On perturbed Szego recurrences

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Fekete-Szego problem for concave univalent functions

We consider the Fekete-Szego problem with real parameter lambda for the class Co(alpha) of concave univalent functions. (C) 2010 Elsevier Inc. All rights reserved.

Phase synchronization in brain networks derived from correlation between probabilities of recurrences in functional MRI data

It is increasingly being recognized that resting state brain connectivity derived from functional magnetic resonance imaging (fMRI) data is an important marker of brain function both in healthy and clinical populations. Though linear correlation has been extensively used to characterize brain connectivity, it is limited to detecting first order dependencies. In this study, we propose a framework where in phase synchronization (PS) between brain regions is characterized using a new metric ``correlation between probabilities of recurrence'' (CPR) and subsequent graph-theoretic analysis of the ensuing networks. We applied this method to resting state fMRI data obtained from human subjects with and without administration of propofol anesthetic. Our results showed decreased PS during anesthesia and a biologically more plausible community structure using CPR rather than linear correlation. We conclude that CPR provides an attractive nonparametric method for modeling interactions in brain networks as compared to standard correlation for obtaining physiologically meaningful insights about brain function.

Prevention of recurrences in frequently relapsing herpes labialis with thymopentin a randomized double-blind placebo-controlled multicenter study

The present randomized, placebo-controlled double-blind multicenter study included a population of 36 subjects with frequent recurrences (at least once a month) of herpes labialis. Most of the patients had failed to respond adequately to previous treatment with other therapeutic tools, including acyclovir. Either 50 mg of thymopentin or of placebo was administered 3 times a week, by the subcutaneous route, for 6 weeks. Subsequently, the patients were observed for nearly 6 months on the average. The results achieved with thymopentin for the individual parameters were significantly superior to those obtained with placebo; thus significant improvement was seen in patients on thymopentin in the duration of the longest symptomfree period (prolonged from 2.1 weeks to 20.9 weeks, p = 0.000), in the number of relapses (reduced from 1.6 to 0.4 episodes/month, p = 0.001), and in the total duration of herpes symptoms per month (shortened from 2.0 to 0.3 weeks, p = 0.000). Placebo treatment also resulted in considerable improvement (p < 0.05 or 0.01), but was significantly inferior to the improvement obtained with thymopentin. The longest symptomfree period in the placebo group was prolonged from 2.4 to 11.2 weeks. The number of relapses per month was reduced from 1.4 to 0.8, and the total duration of herpes symptoms per month from 2 to 0.9 weeks. The results of intergroup analyses, in which the observed parameters and the improvement achieved in either group were compared, significantly favored thymopentin treatment. The effect of thymopentin was in all but one parameters superior to that of placebo and highly significant (p < 0.01). © 1985 Humana Press Inc.

Słowo wstępne: W obliczu nadchodzącej fali reform szkolnictwa wyższego w Polsce. Argumentacja i wizja wspierająca najważniejsze kierunki zmian

Polska zrobiła w obszarze reform w latach 2009-2011 pierwsze kroki w kierunku, na który patrzymy bardzo życzliwie. Jednak pierwsze kroki wymagają kroków kolejnych – bardziej stanowczych i bardziej skoordynowanych, opartych na fundamencie zmian już wprowadzanych w życie – którym będzie towarzyszyć przekonująca wizja przyszłości, a także adekwatne do skali przewidywanych zmian publiczne nakłady finansowe. Wizja jest niezbędna. Wspólnota akademicka, a przede wszystkim jej najmłodsze pokolenie, musi wiedzieć, na jakich podstawach ma budować swoją akademicką przyszłość i czy jest w stanie się w niej odnaleźć. Warto jasno powiedzieć, że z czasem pojawi się bardziej zróżnicowany system instytucji szkolnictwa wyższego, o różnych możliwościach i różnych zadaniach w różnych miejscach, realizujących różne misje i oferujących różne możliwości awansowe i finansowe. Warto powiedzieć, że niezbędne – ale i możliwe – będą pionowe migracje w ramach różnicującego się systemu w zależności od indywidualnych zdolności, umiejętności, pracowitości, a przede wszystkim mierzalnych osiągnięć naukowych. Należy także przypomnieć, że profesja akademicka nie daje równych szans wszystkim, ponieważ talenty naukowe w ramach wspólnoty akademickiej nie rozkładają się równo, ale z pewnością daje duże szanse najzdolniejszym; że w najlepszych ośrodkach naukowy wymiar kariery akademickiej, tak jak w świecie zachodnim, jest najważniejszy, a wszystkie pozostałe są tylko jego tłem; że z czasem wzorce pracy akademickiej i wzorce akademickich zarobków – w wybranych miejscach i dla wybranych grup badaczy – będą przypominać wzorce znane z najlepszych systemów zachodnich; i wreszcie, że w tych wybranych miejscach (zwanych uniwersytetami badawczymi czy flagowymi) uprawianie nauki nie będzie jednostkowym, częściowo niezrozumiałym i częściowo jedynie tolerowanym, hobby.

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.

Do patients benefit from routine follow-up to detect recurrences after radical cystectomy and ileal orthotopic bladder substitution?

The need for and intensity of follow-up to detect disease recurrence after radical cystectomy (RC) for transitional cell carcinoma (TCC) remains a matter for debate.

Elective neck dissection for carcinomas of the oral cavity: occult metastases, neck recurrences, and adjuvant treatment of pathologically positive necks

BACKGROUND: Supraomohyoid neck dissection (SOHND) is currently performed in patients with carcinoma of the oral cavity with clinically negative neck. Most investigators consider SOHND as a staging procedure. METHODS: Records of 100 patients with cancer of the oral cavity and clinically negative neck undergoing SOHND were reviewed. The rate and significance of occult metastases are evaluated, the neck recurrences are analyzed and the indication of adjuvant radiation of pN+ necks is discussed. RESULTS: In 34 of 1814 of analyzed lymph nodes, metastatic disease was detected as follows: 30 macrometastases and 4 micrometastases. In 13 of 34 metastases (38%), extracapsular spread was observed. Twenty of 100 patients (20%) had to be upstaged. In 9 of 87 (10%) patients without local recurrence and with a minimal follow-up of 24 months, 5 ipsilateral (4 within the dissection field) and 5 contralateral neck recurrences were observed. Regional recurrence developed in 4% and 35% of patients with pN0 and pN+ necks, respectively. CONCLUSIONS: In 20% of patients with oral cavity tumors and pN0 neck, occult metastases were disclosed. Neck recurrences developed significantly more often in patients with pN+ than in those with pN0 necks. To evaluate the exact indication for an adjuvant treatment of patients with cN0/pN+ necks, prospective studies should be performed.