Zero sets of bivariate Hermite polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

∗ Research partially supported by INTAS grant 97-1644

Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function

AMS Subject Classification 2010: 11M26, 33C45, 42A38.

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Connection coefficients and zeros of orthogonal polynomials

We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Monotonicity of zeros of Laguerre polynomials

Denote by X(nk)(alpha), k = 1, ..., n, the zeros of the Laguerre polynomial L(n)((alpha))(X). We establish monotonicity with respect to the parameter at of certain functions involving X(nk)(alpha). As a consequence we obtain sharp upper bounds for the largest zero of L(n)((alpha))(X). (C) 2009 Elsevier B.V. All rights reserved.

Distances between critical points and midpoints of zeros of hyperbolic polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Increased Levels of NOTCH1, NF-kappa B, and Other Interconnected Transcription Factors Characterize Primitive Sets of Hematopoietic Stem Cells

As previously shown, higher levels of NOTCH1 and increased NF-kappa B signaling is a distinctive feature of the more primitive umbilical cord blood (UCB) CD34+ hematopoietic stem cells (HSCs), as compared to bone marrow ( BM). Differences between BM and UCB cell composition also account for this finding. The CD133 marker defines a more primitive cell subset among CD34+ HSC with a proposed hemangioblast potential. To further evaluate the molecular basis related to the more primitive characteristics of UCB and CD133+ HSC, immunomagnetically purified human CD34+ and CD133+ cells from BM and UCB were used on gene expression microarrays studies. UCB CD34+ cells contained a significantly higher proportion of CD133+ cells than BM (70% and 40%, respectively). Cluster analysis showed that BM CD133+ cells grouped with the UCB cells ( CD133+ and CD34+) rather than to BM CD34+ cells. Compared with CD34+ cells, CD133+ had a higher expression of many transcription factors (TFs). Promoter analysis on all these TF genes revealed a significantly higher frequency ( than expected by chance) of NF-kappa B-binding sites (BS), including potentially novel NF-kappa B targets such as RUNX1, GATA3, and USF1. Selected transcripts of TF related to primitive hematopoiesis and self-renewal, such as RUNX1, GATA3, USF1, TAL1, HOXA9, HOXB4, NOTCH1, RELB, and NFKB2 were evaluated by real-time PCR and were all significantly positively correlated. Taken together, our data indicate the existence of an interconnected transcriptional network characterized by higher levels of NOTCH1, NF-kappa B, and other important TFs on more primitive HSC sets.

Near zero magnetostriction of Fe-Ti alloys

Fe(100-x)Ti(x) alloys (x = 10, 15, 20) were studied with respect to their microstructure and magnetostriction. Depending on heat treatment temperature and composition, the sample retained either the alpha-phase (A2 structure) or the alpha-phase plus the TiFe(2) Laves phase (C14 structure). The saturation magnetostriction measured at 238K is negative, about -11 ppm. However, for fields up to 0.4 T the magnetostriction is barely zero, a very interesting result. High values of magnetostriction are of interest for applications mainly in sensors and actuators, but zero magnetostriction is also a remarkable property, desirable for many applications such as electric transformers and fluxgate sensor cores. Therefore, the Fe(100-x)Ti(x) (x < 20 at%) are an attractive option to be considered for these applications.

Effect of oral creatine supplementation on near-maximal strength and repeated sets of high-intensity bench press exercise

This study examined the effects of 26 days of oral creatine monohydrate (Cr) supplementation on near-maximal muscular strength, high-intensity bench press performance, and body composition. Eighteen male powerlifters with at least 2 years resistance training experience took part in this 28-day experiment. Pre and postmeasurements (Days 1 and 28) were taken of near-maximal muscular strength, body mass, and % body fat. There were two periods of supplementation Days 2 to 6 and Days 7 to 27. ANOVA and t-tests revealed that Cr supplementation significantly increased body mass and lean body mass with no changes in % body fat. Significant increases in 3-RM strength occurred in both groups, both absolute and relative to body mass; the increases were greater in the Cr group. The change in total repetitions also increased significantly with Cr supplementation both in absolute terms and relative to body mass, while no significant change was seen in the placebo (P) group. Creatine supplementation caused significant changes in the number of BP reps in Sets 1, 4, and 5. No changes occurred in the P group. It appears that 26 days of Cr supplementation significantly improves muscular strength and repeated near-maximal BP performance, and induces changes in body composition.

Maximal sets of Hamilton cycles in Kn,n

In this article, we prove that there exists a maximal set of m Hamilton cycles in K-n,K-n if and only if n/4 < m less than or equal to n/2. (C) 2000 John Wiley & Sons, Inc.

Slant or occlusion: global factors resolve stereoscopic ambiguity in sets of horizontal lines

Perceived slant was measured for horizontal lines aligned on one side and of varying lengths whose length disparity was either a constant linear amount for all lines (consistent with uniocular occlusion) or proportional to line length (consistent with global slant). Although the disparity of any line was ambiguous with respect to these two possibilities, slant of individual lines did not occur in the former case, but a subjective contour in depth was reported along the alignment. For proportional disparity of the set, global slant was seen. Adding a constant length to each line on the invalid eye for occlusion resulted in multiple slants. Smooth uniocular variations in alignment shape elicited subjective contours slanting or curving in depth. Global context can disambiguate the depth status of individual disparate lines. (C) 2004 Elsevier Ltd. All rights reserved.