On perturbed Szego recurrences

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.

The Wigner function associated with the Rogers-Szego polynomials

A Wigner function associated with the Rogers-Szego polynomials is proposed and its properties are discussed. It is shown that from such a Wigner function it is possible to obtain well-behaved probability distribution functions for both angle and action variables, defined on the compact support -pi less than or equal to theta < pi, and for m greater than or equal to 0, respectively. The width of the angle probability density is governed by the free parameter q characterizing the polynomials.

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

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.

Szego polynomials and the truncated trigonometric moment problem

We show how Szego polynomials can be used in the theory of truncated trigonometric moment problem.

Szego type polynomials and para-orthogonal polynomials

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

SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations

We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego{double acute} polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego{double acute} polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego{double acute} polynomials and polynomials arising from canonical spectral transformations are obtained. © 2012 American Mathematical Society.

Timpanismo bilateral de bolsa gutural em potro

Uma potra da raça Quarto de Milha com dois meses de idade apresentava aumento de volume bilateral na região da parótida desde algumas horas após o nascimento. Por exame radiográfico diagnosticou-se timpanismo bilateral de bolsa gutural. Realizou-se a abertura cirúrgica da bolsa gutural esquerda e fenestrou-se o septo medial das bolsas guturais. Adicionalmente, procedeu-se à ressecção parcial da mucosa na abertura do orifício guturo-faríngeo. A afecção foi debelada, sem recidivas.

Recidivas e recorrências de carcinomas basocelulares da face

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

Venous ulcer: clinical characteristics and risk factors

BackgroundLower limb venous ulceration ranks among the 10 most common medical problems in Western countries and has significant socioeconomic impact. The aim of this study was to identify the risk factors for unhealed, recurrent, and large ulcers and to characterize patients with active or recently healed venous ulcers.MethodsWe identified 97 patients and assessed 103 ulcerated limbs in 90 patients. All patients underwent clinical examination, arterial and venous system evaluation, ankle-brachial index determination, and ultrasound of the affected limb. Clinical characteristics included age, gender, race, ulcer duration, time since first episode, history of recurrence, localization of ulcer, ulcer area, eczema, ochre dermatitis, lipodermatosclerosis, pain, body mass index, and medical history data. Risk factors were identified by univariate analysis and estimated odds ratios.ResultsWe assessed 90 patients (103 limbs) with active or healed venous leg ulcers, of whom 84.4% were Caucasian and 68.9% were female. Mean age was 56.0 +/- 13.3 years. Ulcers had remained unhealed for < 1 year in 40.7%. Lipodermatosclerosis, lower limb hyperpigmentation, edema, and eczema were seen in 96.7%, 95.6%, 94.4%, and 51.1% of patients, respectively. Pain was a frequent symptom in 74.4%. Body mass index was assessed in 85 patients: 30.6% were slightly, 36.5% moderately, and 7% severely obese. Patient age > 60 years (odds ratio [OR] 4.0), extensive lipodermatosclerosis (OR 8.7), and previous history of ulceration (OR 19.9) were risk factors for unhealed ulcers. Time since first ulcer episode >= 2 years (OR 29.2) and incompetence of venous systems (OR 1.6) were risk factors for recurrence.ConclusionsLongstanding and large ulcers and recurrences are the main problems encountered by venous ulcer patients. Severe lipodermatosclerosis, previous ulcer history, and time since first ulcer episode >= 2 years are significant risk factors.

Abordagem de pacientes com úlcera da perna de etiologia venosa

Úlceras venosas são comuns na população adulta, causando significante impacto social e econômico devido a sua natureza recorrente e ao longo tempo decorrido entre sua abertura e cicatrização. Quando não manejadas adequadamente, as úlceras venosas têm altas taxas de falha de cicatrização e recorrência. Apesar da elevada prevalência e da importância da úlcera venosa, ela é freqüentemente negligenciada e abordada de maneira inadequada. Esta revisão discute abordagem diagnóstica e terapêutica das úlceras venosas. O diagnóstico clínico baseia-se em história e exame físico, com ênfase nos sinais e sintomas associados e palpação dos pulsos dos membros inferiores. A ultra-sonografia Doppler deve ser utilizada para determinar o índice pressórico entre o tornozelo e o braço, e exames não invasivos, como o duplex scan, devem ser realizados para avaliar o sistema venoso superficial, profundo e perfurante. Para abordagem terapêutica são fundamentais os diagnósticos clínico e laboratorial corretos, além do diagnóstico e tratamento adequados das complicações das úlceras crônicas. Os esforços devem ser direcionados para a cicatrização da úlcera e, posteriormente, para evitar as recidivas. O grande avanço no conhecimento da fisiopatogenia das úlceras venosas tem permitido o desenvolvimento de novas modalidades de tratamento clínico e cirúrgico.

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.

Tratamento cirúrgico na recidiva retroperitoneal tardia por carcinoma renal de células claras após nefrectomia radical

Late renal cell carcinoma recurrence in the renal fossa is a rare event. This condition occurs in 1 to 2% of radical nephrectomies. We reported a late recurrence at the renal fossa about four and half years after radical nephrectomy due to a renal cell carcinoma (RCC) without metastasis elsewhere. Diagnosis in an outpatient follow-up was made during an abdominal computed tomography and we observed a retroperitoneal mass in the renal fossa. The excision at the recurrence area was made through a subcostal transversal incision without any difficulty. After 6 months from this second procedure, there was no evidence of recurrence. The surgical aggressive treatment for late retroperitoneal RCC recurrence is a good method in this rare situation. Abdominal computed tomography must be done during long periods of follow-up for patients with radical nephrectomy for RCC to search for late retroperitoneal recurrences.