Chain sequences and symmetric generalized orthogonal polynomials

in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Use of Genetically Modified Glial Cells Overexpressing Laminin α1-Chain Peptides in Neurite Outgrowth Studies

1. C6 glioma cells were transfected with two constructs carrying C-terminal laminin alpha1-chain sequences of 117 and 114 bp length, respectively. These sequences are specifically known to code for peptides which have neurite-promoting activity. 2. The stable expression and secretion of the two peptides was detected by Northern and Western blot analysis. 3. Primary neuronal cultures derived from embryonic mouse forebrain were cocultured with these transfected cells and exhibited a substantial increase in neurite outgrowth and in survival time. Conditioned media from the transfected cells generated similar effects. 4. Organotypic cultures from embryonic mouse brain were used as a second system as being closer to the in vivo situation. Again, coculture of brain slices with transfected cells or treatment with laminin peptide-containing media increased neuronal outgrowth.

The new concepts and new developments in hte theory of polymer crystallization

Recently a debate about the initial crystallization process which has not been the hotspot for a long time since the theory proposed by Hoffman- Lauritzen (LH) dominated the field arose again. For a long time the Hoffman-Lauritzen model was always confronted by criticism,and some of the points were taken up and led to modifications, but the foundation remained unchanged which deemed that before the nucleation and crystallization the system was uniform. In this article the classical nucleation and growth theory of polymer crystallization was reviewed, and the confusion of the explanations to the polymer crystallization phenomenon was pointed out. LH theory assumes that the growth of lamellae is by the direct attachment of chain sequences from the melt onto smooth lateral sides.

Study on the oriented recrystallization of carbon-coated polyethylene oriented ultrathin films

It is confirmed that a layer of vacuum-evaporated carbon on the surface of a preoriented ultrathin polymer film can lead to an oriented recrystallization of the polymer film. This has been attributed to a strong fixing effect of vacuum-evaporated carbon layer on the film surface of the polymer. To study the origin of the strong fixing effect of vacuum-evaporated carbon layer on the polymer films, the melting and recrystallization behaviors of the preoriented ultrathin PE film with a vacuum-evaporated carbon layer were studied by using atomic force microscopy, electron diffraction, Fourier transform infrared spectroscopy, and Raman spectroscopy. We found that there exists some extent of chain orientation of carbon-coated polyethylene (PE) preoriented ultrathin film above its melting temperature. These oriented PE chain sequences act as nucleation sites and induce the oriented recrystallization of preoriented PE film from melt. Raman spectroscopy results suggest that new carbon-carbon bonds between the carbon layer and the oriented PE film are created during the process of vacuum carbon evaporation. As a result, some of the PE chain stems are fixed to the coated carbon substrate via covalent bond. Such a bonding has retarded the relaxation of the PE chains at the spot and, therefore, preserves the original orientation of the PE stems at high temperature, which in turn derives the recrystallization of the PE chains in an oriented structure.

Szego polynomials: some relations to L-orthogonal and orthogonal polynomials

We consider the real Szego polynomials and obtain some relations to certain self inversive orthogonal L-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on real intervals. We also consider the polynomials obtained when the coefficients in the recurrence relations satisfied by the self inversive orthogonal L-polynomials are rotated. (C) 2002 Elsevier B.V. B.V. All rights reserved.

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

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Sieved para-orthogonal polynomials on the unit circle

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Para-orthogonal polynomials from constant Verblunsky coefficients

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On Understanding How Developers Use the Spotter Search Tool

Analyzing how software engineers use the Integrated Development Environment (IDE) is essential to better understanding how engineers carry out their daily tasks. Spotter is a code search engine for the Pharo programming language. Since its inception, Spotter has been rapidly and broadly adopted within the Pharo community. However, little is known about how practitioners employ Spotter to search and navigate within the Pharo code base. This paper evaluates how software engineers use Spotter in practice. To achieve this, we remotely gather user actions called events. These events are then visually rendered using an adequate navigation tool chain. Sequences of events are represented using a visual alphabet. We found a number of usage patterns and identified underused Spotter features. Such findings are essential for improving Spotter.

