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.

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.

Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Sieved para-orthogonal polynomials on the unit circle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A polymerase chain reaction for the detection of Brucella canis in semen of naturally infected dogs

The objective was to evaluate a PCR assay for the detection of Brucella canis in canine semen, comparing its performance with that of bacterial isolation, serological tests and PCR assay of blood. Fifty-two male dogs were examined clinically to detect reproductive abnormalities and their serum was tested by the rapid slide agglutination test, with and without 2-mercaptoethanol (2ME-RSAT and RSAT, respectively). In addition, microbiological culture and PCR assays were performed on blood and semen samples. The findings of the semen PCR were compared (Kappa coefficient and McNemar test) to those of blood PCR, culture of blood and semen, RSAT, and 2ME-RSAT. Nucleic acid extracts from semen collected from dogs not infected with B. canis were spiked with decreasing amounts of B. canis RM6/66 DNA and the resulting samples subjected to PCR. In addition, semen samples of non-infected dogs were spiked with decreasing amounts of B. canis CFU and the resulting suspensions were used for DNA extraction and amplification. of the 52 dogs that were examined, the following tests were positive: RSAT, 16 (30.7%); 2ME-RSAT, 5 (9.6%); blood culture, 14 (26.9%); semen culture, 11 (21.1%); blood PCR, 18 (34.6%); semen PCR, 18 (34.6%). The PCR assay detected as few as 3.8 fg of B. canis DNA experimentally diluted in 444.9 ng of canine DNA (extracted from semen samples of noninfected dogs). In addition, the PCR assay amplified B. canis genetic sequences from semen samples containing as little as 1.0 x 10(0) cfu/mL. We concluded that PCR assay of semen was a good candidate as a confirmatory test for the diagnosis of brucellosis in dogs; its diagnostic performance was similar to blood culture or blood PCR. Furthermore, the PCR assay of semen was more sensitive than the 2ME-RSAT or semen culture. Examination of semen by PCR should be included for diagnosis of brucellosis prior to natural mating or AI; in that regard, some dogs that were negative on serological and microbiological examinations as well as blood PCR were positive on PCR of semen. (c) 2007 Elsevier B.V. All rights reserved.

A polymerase chain reaction for detection of Brucella canis in vaginal swabs of naturally infected bitches

A PCR assay for the detection of Brucella canis in canine vaginal swab samples was evaluated, comparing its performance with that of bacterial isolation, serological tests, and a blood PCR assay. One hundred and forty-four female dogs were clinically examined to detect reproductive problems and they were tested by the rapid slide agglutination test, with and without 2-mercaptoethanol (2ME-RSAT and RSAT, respectively). In addition, microbiological culture and PCR were performed on blood and vaginal swab samples. The results of the vaginal swab PCR were compared to those of the other tests using the Kappa coefficient and McNemar test. of the 144 females that were examined, 66 (45.8%) were RSAT positive, 23 (15.9%) were 2ME-RSAT positive, 49 (34.02%) were blood culture positive, 6 (4.1%) were vaginal swab culture positive, 54 (37.5%) were blood PCR positive, 52 (36.2%) were vaginal swab PCR positive, and 50.69% (73/144) were positive by the combined PCR. The PCR was able to detect as few as 3.8 fg of B. canis DNA experimentally diluted in 54 ng of canine DNA, extracted from vaginal swab samples of non-infected bitches. In addition, the PCR assay amplified B. canis genetic sequences from vaginal swab samples containing 1.0 x 10(0) cfu/mL. In conclusion, vaginal swab PCR was a good candidate as a confirmatory test for brucellosis diagnosis in bitches suspected to be infected, especially those negative on blood culture or blood PCR; these animals may be important reservoirs of infection and could complicate attempts to eradicate the disease in confined populations. (C) 2007 Elsevier B.V. All rights reserved.

Plant or fungal sequences? An alternative optimized PCR protocol to avoid ITS (nrDNA) misamplification

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

Shigatoxigenic Escherichia coli serogroups O157, O111 and O113 in feces, water and milk samples from dairy farms

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

Development of a scar marker for Pierce's Disease strains of Xylella fastidiosa

O objetivo deste trabalho foi desenvolver um oligonucleotídeo iniciador para reação em cadeia da polimerase (PCR) específico para as estirpes de Xylella fastidiosa que causam o mal de Pierce (PD) em videira (Vitis vinifera). Amplificações de DNA de 23 diferentes hospedeiros, usando o conjunto de oligonucleotídeos REP1-R (5'-IIIICGICGIATCCIGGC-3') e REP 2 (5'-ICGICTTATCI GGCCTAC-3') utilizando o programa: 94 ºC/2 min; 35 X (94 ºC/1 min, 45 ºC/1 min; 72 ºC/1 min and 30 s) 72 ºC/5 min, produziu um fragmento de 630 pb que diferenciou as estirpes de videiras dos demais. Entretanto, padrões de bandeamento REP não são considerados confiáveis para detecção devido ao par de oligonucleotídeos REP 1 e REP 2 corresponderem a seqüências repetitivas encontradas por todo o genoma bacteriano. Desse modo, o produto amplificado de 630 pb foi eluído do gel de agarose, purificado e seqüenciado. A informação da seqüência nucleotídica foi usada para identificar e sintetizar um oligonucleotídeo específico para o isolado de X. fastidiosa causadora do mal de Pierce denominado Xf-1 (5'-CGGGGGTGTAGGAGGGGTTGT-3'), que foi utilizado juntamente com o oligonucleotídeo REP-2 nas condições 94 ºC/2 min; 35 X (94 ºC/1 min, 62 ºC/1 min; 72 ºC/1 min and 30 s) 72 ºC/10 min. Os DNAs das estirpes de X. fastidiosa de outros hospedeiros [amêndoa (Prumus amygdalus), citros (Citrus spp.), café (Coffea arabica), olmo (Ulmus americana), amora (Morus rubra), carvalho (Quercus rubra), vinca (Catharantus roseus), ameixa (Prunus salicina) e ragweed (Ambrosia artemisiifolia)] e de bactérias Gram negativas e positivas foram submetidos a amplificação com o conjunto de oligonucleotídeos Xf-1/REP 2. Um fragmento, de aproximadamente 350 pb, foi amplificado apenas com o DNA de X. fastidiosa isolada de videira.

