Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Relationships of extant lower Brachycera (Diptera): a quantitative synthesis of morphological characters

With over 80 000 described species, Brachycera represent one of the most diverse clades of organisms with a Mesozoic origin. Larvae of the majority of early lineages are detritivores or carnivores. However, Brachycera are ecologically innovative and they now employ a diverse range of feeding strategies. Brachyceran relationships have been the subject of numerous qualitative analyses using morphological characters. These analyses are often based on characters from one or a few character systems and general agreement on relationships has been elusive. In order to understand the evolution of basal brachyceran lineages, 101 discrete morphological characters were scored and compiled into a single data set. Terminals were scored at the family level, and the data set includes characters from larvae, pupae and adults, internal and external morphology, and male and female terminalia. The results show that all infraorders of Brachycera are monophyletic, but there is little evidence for relationships between the infraorders. Stratiomyomorpha, Tabanomorpha, and Xylophagomorpha together form the sister group to Muscomorpha. Xylophagomorpha and Tabanomorpha are sister groups. Within Muscomorpha, the paraphyletic Nemestrinoidea form the two most basal lineages. There is weak evidence for the monophyly of Asiloidea, and Hilarimorphidae appear to be more closely related to Eremoneura than other muscomorphs. Apsilocephalidae, Scenopinidae and Therevidae form a clade of Asiloidea. This phylogenetic evidence is consistent with the contemporaneous differentiation of the main brachyceran lineages in the early Jurassic. The first major radiation of Muscomorpha were asiloids and they may have diversified in response to the radiation of angiosperms in the early Cretaceous.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

The role of melanocortin-1 receptor polymorphism in skin cancer risk phenotypes

We have examined melanocortin-1 receptor (MC1R) variant allele frequencies in the general population and in a collection of adolescent dizygotic and monozygotic twins to determine statistical associations of pigmentation phenotypes with increased skin cancer risk. This included hair and skin color, freckling, mole count and sun exposed skin reflectance. Nine variants were studied and designated as either strong R (OR = 63; 95% CI 32-140) or weak r (OR = 5; 95% CI 3-11) red hair alleles. Penetrance of each MC1R variant allele was consistent with an allelic model where effects were multiplicative for red hair but additive for skin reflectance. To assess the interaction of the brown eye color gene BEY2/OCA2 on the phenotypic effects of variant MC1R alleles we imputed OCA2 genotype in the twin collection. A modifying effect of OCA2 on MC1R variant alleles was seen on constitutive skin color, freckling and mole count. In order to study the individual effects of these variants on pigmentation phenotype we have established a series of human primary melanocyte strains genotyped for the MC1R receptor. These include strains which are MC1R wild-type consensus, variant heterozygotes, and homozygotes for strong R alleles Arg151Cys and Arg160Trp. Ultrastructural analysis demonstrated that only consensus strains contained stage III and IV melanosomes in their terminal dendrites whereas Arg151Cys and Arg160Trp homozygous strains contained only immature stage I and II melanosomes. Such genetic association studies combined with the functional analysis of MC1R variant alleles in melanocytic cells should provide a link in understanding the association between pigmentary phototypes and skin cancer risk.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.

Representações e práticas educativas de mães referentes a filhos atendidos pelo Conselho Tutelar

Apoio CNPq/Capes-Procad.

Environmental issues and international relations, a new global (dis)order - the role of International Relations in promoting a concerted international system

Is it possible to talk about the rise of a new global (dis)order founded on the challenges posed by environmental issues? Through the review of the state of the art on the subject, this article analyzes the growing importance of the environment, and natural resources in particular, in international relations; and aims to raise awareness among International Relations scholars to the potential positive impact of the development of the discipline in integration with global environmental change studies.

Reshaping European Union development policy: collective choices and the new global order

Abstract The European Union (EU) is one of the world´s leading donors in official development assistance (ODA) to give a strong weight in the relationship with recipient partner countries, in particular with those that are more dependent on it. Besides the material weight of its funding, the EU has retained historical ties and influence in diplomatic, political and economic terms in many of its ODA recipient partner countries (particular in Sub-Saharan Africa). Since the 2000s, the EU development policy has not only undergone major structural changes in its institutional framework but also has started to face a new international aid scenario. This paper explores why a normative-based EU development policy is being challenged by reformed EU institutions and a new global order, and how the EU is attempting to respond to this context in face of the deepest recession since the end of the Second World War.

Higher-order lazy functional slicing

Program slicing is a well known family of techniques intended to identify and isolate code fragments which depend on, or are depended upon, specific program entities. This is particularly useful in the areas of reverse engineering, program understanding, testing and software maintenance. Most slicing methods, and corresponding tools, target either the imperative or the object oriented paradigms, where program slices are computed with respect to a variable or a program statement. Taking a complementary point of view, this paper focuses on the slicing of higher-order functional programs under a lazy evaluation strategy. A prototype of a Haskell slicer, built as proof-of-concept for these ideas, is also introduced