Hermeneutics, accreting receptions, hypermedia: A tool for reference versus a tool for instruction

We provide a select overview of tools supporting traditional Jewish learning. Then we go on to discuss our own HyperJoseph/HyperIsaac project in instructional hypermedia. Its application is to teaching, teacher training, and self-instruction in given Bible passages. The treatment of two narratives has been developed thus far. The tool enables an analysis of the text in several respects: linguistic, narratological, etc. Moreover, the Scriptures' focality throughout the cultural history makes this domain of application particularly challenging, in that there is a requirement for the tool to encompass the accretion of receptions in the cultural repertoire, i.e., several layers of textual traditions—either hermeneutic (i.e., interpretive), or appropriations—related to the given core passage, thus including "secondary" texts (i.e., such that are responding or derivative) from as disparate realms as Roman-age and later homiletics, Medieval and later commentaries or supercommentaries, literary appropriations, references to the arts and modern scholarship, etc. in particular, the Midrash (homiletic expansions) is adept at narrative gap filling, so the narratives mushroom at the interstices where the primary text is silent. The genealogy of the project is rooted in Weiss' index of novelist Agnon's writings, which was eventually upgraded into a hypertextual tool, including Agnon's full-text and ancillary materials. Those early tools being intended primarily for reference and research-support in literary studies, the Agnon hypertext system was initially emulated in the conception of HyperJoseph, which is applied to the Joseph story from Genesis. Then, the transition from a tool for reference to an instructional tool required a thorough reconception in an educational perspective, which led to HyperIsaac, on the sacrifice of Isaac, and to a redesign and upgrade of HyperJoseph as patterned after HyperIsaac.

Tree species-area and species-diameter relationships at three lowland rain forest sites in Sumatra

Data from three forest sites in Sumatra (Batang Ule, Pasirmayang and Tebopandak) have been analysed and compared for the effects of sample area cut-off, and tree diameter cut-off. An 'extended inverted exponential model' is shown to be well suited to fitting tree-species-area curves. The model yields species carrying capacities of 680 for Batang Ule, 380 species for Pasirmayang, and 35 for Tebopandak (tree diameter >10cm). It would seem that in terms of species carrying capacity, Tebopandak and Pasirmayang are rather similar, and both less diverse than the hilly Batang Ule site. In terms of conservation policy, this would mean that rather more emphasis should be put on conserving hilly sites on a granite substratum. For Pasirmayang with tree diameter >3cm, the asymptotic species number estimate is 567, considerably higher than the estimate of 387 species for trees with diameter >10cm. It is clear that the diameter cut-off has a major impact on the estimate of the species carrying capacity. A conservative estimate of the total number of tree species in the Pasirmayang region is 632 species! In sampling exercises, the diameter cut-off should not be chosen lightly, and it may be worth adopting field sampling procedures which involve some subsampling of the primary sample area, where the diameter cut-off is set much lower than in the primary plots.

A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier--Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to flow through a constricted channel, and results are obtained for Reynolds numbers, based on half the flow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 (1980), pp. 393-414] and the asymptotic theory of Smith [J. Fluid Mech., 90 (1979), pp. 725-754].

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.