Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

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.

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.

Everyday incivility: towards a benchmark

Commonplace incivility is a topic of longstanding interest within social theory, perhaps best exemplified by Goffman's studies of the interaction order. Nevertheless we know very little about its distribution and expression in everyday life. Current empirical work is dominated by criminological agendas. These tend to focus on more serious and illegal activities rather than minor deviant acts that are simply inconsiderate or rude. The paper reports findings from a focus group study conducted in Melbourne, Australia that set out to benchmark everyday incivilities. The results suggest that perpetrators of incivility have a surprisingly broad social distribution as does the range of locales that might be characterised as 'high risk'. Turning to the work of Putnam and Wolfe, we call for a research focus on low-level incivilities as key symptoms of the state of civic virtue and the strength of moral ties within civil society. Drawing on Virilio, Bauman and Durkheim, it is suggested that the experience of incivility is underpinned by the growth of freedom and movement in contemporary urban settings, and has ambivalent implications that not only invoke boundary maintenance and retreatism, but also offer the possibility for boundary expansion and tolerance of difference.

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.

Processos de exclusão da/na escola no período da Primeira República (1889-1930) no Estado do Espírito Santo

O objetivo desta tese é analisar que práticas de tradução educacional foram feitas em relação às crianças e jovens excluídos da/na escola da Primeira República (1889-1930) no Estado do Espírito Santo. Período este em que a cultura ocidental, mais especificamente a europeia, exercia forte influência nas políticas de regulação e de emancipação do Brasil. Assim constando, na área educacional, muitas das experiências e teorias defendidas e socializadas na Europa foram traduzidas para o Brasil, e por extensão, para o Espírito Santo. Para compreender as traduções na área educacional, situada no contexto da modernidade é que se reportou a Boaventura de Sousa Santos, à luz das ferramentas disponíveis pela Sociologia das Ausências, pela Sociologia das Emergências, bem como o Trabalho de Tradução. A proposta de pesquisa está ancorada numa perspectiva qualitativa de base hermenêutica e, para construir a investigação, foram utilizadas fontes históricas bibliográficas e documentais. As fontes de investigação permitiram explicar parte das possíveis razões para as exclusões da escola ou defesas de segregação (exclusão na escola). Estas exclusões se concentram em torno de cinco tempos: 1909, 1917, 1923, 1924 e 1929. Nos anos de 1909 e 1924, disserta-se pela via educacional, sobre as práticas da área jurídica em relação aos órfãos. A Escola Normal do Espírito Santo, por sua vez, reproduzia a ideia de ordem ao atrelar a Pedagogia à educação cívica. Em 1917, a partir do episódio relativo a uma jovem, associada a um possível caso de loucura/alienação mental, é abordada a influência da área médica na área educacional, no Estado do Espírito Santo. Quanto à década de 20, existiu todo um discurso sobre o estudo da criança, na formação de educadores, como tentativa de apreender a totalidade do ser humano. Algumas práticas de tradução construtivas na área educacional foram evidenciadas, como por exemplo, quando o professor Elpídio Pimentel sugere que os educadores trabalhem com o que o aluno sabe ou poderá aprender. Ao final do trabalho, percebe-se que, muitas exclusões poderiam ter sido evitadas, mas para isso, a sociedade, os educadores teriam que ter adotado uma outra postura em relação às práticas de tradução: talvez uma menos idealizada e que valorizasse o que emergia de potencial nas realidades locais.

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.