Dynamics of a charged particle in a dissipative Fermi-Ulam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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)

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

On the zeros of polynomials: An extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier B.V. All rights reserved.

Stabilizing a class of time delay systems using the Hermite-Biehler theorem

In this paper we use the Hermite-Biehler theorem to establish results for the design of fixed order controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. (C) 2003 Elsevier B.V. All rights reserved.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

A gene signature in histologically normal surgical margins is predictive of oral carcinoma recurrence

Background: Oral Squamous Cell Carcinoma (OSCC) is a major cause of cancer death worldwide, which is mainly due to recurrence leading to treatment failure and patient death. Histological status of surgical margins is a currently available assessment for recurrence risk in OSCC; however histological status does not predict recurrence, even in patients with histologically negative margins. Therefore, molecular analysis of histologically normal resection margins and the corresponding OSCC may aid in identifying a gene signature predictive of recurrence.Methods: We used a meta-analysis of 199 samples (OSCCs and normal oral tissues) from five public microarray datasets, in addition to our microarray analysis of 96 OSCCs and histologically normal margins from 24 patients, to train a gene signature for recurrence. Validation was performed by quantitative real-time PCR using 136 samples from an independent cohort of 30 patients.Results: We identified 138 significantly over-expressed genes (> 2-fold, false discovery rate of 0.01) in OSCC. By penalized likelihood Cox regression, we identified a 4-gene signature with prognostic value for recurrence in our training set. This signature comprised the invasion-related genes MMP1, COL4A1, P4HA2, and THBS2. Overexpression of this 4-gene signature in histologically normal margins was associated with recurrence in our training cohort (p = 0.0003, logrank test) and in our independent validation cohort (p = 0.04, HR = 6.8, logrank test).Conclusion: Gene expression alterations occur in histologically normal margins in OSCC. Over-expression of the 4-gene signature in histologically normal surgical margins was validated and highly predictive of recurrence in an independent patient cohort. Our findings may be applied to develop a molecular test, which would be clinically useful to help predict which patients are at a higher risk of local recurrence.

DNA methylation patterns in bladder cancer and washing cell sediments: a perspective for tumor recurrence detection

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

Surgical treatment of renal cell carcinoma recurrence at the renal fossa following radical nephrectomy

CONTEXTO: A recorrência local única do carcinoma renal de células claras em seu leito renal após nefrectomia radical é um evento raro. Estima-se que essa situação ocorra em 0,8% a 3,6% do total de procedimentos. Comumente, seu diagnóstico é realizado através de tomografia computadorizada de abdômen ou ultra-som renal usados no acompanhamento desses pacientes. É polêmico qual o melhor tratamento dessa rara condição entre urologistas e oncologistas devido aos poucos relatos em literatura. RELATO DE CASO: Relatamos um caso de recidiva neoplásica única no leito renal após quatro anos e meio da nefrectomia radical por adenocarcinoma de células claras, sem evidência de metástases a distância em outros órgãos. O diagnóstico foi realizado por meio de tomografia abdominal em acompanhamento ambulatorial, observando-se massa retroperitoneal em topografia renal. A massa foi retirada por meio de uma incisão subcostal ampliada, em cirurgia sem intercorrências. O paciente evoluiu bem no pós-operatório. Após um ano e meio do procedimento, foi evidenciada uma metástase no pulmão esquerdo, e seis meses após, outra recorrência metastática na nona costela anterior à direita, mesmo com paciente totalmente assintomático. O tratamento cirúrgico agressivo em recorrência local única é um bom método para controlar essa rara doença. Tomografia computadorizada de abdômen deve ser feita em acompanhamento de carcinoma renal por longos períodos após a nefrectomia radical para o diagnóstico de recorrências tardias e o tratamento deve ser feito como o de uma metástase recorrente única.

Polynomials generated by a three term recurrence relation: bounds for complex zeros

This paper deals with the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to find bounds, in terms of the coefficients of the recurrence relation, for the regions where the zeros are located. In most part, the zeros are explored through an Eigenvalue representation associated with a corresponding Hessenberg rnatrix. Applications to Szego polynomials, para-orthogonal polynomials and polynomials with non-zero complex coefficients are considered. (C) 2004 Elsevier B.V. All rights reserved.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

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

Finiteness theorem for topological contact equivalence of map germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)