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

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

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

The endogenous caspase-8 inhibitor c-FLIPL regulates ER morphology and crosstalk with mitochondria

Components of the death receptors-mediated pathways like caspase-8 have been identified in complexes at intracellular membranes to spatially restrict the processing of local targets. In this study, we report that the long isoform of the cellular FLICE-inhibitory protein (c-FLIPL), a well- known inhibitor of the extrinsic cell death initiator caspase-8, localizes at the endoplasmic reticulum (ER) and mitochondria-associated membranes (MAMs). ER morphology was disrupted and ER Ca2+-release as well as ER-mitochondria tethering were decreased in c-FLIP-/- mouse embryonic fibroblasts (MEFs). Mechanistically, c-FLIP ablation resulted in enhanced basal caspase-8 activation and in caspase-mediated processing of the ER-shaping protein reticulon-4 (RTN4) that was corrected by re-introduction of c-FLIPL and caspase inhibition, resulting in the recovery of a normal ER morphology and ER-mitochondria juxtaposition. Thus, the caspase-8 inhibitor c-FLIPL emerges as a component of the MAMs signaling platforms, where caspases appear to regulate ER morphology and ER-mitochondria crosstalk by impinging on ER-shaping proteins like the RTN4

Inequalities in higher education in low‐ and middle‐income countries:A scoping review of the literature

Motivation:  Higher  education  is  regarded  as  a  key  instrument  to  enhance  socioeconomic  mobility  andreduce inequalities. Recent literature reviews have examined inequalities in the higher education systemsof  high-income  countries,  but  less  is  known  about  the  situation  in  low-  and  middle-income  countries,where higher education is expanding fast.Purpose:  The  article  reviews  the  academic  literature  on  higher  education  in  low-  and  middle-incomecountries using a research framework inspired by social justice and capability approaches. It considers the financial,  socio-cultural,  human,  and  political  resource  domains  on  which  people  draw,  and  how  they relate to access, participation, and outcomes in higher education.Methods: A literature search for studies explicitly discussing in-country  inequalities  in  higher  education revealed  22  publications. Substantial  knowledge  gaps remain,  especially  regarding  the  political  (and decision-making)  side  of  inequalities;  the  ideologies  and  philosophies  underpinning  higher  education systems; and the linkages between resource domains, both micro and macro.Findings:  The  review  highlights  key  elements  for  policy-makers  and  researchers:  (1)  the  financial  lens alone  is  insufficient  to  understand  and  tackle  inequalities,  since  these  are  also  shaped  by  human  and other non-financial factors; (2) socio-cultural constructs are central in explaining unequal outcomes; and (3) inequalities develop throughout one’s life and need to be considered during, but also before and afterhigher education.  The scope  of  inequalities  is  wide, and  the literature  offers a  few ideas  for short-term fixes such as part-time and online education.Policy implications: Inclusive policy frameworks for higher education should include explicit goals related to (in)equality,  which  are  best  measured in  terms  of  the  extent  to  which  certain  actions  or  choices are feasible for all. Policies in these frameworks, we argue, should go beyond providing financial support, and also address socio-cultural and human resource constraints and challenges in retention, performance, and labour market outcomes. Finally, they should consider relevant contextual determinants of inequalities.</p

The Asian 'Noodle Bowl': Is it Serious for Business

A lively debate is taking place over the impact of free trade agreements (FTAs) on East Asia's business between those who view the agreements as a harmful Asian noodle bowl - i.e., overlapping regional trade agreements - of trade deals and others who see net beneficial effects in terms of regional liberalization and a building block to multilateral liberalization. A lack of enterprise-level data has made it difficult to resolve the debate. Providing new evidence from surveys of 609 East Asian firms (in Japan, Singapore, Republic of Korea [hereafter Korea], Thailand, and Philippines), this paper seeks to address the critical question of whether the Asian noodle bowl of multiple overlapping FTAs is harmful to business activity, particularly for small- and medium-sized enterprises (SMEs). The surveys suggest that the Asian noodle bowl does not seem to have severely harmed the region's business activity to date. Use of FTA preferences is higher than expected from previous studies (22% of responding firms). Furthermore, only 27% of responding firms said that multiple rules of origin significantly added to business cost. However, as more currently under negotiation FTAs take effect and the complexity of the Asian noodle bowl increases, the business impact is likely to intensify. Implementation of key policies and closer publicprivate sector cooperation can help mitigate negative effects and facilitate a more SMEinclusive business response to FTAs. Suggestions include: encouraging most favored nation (MFN) liberalization, rationalization of rules of origin, upgrading origin administration, increased awareness of FTA provisions, improving business participation in FTA consultations, and SME support

Mutational Analyses of the Influenza A Virus Polymerase Subunit PA Reveal Distinct Functions Related and Unrelated to RNA Polymerase Activity

Influenza A viral polymerase is a heterotrimeric complex that consists of PA, PB1, and PB2 subunits. We previously reported that a di-codon substitution mutation (G507A-R508A), denoted J10, in the C-terminal half of PA had no apparent effect on viral RNA synthesis but prevented infectious virus production, indicating that PA may have a novel role independent of its polymerase activity. To further examine the roles of PA in the viral life cycle, we have now generated and characterized additional mutations in regions flanking the J10 site from residues 497 to 518. All tested di-codon mutations completely abolished or significantly reduced viral infectivity, but they did so through disparate mechanisms. Several showed effects resembling those of J10, in that the mutant polymerase supported normal levels of viral RNA synthesis but nonetheless failed to generate infectious viral particles. Others eliminated polymerase activity, in most cases by perturbing the normal nuclear localization of PA protein in cells. We also engineered single-codon mutations that were predicted to pack near the J10 site in the crystal structure of PA, and found that altering residues K378 or D478 each produced a J10-like phenotype. In further studies of J10 itself, we found that this mutation does not affect the formation and release of virion-like particles per se, but instead impairs the ability of those particles to incorporate each of the eight essential RNA segments (vRNAs) that make up the viral genome. Taken together, our analysis identifies mutations in the C-terminal region of PA that differentially affect at least three distinct activities: protein nuclear localization, viral RNA synthesis, and a trans-acting function that is required for efficient packaging of all eight vRNAs