Generalized honeycomb torus is Hamiltonian

Generalized honeycomb torus is a candidate for interconnection network architectures, which includes honeycomb torus, honeycomb rectangular torus, and honeycomb parallelogramic torus as special cases. Existence of Hamiltonian cycle is a basic requirement for interconnection networks since it helps map a "token ring" parallel algorithm onto the associated network in an efficient way. Cho and Hsu [Inform. Process. Lett. 86 (4) (2003) 185-190] speculated that every generalized honeycomb torus is Hamiltonian. In this paper, we have proved this conjecture. (C) 2004 Elsevier B.V. All rights reserved.

Diameter of parallelogramic honeycomb torus

The determination of the diameter of an interconnection network is essential in evaluating the performance of the network. Parallelogramic honeycomb torus is an attractive alternative to classical torus network due to smaller vertex degree, and hence, lower implementation cost. In this paper, we present the expression for the diameter of a parallelogramic, honeycomb torus, which extends a known result about rhombic: honeycomb torus. (c) 2005 Elsevier Ltd. All rights reserved.

Stability of stationary solutions of the forced Navier-Stokes equations on the two-torus

We study the linear and nonlinear stability of stationary solutions of the forced two-dimensional Navier-Stokes equations on the domain [0,2π]x[0,2π/α], where α ϵ(0,1], with doubly periodic boundary conditions. For the linear problem we employ the classical energy{enstrophy argument to derive some fundamental properties of unstable eigenmodes. From this it is shown that forces of pure χ2-modes having wavelengths greater than 2π do not give rise to linear instability of the corresponding primary stationary solutions. For the nonlinear problem, we prove the equivalence of nonlinear stability with respect to the energy and enstrophy norms. This equivalence is then applied to derive optimal conditions for nonlinear stability, including both the high-and low-Reynolds-number limits.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Effect of ENSO phase on large-scale snow water equivalent distribution in a GCM

Understanding links between the El Nino-Southern Oscillation (ENSO) and snow would be useful for seasonal forecasting, but also for understanding natural variability and interpreting climate change predictions. Here, a 545-year run of the general circulation model HadCM3, with prescribed external forcings and fixed greenhouse gas concentrations, is used to explore the impact of ENSO on snow water equivalent (SWE) anomalies. In North America, positive ENSO events reduce the mean SWE and skew the distribution towards lower values, and vice versa during negative ENSO events. This is associated with a dipole SWE anomaly structure, with anomalies of opposite sign centered in western Canada and the central United States. In Eurasia, warm episodes lead to a more positively skewed distribution and the mean SWE is raised. Again, the opposite effect is seen during cold episodes. In Eurasia the largest anomalies are concentrated in the Himalayas. These correlations with February SWE distribution are seen to exist from the previous June-July-August (JJA) ENSO index onwards, and are weakly detected in 50-year subsections of the control run, but only a shifted North American response can be detected in the anaylsis of 40 years of ERA40 reanalysis data. The ENSO signal in SWE from the long run could still contribute to regional predictions although it would be a weak indicator only

Tin and mercury

This chapter contains sections titled: Introduction Geogenic Occurrence Sources of Soil Contamination Chemical Behaviour in Soils Risks from Tin and Mercury in Soils References

Global estimates of snow water equivalent from passive microwave instruments: history, challenges and future developments

Snow properties have been retrieved from satellite data for many decades. While snow extent is generally felt to be obtained reliably from visible-band data, there is less confidence in the measurements of snow mass or water equivalent derived from passive microwave instruments. This paper briefly reviews historical passive microwave instruments and products, and compares the large-scale patterns from these sources to those of general circulation models and leading reanalysis products. Differences are seen to be large between the datasets, particularly over Siberia. A better understanding of the errors in both the model-based and measurement-based datasets is required to exploit both fully. Techniques to apply to the satellite measurements for improved large-scale snow data are suggested.

Snow products for assimilation and verification

Snow is an important component of the land surface, and the choice of products for assimilation or verification can have a large impact on the surface analysis. This paper introduces the many sources of snow data that are currently available, both in situ and from remote sensing from space, along with some recent developments. Snow extent products are derived from the biggest range of sensors and are the most widely used, while information on snow mass from space is still too error-prone to be used successfully in assimilation schemes.

A 'Kimberley protest': diamond mining, export sanctions, and poverty in Awatia, Ghana

The temporary suspension of diamond exports in Ghana in 2006 and 2007 is arguably the most significant move to address mounting criticisms of the Kimberley Process Certification Scheme (KPCS), an international initiative aimed at stemming the flow of rough diamonds used to finance wars. The ban, which took effect in November 2006, was much praised, particularly in civil society circles, where it continues to be seen as a genuine effort to prevent the smuggling of ‘conflict diamonds’. At the time, Ghana was accused of harbouring stones originating from rebel-held territories in neighbouring Côte d’Ivoire. No evidence was found in support of the case that it was a repository for ‘conflict diamonds’, however, and exports resumed early in March 2007. This article examines the context for the accusations of Ghana’s implication in the smuggling of illicit diamonds, and draws on recent fieldwork to explain how the suspension has affected Akwatia, the country’s main diamondiferous area. The actions taken raise important questions about how suspected violators – particularly smaller diamond-producing nations – of the KPCS should be handled, and underscore how global compacts can have a host of negative repercussions at the village level.

Preparation of (–)-epigallocatechin gallate from commercial green tea by caffeine precipitation and solvent partition

A method has been developed which enables the easy and inexpensive preparation of gram quantities of (–)-epigallocatechin gallate from green tea (Camellia sinensis). A decaffeinated aqueous brew of commercial green tea is treated with caffeine (30 m ). The precipitate is redissolved after decaffeination with chloroform and further purified by solvent partition with ethyl hexanoate and propyl acetate. Commercial leaf (25 g) yields 400 mg (–)-epigallocatechin gallate at better than 80% purity, as judged by reversed phase HPLC.