Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

Synchronization and Basins of Synchronized in Two-Dimensional Piecewise Maps Via Coupling Three Pieces of One-Dimensional Maps

This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

The hospital survey on patient safety culture in Portuguese hospitals: instrument validity and reliability

Purpose – Quantitative instruments to assess patient safety culture have been developed recently and a few review articles have been published. Measuring safety culture enables healthcare managers and staff to improve safety behaviours and outcomes for patients and staff. The study aims to determine the AHRQ Hospital Survey on Patient Safety Culture (HSPSC) Portuguese version's validity and reliability. Design/methodology/approach – A missing-value analysis and item analysis was performed to identify problematic items. Reliability analysis, inter-item correlations and inter-scale correlations were done to check internal consistency, composite scores. Inter-correlations were examined to assess construct validity. A confirmatory factor analysis was performed to investigate the observed data's fit to the dimensional structure proposed in the AHRQ HSPSC Portuguese version. To analyse differences between hospitals concerning composites scores, an ANOVA analysis and multiple comparisons were done. Findings – Eight of 12 dimensions had Cronbach's alphas higher than 0.7. The instrument as a whole achieved a high Cronbach's alpha (0.91). Inter-correlations showed that there is no dimension with redundant items, however dimension 10 increased its internal consistency when one item is removed. Originality/value – This study is the first to evaluate an American patient safety culture survey using Portuguese data. The survey has satisfactory reliability and construct validity.

Big Bang bifurcations and allee effect in Blumberg’s dynamics

This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

Environmental sustainability in superior education: case study of Lisbon College of Health Technology

Over the centuries there has been a growing trend of societies and it is possible to verify their economic growth. This growth has provided an increased pressure on natural resources, often over-reaching the boundaries of each country, which has called into question the level of environmental sustainability in different countries. Sustainability is understood as a complex concept involving ecological, social, economic dimensions and temporal urban processes. Therefore, Firmino (2009) suggests that the ecological footprint (EF) allows people to establish dependency relations between human activities and the natural resources required for such activities and for the absorption of waste generated. According to Bergh & Verbruggen (1999) the EF is an objective, impartial and one-dimensional indicator that enables people to assess the sustainability. The Superior Schools have a crucial role in building the vision of a sustainable future as a reality, because in transmitting values and environmental principles to his students, are providing that they, in exercising his professional activity, make decisions weighing the environmental values. This ensures improved quality of life. The present study aims to determine the level of environmental sustainability of the Academic Community of Lisbon College of Health Technology (ESTeSL), by calculating the EF, and describe whether a relation between Footprint and various socio-demographic characteristics of the subjects.

Dispositional optimism is unidimensional or bidimensional? The Portuguese Revised Life Orientation Test

The aim of the study is to adapt and then discuss the appropriateness of the Life Orientation Test as a one or two dimension scale. The research includes two studies; one is composed of a sequential sample of 280 people with multiple sclerosis, 71% female, and another includes a convenience sample of 615 individuals from the community, 51.1% female. Because the construct is built upon a theoretical assumption that has one dimension, we examine the hypothesis of one or two factor solutions through confirmatory factor analysis, and the two-dimension solution premise demonstrates better adjustment for both samples. The other psychometric properties explored show appropriate results for the Portuguese sample, and similar to the original ones; the Test therefore seems appropriate for use in cross cultural studies. Based on our results, we discuss whether the questionnaire is a one or two dimension instrument, concluding that it appears appropriate to accept the recommendations of the original authors to use it as a one-dimensional tool and, when necessary, to use both dimensions. - RESUMO: El objetivo del estudio es adaptar y discutir la adecuación de la prueba de Orientación de la Vida en una o dos escalas de dimensión. La investigación engloba dos estudios, uno constituido por una muestra secuencial de 280 personas con esclerosis múltiple, 71% mujeres y otro con una muestra de conveniencia de la comunidad de 615 individuos, 51,1% del sexo femenino. Como el constructo se asienta sobre la presunción teórica de que tiene una dimensión, inspeccionamos la hipótesis de una o dos soluciones de factor a través del análisis factorial confirmatorio y la hipótesis de dos dimensiones manifiesta un mejor ajuste para ambas muestras. Las otras propiedades psicométricas exploradas muestran los resultados apropiados para la muestra portuguesa, y semejantes a los originales. Parece apropiado para los estudios culturales transversales. Basándonos en nuestros resultados, discutimos si el cuestionario es un instrumento de una o dos dimensiones, concluyéndose que parece conveniente seguir las recomendaciones de los autores originales, para utilizarlo como un instrumento unidimensional y, si fuera necesario necesario, utilizar cada una de las dimensiones.

Notas sobre o mundo social do livro: a construção do editor e da edição

Personagem-filtro, intérprete, mas também interventor, prescrevendo, legitimando e ordenando o universo tipográfico, o editor surge como figura múltipla e socialmente investida de atributos e práticas mediadoras na sua relação com o dado textual. Produtor de valor e materialidade, o editor inscreve o projecto do livro num espaço social colaborativo de trabalho, o campo da edição. Este artigo procura sistematizar teoricamente alguns tópicos relativos à articulação do editor com a construção social do campo editorial e a edificação da cultura impressa. Empreender semelhante exploração é abdicar forçosamente de uma visão linear, unidimensional e historicamente asséptica do mundo social e cultural do livro, cuja morfologia e suportes conhecem crescentemente os desafios da desmaterialização.