Immobilization of streptavidin in sol-gel films: Application on the diagnosis of hepatitis C virus

Recent advances have accelerated the development of biosensors for the analysis of specific gene sequences. In this kind of biosensor, a DNA probe is immobilized on a transducer and the hybridization with the target DNA is monitored by suitable methodology. In the present work, the streptavidin (STA) was encapsulated in thin films siloxane-poly(propylene oxide) hybrids prepared by sol-gel method and deposited on the graphite electrode surface by dip-coating process. Biotinylated 18-mer probes were immobilized through STA and a novel amperometric DNA biosensor for the detection and genotyping of the hepatitis C virus (genotypes 1, 2A/C, 2B and 3) is described. The HCV RNA from serum was submitted to reverse transcriptase-linked polymerase chain reaction (RT-PCR) and biotin-labeled cDNA was obtained. Thus, the cDNA was hybridized to the target-specific oligonucleotide probe immobilized on the graphite electrode surface and following the avidin-peroxidase conjugate was added. The enzymatic response was investigated by constant potential amperometry at -0.45 V versus Ag/AgCl using H2O2 and KI solutions. HCV RNA negative and positive controls and positive samples of sera patients were analyzed and the results were compared to commercial kit. The proposed methodology appeared to be suitable and convenient tool for streptavidin immobilization and diagnose of HCV disease. (c) 2006 Elsevier B.V. All rights reserved.

EBNA-1 gene sequences in Brazilian and American patients with Hodgkin's disease

We examined the types of Epstein-Barr virus-associated nuclear antigen-1 (EBNA-1) gene carboxy (C)-terminal mutations occurring in Hodgkin's disease (HD) and reactive tissues from two different geographic regions. Previously reported EBNA-1 C-terminal region amino acid sequence variants, based on the amino acid at codon 487, include Prototype (P)-ala, which is found in the B95.8-derived prototype virus, P-thr, Variant (V)-leu, V-val, and V-pro. Using polymerase chain reaction (PCR) to amplify portions of the EBNA-1 gene, followed by DNA sequencing, we found a single EBNA-1 gene sequence variant in each tissue, whether reactive or neoplastic and whether from Brazil or the United States. Variant EBNA-1 gene sequences were more common in both neoplastic and non-neoplastic tissues from different geographic areas than the so-called prototype sequence. In the 17 Brazilian HD cases, 4 cases had P-thr variants and 13 had V-leu variants. In the six reactive tissues from Brazil, one had a P-ala variant, two had P-thr variants, and three had V-leu variants. In the 12 American HD cases, 2 had P-ala variants, 6 had P-thr variants, and 4 had V-leu variants. The 11 American reactive tissues included 2 P ala variants, 5 P-thr variants, and 4 V-leu variants. In both countries, there were similar variant EBNA-1 sequences present in normal tissues and HD cases. Compared with the P ala and P-thr cases, the V-leu cases were more likely to have the 30-bp latent membrane protein 1 (LMP1) gene deletion (P = 0.0075). In addition, cases of HD with the V-leu were statistically associated with a substitution of asparagine for glutamine at codon 322 of the C-terminal portion of the LMP1 gene. Our results suggest that any variation in EBNA-1 gene sequence is caused by a polymorphism present in pre-existing viral strains in the underlying population, and not a mutation occurring during oncogenesis. (C) 1999 by the American Society of Hematology.

A novel in situ Polymerase chain reaction hybridisation assay for the direct detection of bovine herpesvirus type 5 in formalin-fixed, paraffin-embedded tissues

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

Direct detection of infectious bursal disease virus from clinical samples by in situ reverse transcriptase-linked polymerase chain reaction

The presence of the very virulent (vv) Brazilian strain of infectious bursal disease virus (IBDV) was determined in the bursa of Fabricius, thymus and liver of 2-week-old broilers from a flock with a higher than expected mortality. For this purpose, a direct in situ reverse transcriptase (RT)-linked polymerase chain reaction (PCR) method was developed using specific primers for vvIBDV. Unlabelled forward and reverse biotinylated oligonucleotides were used for RT-PCR in a one-step method and the respective products were revealed by a direct enzymatic reaction. The results were compared with those obtained by standard RT-PCR using general primers for IBDV and virus isolation. The virus isolation, RT-PCR and in situ RT-PCR revealed positive results on the bursa of Fabricius in 86%, 80% and 100%, respectively. The in situ RT-PCR detected vvIBDV in all tested thymus and liver samples, whereas the standard RT-PCR detected virus in 80% and 90% of the samples, respectively. After three consecutive passages on chicken embryonated eggs, IBDV was isolated from 64% of the thymus samples and 30% of the liver samples. In the present study, no classical or antigenic variants of IBDV were detected. The developed in situ RT-PCR assay was able to detect the very virulent strain of IBDV with a higher sensitivity than the conventional RT-PCR and virus isolation.