On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Unified modified divided difference implementation of Adams and BDF formulas /

"March 1980."

Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Research Ethics in Divided and Violent Societies: Seizing the Ethical Opportunity

This chapter explores how to conduct social research in divided and violent societies by developing the concept of the ‘ethical opportunity’. The ‘ethical opportunity’ is situated in a brief discussion of ‘action’ and feminist approaches to research. It argues that seizing the ethical opportunity requires researchers to: plan for their personal safety, plan for participants’ personal safety and plan how they will communicate and disseminate their results. It draws on the author’s personal experience researching in South Africa, Zimbabwe and Northern Ireland, concluding that it is in the communication and dissemination phase that researchers’ hopes for ‘making a difference’ may be realised or dashed. It cautions would-be researchers to manage their own – and research participants’ – expectations about what social research can achieve. Its effects may not often be as transforming and liberating as idealistic researchers hope for, but that should not dissuade them from striving towards those ends.

Joining together or pushing apart? Building relations and exploring difference through shared education in Northern Ireland

In divided societies, the promotion of cross-cultural contact through the education system has been central to efforts to improve intergroup relations. This approach is informed by an understanding of the contact hypothesis, which suggests that positive contact with a member of a different group should contribute to improvements in attitudes towards the group as a whole. While a substantial body of research provides support for contact theory, critics have argued that its emphasis on harmonious encounters can result in the neglect of group differences and associated issues of conflict and discrimination during contact. The research discussed in this article explores this tension with reference to two shared education projects in Northern Ireland. Research data, gathered primarily through interviews with pupils, confirms that divisive issues are rarely addressed during contact and explores several influences on this: the nature of pupils’ relationships, the programme structure, and the prevailing social norms of avoidance.

Recognising difference while promoting cohesion: the role of collaborative networks in education

The chapter outlines various approaches taken to the challenge of divided societies through education systems and links this to debates on political approaches to conflict resolution in Northern Ireland. The education debate has structural and affective components, while the political debate revolves around the privileging of identity or commonality. Applying the principle of recognition and the importance of tolerance is seen to provide a range of policy options, but the evidence of education interventions in Northern Ireland does not highlight any one policy option as the most effective, nor did the end of the violent conflict produce a new consensus on a way forward. The chapter argues that a key additional element to effective practice might be provided through the promotion of shared education through collaborative networks of schools which allows for the continued operation of separate schools while promoting an integrated experience for pupils and teachers.

Embracing difference and the deferral of self-government: a critical analysis of the framing and practice of contemporary peace building

This thesis analyses how dominant policy approaches to peacebuilding have moved away from a single and universalised understanding of peace to be achieved through a top-down strategy of democratisation and economic liberalisation, prevalent at the beginning of 1990s. Instead, throughout the 2000s, peacebuilders have increasingly adopted a commitment to cultivating a bottom-up and hybrid peace building process that is context-sensitive and intended to be more respectful of the needs and values of post-war societies. The projects of statebuilding in Kosovo and, to a lesser extent, in Bosnia are examined to illustrate the shift. By capturing this shift, I seek to argue that contemporary practitioners of peace are sharing the sensibility of the theoretical critics of liberalism. These critics have long contended that post-war societies cannot be governed from ‘above’ and have advocated the adoption of a bottom-up approach to peacebuilding. Now, both peace practitioners and their critics share the tendency to embrace difference in peacebuilding operations, but this shift has failed to address meaningfully the problems and concerns of post-conflict societies. The conclusion of this research is that, drawing on the assumption that these societies are not capable of undertaking sovereign acts because of their problematic inter-subjective frames, the discourses of peacebuilding (in policy-making and academic critique) have increasingly legitimised an open-ended role of interference by external agencies, which now operate from ‘below’. Peacebuilding has turned into a long-term process, in which international and local actors engage relationally in the search for ever-more emancipatory hybrid outcomes, but in which self-government and self-determination are constantly deferred. Processes of emphasising difference have thus denied the political autonomy of post-war societies and have continuously questioned the political and human equality of these populations in a hierarchically divided world.

Families divided : culture and control in small family business

In this article, we explore the dynamics of control, compliance and resistance using two case studies where ‘family’ has symbolic, material and ideological significance. While the ‘family’ metaphor is often invoked to suggest a normative unity and integration in large organizations, we investigate the use of shared understandings of divisions (Parker 1995) and difference, as well as unity and similarity, in constituting organizational culture in two small family-owned firms. Diverging from mainstream family business research, we adopt a critical and interpretative approach that incorporates employee perspectives and explores how forms of control and resistance need to be understood in relation to their local contexts. We also argue that organization studies could benefit from revisiting progressive assumptions that equate developments in forms of organization with forms of organizational control.

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Genetic trends in the expected progeny difference of the asymptotic weight of Nelore females

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

Combined training (aerobic plus strength) potentiates a reduction in body fat but demonstrates no difference on the lipid profile in postmenopausal women when compared to aerobic training with a similar training load

The aim of this study was to verify the effects of aerobic and combined training on the body composition and lipid profile of obese postmenopausal women and to analyze which of these models is more effective after equalizing the training load. Sixty five postmenopausal women (age=61.0±6.3 years) were divided into three groups: Aerobic Training (AT,n= 15), Combined Training (CT,[strength+aerobic],n=32) and control group (CG,n=18). Their body composition: upper body fat (TF), fat mass (FM), percentage of fat mass and fat free mass (FFM) were estimated by DXA. The lipid profile, total cholesterol, HDL-cholesterol and LDL-cholesterol were assessed. There was a statistically significant difference in the TF (AT= -4.4 %, CT= -4.4%, and CG= 1.0%, p= 0.001) and FFM (AT= 1.7%, CT= 2.6%, and CG= -1.4%, p= 0.0001) between the experimental and the control groups. Regarding the percentage of body fat, there was a statistically significant difference only between the CT and CG groups (AT= -2.8%, CT= -3.9% and CG= 0.31%, p= 0.004). When training loads were equalized, the aerobic and combined training decreased core fat and increased fat-free mass, but only the combined training potentiated a reduction in percentage of body fat in obese postmenopausal women after the training program. HDL-c levels increased in the combined group and the chol/HDL ratio (atherogenic index) decreased in the aerobic group, however, there were no significant differences between the intervention programs. Taken together, both the exercise training programs were effective for improving body composition and inducing an anti-atherogenic status.

A Divided City in a Common Market: EU Citizenship and Everyday Instrumentalities on the Polish-German Border

Based on an ethnographic case study in the border cities of Frankfurt (Oder), Germany and Słubice, Poland, this article explores the construction and maintenance of ethnic difference within the transnational economic and social spaces created by the European Union's common market. Through an examination of three domains of cross-border citizenship practice - shopping and consumption, housing and work - this article argues that even as the European Union deploys policies aimed at creating de-territorialised and supranational forms of identity and citizenship, economic asymmetries and hierarchies of value embedded within these policies grant rights differentially in ways that continue to be linked to ethnicity and nationality.