Herbrand's Theorem and Equational Reasoning: Problems and Solutions

The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the so-called simultaneous rigid E-unification problem. In the second part, we survey recent result on the simultaneous rigid E-unification problem.

Oral zinc sulfate solutions inhibit sweet taste perception

We investigated the ability of zinc sulfate (5, 25, 50 mM) to inhibit the sweetness of 12 chemically diverse sweeteners, which were all intensity matched to 300 mM sucrose [800 mM glucose, 475 mM fructose, 3.25 mM aspartame, 3.5 mM saccharin, 12 mM sodium cyclamate, 14 mM acesulfame-K, 1.04 M sorbitol, 0.629 mM sucralose, 0.375 mM neohesperidin dihydrochalcone (NHDC), 1.5 mM stevioside and 0.0163 mM thaumatin]. Zinc sulfate inhibited the sweetness of most compounds in a concentration dependent manner, peaking with 80% inhibition by 50 mM. Curiously, zinc sulfate never inhibited the sweetness of Na-cyclamate. This suggests that Na-cyclamate may access a sweet taste mechanism that is different from the other sweeteners, which were inhibited uniformly (except thaumatin) at every concentration of zinc sulfate. We hypothesize that this set of compounds either accesses a single receptor or multiple receptors that are inhibited equally by zinc sulfate at each concentration.

Applying external solutions to organizational development : elearning as a platform for internal growth

Innovations in technology have facilitated eLearning process development, bringing significant impact into education. eLearning is not simply putting study materials online on the Web, nor is it a substitute for traditional classroom teaching (KPMG, 2002). Businesses worldwide have been using eLearning as a facilitator in organisational development through knowledge sharing, especially in the area of web based training and project management. eLearning has also become a large area of potential business for many organisations. In this study, we explore how eLearning has helped an organisation based in India – Tata Interactive Systems (part of TATA conglomerate), which provides eLearning solutions for businesses locally and globally. In this single case study, we explored how the organisation has not only utilised eLearning as an internal development process, but also successfully converted this learning into business opportunities for itself. To study the development process, we have applied the process theories of Van De Ven and Poole (1995).

Similarity solutions of partial differential equations using DESOLV

We present and describe new reduction routines included in DESOLV which, in many cases, may allow the complete automation of the determination of similarity solutions of partial differential equations.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile.

We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.