Uniform estimates of attracting sets of extended Lurie systems using LMIs

This research presents a systematic procedure to obtain estimates, via extended Lyapunov functions, of attracting sets of a class of nonlinear systems, as well as an estimate of their stability regions. The considered class of nonlinear systems, called in this note the extended Lurie system, consists of nonlinear systems like those of the Lurie problem where one of the nonlinear functions can violate the sector conditions of the Lurie problem around the origin. In case of nonautonomous systems the concept of absolute stability is extended and uniform estimates of the attracting set are obtained. Two classical nonlinear systems, the forced duffing equation and the Van der Pol system, are analyzed with the proposed procedure.

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.

Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Increased Levels of NOTCH1, NF-kappa B, and Other Interconnected Transcription Factors Characterize Primitive Sets of Hematopoietic Stem Cells

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

Preliminary core sets of measures for disease activity and damage assessment in juvenile systemic lupus erythematosus and juvenile dermatomyositis

Objective. To identify preliminary core sets of outcome variables for disease activity and damage assessment in juvenile systemic lupus erythematosus (JSLE) and juvenile dermatomyositis (JDM). Methods. Two questionnaire surveys were mailed to 267 physicians from 46 different countries asking each member to select and rank the response variables used when assessing clinical response in patients with JSLE or JDM. Next, 40 paediatric rheumatologists from 34 countries met and, using the nominal group technique, selected the domains to be included in the disease activity and damage core sets for JSLE and JDM. Results. A total of 41 response variables for JSLE and 37 response variables for JDM were selected and ranked through the questionnaire surveys. In the consensus conference, domains selected for both JSLE and JDM activity or damage core sets included the physician and parent/patient subjective assessments and a global score tool. Domains specific for JSLE activity were the immunological tests and the kidney function parameters. Concerning JDM, functional ability and muscle strength assessments were indicated for both activity and damage core sets, whereas serum muscle enzymes were included only in the activity core set. A specific paediatric domain called 'growth and development' was introduced in the disease damage core set for both diseases and the evaluation of health-related quality of life was advised in order to capture the influence of the disease on the patient lifestyle. Conclusions. We developed preliminary core sets of measures for disease activity and damage assessment in JSLE and JDM. The prospective validation of the core sets is in progress.

Description and genetic analysis of three sets of monozygotic twins resulting from transfers of single embryos to recipient mares

Case Description-3 sets of monozygotic twins resulting from transfers of single embryos to recipient mares were examined. Clinical Findings-In all 3 recipient mares with twin pregnancies, only 1 embryonic vesicle was detected before day 25 of gestation. In 1 recipient mare, 2 apparent adjacent vesicles, each containing an embryo with a heartbeat, were visualized on ultrasonographic examination on day 37 of gestation. The other 2 recipient mares underwent ultrasonographic examination on day 30 of gestation, at which time only 1 vesicle and embryo was identified. In these latter 2 recipient mares, however, a thorough ultrasonographic examination for a second conceptus on day 30 had not been performed, as only 1 embryo had been transferred and visualized on early ultrasonographic examination. Treatment and Outcome-All twin pregnancies resulted in death of both fetuses. Genetic analysis confirmed that each set of monozygotic twins originated from the transferred embryo. Clinical Relevance-Monozygotic twin pregnancy may occur after embryo transfer; thus recipient mares should be examined thoroughly for multiple conceptuses, especially between 25 and 30 days of gestation. At this time, the allantoides of monozygotic twins should be visible ultrasonographically and effective management may still be possible.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Energy expenditure during multiple sets of leg press and bench press

The purpose of this study was to quantify energy expenditure (EE) during multiple sets of leg press (LP) and bench press (BP) exercises in 10 males with at least 1 yr of resistance training (RT). The subjects underwent two sessions to determine 1 repetition maximum (1RM) on the BP and LP and one protocol consisting of a warm up and 4 sets for 10 repetitions at 70% 1RM with a 3-min rest period between sets for each exercise. Energy expenditure was calculated as the sum of oxygen uptake (aerobic component), EPOC, and lactate production (anaerobic component). There were no significant differences in EE between exercises for sets 1 to 4 and the total energy expended. However, statistical analysis revealed a significant difference (P<0.05) between exercises in RT economy (BP, 0.0206 ± 0.0044 kcal·kg-1 vs. LP, 0.0051 ± 0.0015 kcal·kg-1). Within exercise comparison showed set 4 was significantly different from sets 1 and 3 for BP, and for LP a significant difference was found between set 4 and sets 1, 2 and 3. Our results point to an increase in EE during multiple sets at 70% 1RM and show that in spite of the difference in muscle mass involved and total work done during each type of exercise, EE was not different due to greater economy during the LP.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures

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

Description of the attainable sets of one-dimensional differential inclusions

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Attribute charts for monitoring the mean vector of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)