A refinement of the gauss-lucas theorem

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q-theta decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either theta or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus (Q(PV)) as continuation parameter (mu) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used in predictor step. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approach for the IEEE test systems (14, 30, 57 and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. (C) 2003 Elsevier B.V. All rights reserved.

NONLINEAR DIFFUSION PROCESS IN A BENARD SYSTEM AT THE CRITICAL-POINT FOR THE ONSET OF CONVECTION

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

Comparison of hexamethyidisilazane and critical point drying treatments for SEM analysis of anaerobic biofilms and granular sludge

We present a fast procedure for scanning electron microscopy (SEM) analysis in which hexamethyldisilazane (HMDS) solvent, instead of the critical point drying, is used to remove liquids from a microbiological specimen. The results indicate that the HMDS solvent is suitable for drying samples of anaerobic cells for examination by SEM and does not cause cell structure disruption.

On the number of critical periods for planar polynomial systems

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree l with at least 2[(l - 2)/2] critical periods as well as study concrete families of potential, reversible and Lienard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not. increases with the order of the perturbation. (C) 2007 Elsevier Ltd. All rights reserved.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part II. Performance evaluation

The parameterized fast decoupled power flow (PFDPF), versions XB and BX, using either theta or V as a parameter have been proposed by the authors in Part I of this paper. The use of reactive power injection of a selected PVbus (Q(PV)) as the continuation parameter for the computation of the maximum loading point (MLP) was also investigated. In this paper, the proposed versions obtained only with small modifications of the conventional one are used for the computation of the MLP of IEEE test systems (14, 30, 57 and 118 buses). These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approaches are presented and discussed. The results show that the characteristics of the conventional FDPF method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that these versions can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. A trivial secant predictor, the modified zero-order polynomial, which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used for the predictor step. (C) 2003 Elsevier B.V. All rights reserved.

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A new approach to the experimental determination of the critical temperature of metamagnets

A new approach to the experimental determination of the critical temperature of metamagnetic samples with non-zero demagnetizing factors is presented. The method is applied to metamagnetic Ni(NO3)2·2H2O, allowing the conclusion that this salt exhibits a tricritical point. Pressure dependence of the critical temperature, and the existence of a pressure-induced metamagnetic transition are also reported. © 1986.

Vacuum energy and the fixed point of QED

The vacuum energy of QED, as a function of the coupling constant α, is shown to have an absolute minimum at the critical coupling αc=π/3. The effect of chiral symmetry breaking diminishes as the coupling is increased. We argue that these aspects of the vacuum energy shall remain unaltered beyond the ladder approximation.

Critical periods of weed control in naturally green colored cotton BRS Verde

Cotton with naturally colored fiber is increasing as a commercial crop due specially to its textile processing with reduced environmental impact, as dying is not necessary. The critical period of weed control and the weed community were studied in a field with the naturally green colored fiber cv. BRS Verde cultivated in Missao Velha, Brazil. Without weed control during all the cycle, a reduction of 82.9% in yield was observed. The critical period of weed control was between 31 and 74 days after emergence for a reduction of 5% in yield. The weed community was composed of 21 species, with higher relative importance and dominance of monocotyledonous species. The beginning of the critical period was found to be more influential on yield than the ending. Thus, defining the right moment to start weed control can be more important to yield than determining the moment to cease it. (C) 2011 Elsevier B.V. All rights reserved.

Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Darunavir: A Critical Review of Its Properties, Use and Drug Interactions

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

Critical analysis of the international classification of headache disorders diagnostic criteria (ICHD I-1988) and (ICHD II-2004), for migraine in children and adolescents

The present study analyzed the (ICHD I-1988) and ( ICHD II-2004) diagnostic criteria in children and adolescents. Our population consisted of 496 patients of the Headache Outpatient Ward for Children and Adolescents retrospectively studied from 1992 to 2002. Individuals were classified according to three diagnostic groups: Intuitive Clinical Diagnosis ( Gold Standard), ICHD I-1988 and ICHD II-2004. They were statistically compared using the variables: Sensitivity ( S), Specificity (Sp), Positive Predictive Value (PPV), Negative Predictive Value (NPV). When ICHD I-1988 was used, the sensitivity of migraine without and with aura was 21% and 27%, respectively, whereas in ICHD II-2004 it changed to 53% and 71% without affecting specificity. As a conclusion, the current classification criteria ( ICHD II-2004) showed greater sensitivity and high specificity for migraine than ICHD I-1988, although it improved migraine diagnosis in children and adolescents, the sensitivity remains poor.