Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Holocene sediments of Wistari Reef: towards a global quantification of coral reef related neritic sedimentation in the Holocene

Wistari Reef. within the southern Great Barrier Reef. is a shallow coral reef platform featuring a very clearly defined leeward accretionary wedge of carbonate sediments. The total global area of shallowly submerged coral reef has been quantified as 255 000 km(2). The question then becomes: What additional area of sediment of significant thickness is associated with the measured shallow reef areas T At Wistari Reef, the leeward sedimentary wedge has an area and a thickness that are roughly equal to the Holocene sediments that have accumulated on the platform. Several important observations can be made from these data. Firstly. the area of significant neritic carbonate sedimentation ( > 1 m/ka) associated with coral reefs is near 500000 km(2). Secondly, the production rate of neritic carbonates at Wistari Reef is almost 50%, less than the accumulation rate needed to obtain the volume of Holocene reef sediments observed. This implies that both production and accumulation neritic carbonate must have been more than a factor of two higher in the early to mid Holocene. (C) 2001 Elsevier Science B.V. All rights reserved.

A sociolinguistic approach to applied epistemology: Examining technocratic values in global 'knowledge' policy

This special issue presents an excellent opportunity to study applied epistemology in public policy. This is an important task because the arena of public policy is the social domain in which macro conditions for ‘knowledge work’ and ‘knowledge industries’ are defined and created. We argue that knowledge-related public policy has become overly concerned with creating the politico-economic parameters for the commodification of knowledge. Our policy scope is broader than that of Fuller (1988), who emphasizes the need for a social epistemology of science policy. We extend our focus to a range of policy documents that include communications, science, education and innovation policy (collectively called knowledge-related public policy in acknowledgement of the fact that there is no defined policy silo called ‘knowledge policy’), all of which are central to policy concerned with the ‘knowledge economy’ (Rooney and Mandeville, 1998). However, what we will show here is that, as Fuller (1995) argues, ‘knowledge societies’ are not industrial societies permeated by knowledge, but that knowledge societies are permeated by industrial values. Our analysis is informed by an autopoietic perspective. Methodologically, we approach it from a sociolinguistic position that acknowledges the centrality of language to human societies (Graham, 2000). Here, what we call ‘knowledge’ is posited as a social and cognitive relationship between persons operating on and within multiple social and non-social (or, crudely, ‘physical’) environments. Moreover, knowing, we argue, is a sociolinguistically constituted process. Further, we emphasize that the evaluative dimension of language is most salient for analysing contemporary policy discourses about the commercialization of epistemology (Graham, in press). Finally, we provide a discourse analysis of a sample of exemplary texts drawn from a 1.3 million-word corpus of knowledge-related public policy documents that we compiled from local, state, national and supranational legislatures throughout the industrialized world. Our analysis exemplifies a propensity in policy for resorting to technocratic, instrumentalist and anti-intellectual views of knowledge in policy. We argue that what underpins these patterns is a commodity-based conceptualization of knowledge, which is underpinned by an axiology of narrowly economic imperatives at odds with the very nature of knowledge. The commodity view of knowledge, therefore, is flawed in its ignorance of the social systemic properties of ��knowing’.

Integrating the tourism industry: problems and strategies

This paper addresses two interrelated issues in tourism development: horizontal integration within tourism's component sectors and attempts at vertical integration between them. The paper employs a conceptual framework adapted from regulation theory, to assess the dynamics of these processes, particularly in relation to airlines and hotels. Through examining some of the most important examples of both horizontal and vertical integration, it indicates how these have influenced contemporary strategies in the component sectors. The paper goes on to illustrate how trends towards Fordist organization within airlines have conflicted with post-Fordist trends in hotel operations, to undermine attempts at vertical integration across the tourism industry. (C) 2000 Elsevier Science Ltd. All rights reserved.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.