide, cytarabine, melphalan) and ASCT. Patients responding were randomised between bortezomib maintenance (1·3 mg/m2 intravenously once every 2 weeks, for 2 years) and observation. Of 135 eligible patients, 115 (85%) proceeded to ASCT, 60 (44%) were randomised. With a median follow-up of 77·5 months for patients still alive, 5-year event-free survival (EFS) was 51% (95% CI 42–59%); 5-year overall survival (OS) was 73% (95% CI 65–80%). The median follow-up of randomised patients still alive was 71·5 months. Patients with bortezomib maintenance had a 5-year EFS of 63% (95% CI 44–78%) and 5-year OS of 90% (95% CI 72–97%). The patients randomised to observation had 5-year PFS of 60% (95% CI, 40–75%) and OS of 90% (95% CI 72–97%). In conclusion, in this phase II study we found no indication of a positive effect of bortezomib maintenance after ASCT

Centrality dependence of charged particle production at large transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm{NN}}} = 2.76 TeV

The inclusive transverse momentum ($p_{\rm T}$) distributions of primary charged particles are measured in the pseudo-rapidity range $|\eta|<0.8$ as a function of event centrality in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV with ALICE at the LHC. The data are presented in the $p_{\rm T}$ range $0.15<p_{\rm T}<50$ GeV/$c$ for nine centrality intervals from 70-80% to 0-5%. The Pb-Pb spectra are presented in terms of the nuclear modification factor $R_{\rm{AA}}$ using a pp reference spectrum measured at the same collision energy. We observe that the suppression of high-$p_{\rm T}$ particles strongly depends on event centrality. In central collisions (0-5%) the yield is most suppressed with $R_{\rm{AA}}\approx0.13$ at $p_{\rm T}=6$-7 GeV/$c$. Above $p_{\rm T}=7$ GeV/$c$, there is a significant rise in the nuclear modification factor, which reaches $R_{\rm{AA}} \approx0.4$ for $p_{\rm T}>30$ GeV/$c$. In peripheral collisions (70-80%), the suppression is weaker with $R_{\rm{AA}} \approx 0.7$ almost independently of $p_{\rm T}$. The measured nuclear modification factors are compared to other measurements and model calculations.Comment: 17 pages, 4 captioned figures, 2 tables, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/284