Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

A new framework for understanding inequalities between expatriates and host country nationals

An interdisciplinary theoretical framework is proposed for analysing justice in global working conditions. In addition to gender and race as popular criteria to identify disadvantaged groups in organizations, in multinational corporations (MNCs) local employees (i.e. host country nationals (HCNs) working in foreign subsidiaries) deserve special attention. Their working conditions are often substantially worse than those of expatriates (i.e. parent country nationals temporarily assigned to a foreign subsidiary). Although a number of reasons have been put forward to justify such inequalities—usually with efficiency goals in mind—recent studies have used equity theory to question the extent to which they are perceived as fair by HCNs. However, since perceptual equity theory has limitations, this study develops an alternative and non-perceptual framework for analysing such inequalities. Employment discrimination theory and elements of Rawls’s ‘Theory of Justice’ are the theoretical pillars of this framework. This article discusses the advantages of this approach for MNCs and identifies some expatriation practices that are fair according to our non-perceptual justice standards, whilst also reasonably (if not highly) efficient.

Inequalities in dental services utilization among Brazilian low-income children: the role of individual determinants

Objectives: To assess the role of the individual determinants on the inequalities of dental services utilization among low-income children living in the working area of Brazilian`s federal Primary Health Care program, which is called Family Health Program (FHP), in a big city in Southern Brazil. Methods: A cross-sectional population-based study was performed. The sample included 350 children, ages 0 to 14 years, whose parents answered a questionnaire about their socioeconomic conditions, perceived needs, oral hygiene habits, and access to dental services. The data analysis was performed according to a conceptual framework based on Andersen`s behavioral model of health services use. Multivariate models of logistic regression analysis instructed the hypothesis on covariates for never having had a dental visit. Results: Thirty one percent of the surveyed children had never had a dental visit. In the bivariate analysis, higher proportion of children who had never had a dental visit was found among the very young, those with inadequate oral hygiene habits, those without perceived need of dental care, and those whose family homes were under absent ownership. The mechanisms of social support showed to be important enabling factors: children attending schools/kindergartens and being regularly monitored by the FHP teams had higher odds of having gone to the dentist, even after adjusting for socioeconomic, demographic, and need variables. Conclusions: The conceptual framework has confirmed the presence of social and psychosocial inequalities on the utilization pattern of dental services for low-income children. The individual determinants seem to be important predictors of access.

Sex and socioeconomic inequalities of lung cancer mortality in Barcelona, Spain and Sao Paulo, Brazil

The objective of this paper was to assess sex and socioeconomic inequalities in lung cancer mortality in two major cities of Europe and South America. Official information on mortality and population allowed the estimation of sex- and age-specific death rates for Barcelona, Spain and Sao Paulo, Brazil (1995-2003). Mortality trends and levels were independently assessed for each city and subsequently compared. Rate ratios assessed by Poisson regression analysis addressed hypotheses of association between the outcome and socioeconomic covariates (human development index, unemployment and schooling) at the inner-city area level. Barcelona had a higher mortality in men (76.9/100000 inhabitants) than Sao Paulo (38.2/100 000 inhabitants); although rates were decreasing for the former (-2%/year) and levelled-off for the [after. Mortality in women ranked similarly (9.1 for Barcelona, 11.5 for Sao Paulo); with an increasing trend for women aged 35-64 years (+ 7.7%/year in Barcelona and + 2.4%/year in Sao Paulo). The socioeconomic gradient of mortality in men was negative for Barcelona and positive for Sao Paulo; for women, the socioeconomic gradient was positive in both cities. Negative gradients indicate that deprived areas suffer a higher burden of disease; positive gradients suggest that prosmoking lifestyles may have been more prevalent in more affluent areas during the last decades. Sex and socioeconomic inequalities of lung cancer mortality reinforce the hypothesis that the epidemiologic profile of cancer can be improved by an expanded access to existing technology of healthcare and prevention. The continuous monitoring of inequalities in health may contribute to the concurrent promotion of well-being and social justice.

Comparing performance of instrumental drift correction by linear and quadratic adjusting in inductive electromagnetic data

Electromagnetic induction (EMI) method results are shown for vertical magnetic dipole (VMD) configuration by using the EM38 equipment. Performance in the location of metallic pipes and electrical cables is compared as a function of instrumental drift correction by linear and quadratic adjusting under controlled conditions. Metallic pipes and electrical cables are buried at the IAG/USP shallow geophysical test site in Sao Paulo City. Brazil. Results show that apparent electrical conductivity and magnetic susceptibility data were affected by ambient temperature variation. In order to obtain better contrast between background and metallic targets it was necessary to correct the drift. This correction was accomplished by using linear and quadratic relation between conductivity/susceptibility and temperature intending comparative studies. The correction of temperature drift by using a quadratic relation was effective, showing that all metallic targets were located as well deeper targets were also improved. (C) 2010 Elsevier B.V. All rights reserved.

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.

Benders, metric and cutset inequalities for multicommodity capacitated network design

Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities. We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities.

Exact penalties for variational inequalities with applications to nonlinear complementarity problems

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best theoretical results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We close the paper with some preliminary computational tests on the use of a semismooth Newton method to solve the equation derived from the new reformulation. We also compare its performance with the Newton method applied to classical reformulations based on the Fischer-Burmeister function and on the minimum. The new reformulation combines the best features of the classical ones, being as easy to solve as the reformulation that uses the Fischer-Burmeister function while requiring as few Newton steps as the one that is based on the minimum.

On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On relaxed LMI-based design for fuzzy controllers

Relaxed conditions for stability of nonlinear continuous-time systems given by fuzzy models axe presented. A theoretical analysis shows that the proposed method provides better or at least the same results of the methods presented in the literature. Digital simulations exemplify this fact. This result is also used for fuzzy regulators design. The nonlinear systems are represented by fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers axe described by LMIs (Linear Matrix Inequalities), that can be solved efficiently using convex programming techniques.