Perturbation of the T cell repertoire in rheumatoid arthritis

Aberrations in the T cell repertoire with the emergence of oligoclonal populations have been described in patients with rheumatoid arthritis (RA). However, the extent of the repertoire perturbations as well as the underlying mechanisms are not known. We now have examined the diversity of the peripheral CD4 T cell repertoire by determining the frequencies of arbitrarily selected T cell receptor (TCR) β-chain sequences. Healthy individuals displayed a highly diverse repertoire, with a median frequency of individual TCR β-chain sequences of 1 in 2.4 × 107 CD4 T cells. In RA patients, the median TCR β-chain frequency was increased 10-fold, indicating marked contraction of the repertoire (P < 0.001). The loss in TCR diversity was not limited to CD4 memory T cells but also involved the compartment of naive T cells, suggesting that it reflected an abnormality in T cell repertoire formation and not a consequence of antigen recognition in the synovium. Also, control patients with chronic inflammatory disease such as hepatitis C expressed a diverse repertoire indistinguishable from that of normals. Telomere length studies indicated an increased replicative history of peripheral CD4 T cells in RA patients, suggesting an enhanced turnover within the CD4 compartment. Compared with age-matched controls, terminal restriction fragment sizes were 1.7 kilobases shorter (P < 0.001). These data demonstrate an altered CD4 T cell homeostasis in RA that may contribute to the autoimmune response as well as to the immunodeficiency in these patients.

Evaluation of mixed chimerism by in vitro amplification of dinucleotide repeat sequences using the polymerase chain reaction

The influence of mixed hematopoietic chimerism (MC) after allogeneic bone marrow transplantation remains unknown. Increasingly sensitive detection methods have shown that MC occurs frequently. We report a highly sensitive novel method to assess MC based on the polymerase chain reaction (PCR). Simple dinucleotide repeat sequences called microsatellites have been found to vary in their repeat number between individuals. We use this variation to type donor-recipient pairs following allogeneic BMT. A panel of seven microsatellites was used to distinguish between donor and recipient cells of 32 transplants. Informative microsatellites were subsequently used to assess MC after BMT in this group of patients. Seventeen of the 32 transplants involved a donor of opposite sex; hence, cytogenetics and Y chromosome-specific PCR were also used as an index of chimerism in these patients. MC was detected in bone marrow aspirates and peripheral blood in 18 of 32 patients (56%) by PCR. In several cases, only stored slide material was available for analysis but PCR of microsatellites or Y chromosomal material could be used successfully to assess the origin of cells in this archival material. Cytogenetic analysis was possible in 17 patients and MC was detected in three patients. Twelve patients received T-cell-depleted marrow and showed a high incidence of MC as revealed by PCR (greater than 80%). Twenty patients received unmanipulated marrow, and while the incidence of MC was lower (44%), this was a high percentage when compared with other studies. Once MC was detected, the percentages of recipient cells tended to increase. However, in patients exhibiting MC who subsequently relapsed, this increase was relatively sudden. The overall level of recipient cells in the group of MC patients who subsequently relapsed was higher than in those who exhibited stable MC. Thus, while the occurrence of MC was not indicative of a poor prognosis per se, sudden increases in the proportions of recipient cells may be a prelude to graft rejection or relapse.

Sequences of immunoglobulin chains : tabulation and analysis of amino acid sequences of precursors, V-regions, C-regions, J-chain and -microglobulins /

1976 ed. issued under title: Variable regions of immunoglobulin chains.

PCR bias Toward the wild-type k-ras and p53 sequences: Implications for PCR detection of mutations and cancer diagnosis

PCR-based cancer diagnosis requires detection of rare mutations in k- ras, p53 or other genes. The assumption has been that mutant and wild-type sequences amplify with near equal efficiency, so that they are eventually present in proportions representative of the starting material. Work on factor IX suggests that this assumption is invalid for one case of near- sequence identity. To test the generality of this phenomenon and its relevance to cancer diagnosis, primers distant from point mutations in p53 and k-ras were used to amplify wild-type and mutant sequences from these genes. A substantial bias against PCR amplification of mutants was observed for two regions of the p53 gene and one region of k-ras. For k-ras and p53, bias was observed when the wild-type and mutant sequences were amplified separately or when mixed in equal proportions before PCR. Bias was present with proofreading and non-proofreading polymerase. Mutant and wild-type segments of the factor V, cystic fibrosis transmembrane conductance regulator and prothrombin genes were amplified and did not exhibit PCR bias. Therefore, the assumption of equal PCR efficiency for point mutant and wild-type sequences is invalid in several systems. Quantitative or diagnostic PCR will require validation for each locus, and enrichment strategies may be needed to optimize detection of mutants.