Diameters, distortion and eigenvalues

We study the relation between the diameter, the first positive eigenvalue of the discrete $p$-Laplacian and the $\ell_p$-distortion of a finite graph. We prove an inequality relating these three quantities and apply it to families of Cayley and Schreier graphs. We also show that the $\ell_p$-distortion of Pascal graphs, approximating the Sierpinski gasket, is bounded, which allows to obtain estimates for the convergence to zero of the spectral gap as an application of the main result.Comment: Final version, to appear in the European Journal of Combinatoric

Conformally mapped viscous gravity current

We show how the conformal mapping technique can be applied to analyse specific problems in the context of viscous gravity current theory. We examine the edge of steady thin planar viscous gravity currents in the presence of complex external low Reynolds flows. In addition to the uniform ambient flow we look at the case of viscous gravity currents spreading in positively strained flows and around cylindrical bodies. These external flows exert shear stress on the gravity current, which drives it in the streamwise direction. The idealised conditions are re-created in the laboratory using a Hele–Shaw cell with a point source on the bottom plate where the saline is introduced into the flow. The mapped laboratory results are compared to a known similarity solution and the agreement is good. We conclude by identifying a broad class of viscous gravity current problems where this technique may be applied

Bandwidth Enhancement Technique for Bipolar Single Stage Distributed Amplifier Design

This work reports a novel approach to extending the bandwidth of single stage distributed amplifiers (SSDAs). The three-stepped technique involves scaling down the inductance on the input artificial transmission line (ATL); creating a high frequency resonance peak by the addition of shunt capacitance on the input ATL; and compensating for the resulting increased reflection with adapted negative resistance attenuation compensation techniques. Compared with the inductive-peaked cascode technique applied in the SSDA which currently has the highest reported bandwidth, simulation results, based on full foundry transistor models, predict up to 30% improvement in gain-bandwidth (GBW) performance for the same active device at the same bias. In addition, the reduction in the length of the input ATL effectively reduces transmission line losses, thereby improving the overall gain performance

Advances in Evaluating Tsunami Forces on Coastal Structures

At source, tsunami waves have relatively small wave heights (typically 0.5-2m), but very long wavelengths. As these waves approaches the shoreline and enter the shallower waters, their wavelength reduces and their wave height increases dramatically. The resulting waves can cause violent impacts on infrastructure and structures, and the long wavelengths lead to extensive inundation inland causing destruction over large areas of coast as seen recently in Japan (2011). Clearly there is a need for a systematic analysis of the physics of tsunami flows in and around buildings and the forces and pressures they produce on structures as a function of time. The first steps towards such a study are presented. This paper presents preliminary observations obtained from sets of unique physical experiments designed to study the impact of tsunami-like waves on coastal structures towards the development of tsunami design/assessment guidance

Liquid oxygen/liquid hydrogen boost/vane pump for the advanced orbit transfer vehicles auxiliary propulsion system

A rotating, positive displacement vane pump with an integral boost stage was designed to pump saturated liquid oxygen and liquid hydrogen for auxiliary propulsion system of orbit transfer vehicle. This unit is designed to ingest 10% vapor by volume, contamination free liquid oxygen and liquid hydrogen. The final pump configuration and the predicted performance are included

Advances in Evaluating Tsunami Forces on Coastal Structures

At source, tsunami waves have relatively small wave heights (typically 0.5-2m), but very long wavelengths. As these waves approaches the shoreline and enter the shallower waters, their wavelength reduces and their wave height increases dramatically. The resulting waves can cause violent impacts on infrastructure and structures, and the long wavelengths lead to extensive inundation inland causing destruction over large areas of coast as seen recently in Japan (2011). Clearly there is a need for a systematic analysis of the physics of tsunami flows in and around buildings and the forces and pressures they produce on structures as a function of time. The first steps towards such a study are presented. This paper presents preliminary observations obtained from sets of unique physical experiments designed to study the impact of tsunami-like waves on coastal structures towards the development of tsunami design/assessment guidance

Extended Bell and Stirling numbers from hypergeometric exponentiation

Exponentiating the hypergeometric series 0FL(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences bL(n), n = 0,1,2,.... For L >= 0, the bL(n)'s are generalizations of the conventional Bell numbers, b0(n). The corresponding associated Stirling numbers of the second kind are also investigated. For L = 1 one can give a combinatorial interpretation of the numbers b1(n) and of some Stirling numbers associated with them. We also consider the L>1 analogues of Bell numbers for restricted partitions

Nutritional status and sociodemographic characteristics of ‘urban poor’ school children in Onitsha, Southeast Nigeria

Background: The neglect of the health and nutritional status of school aged children has adverse consequences on their long term cognition and survival. Sequel to emerging issues on urbanization and the health ofschool children, this study focused on the nutritional status and sociodemographic characteristics of ‘urban poor’ school children inOnitsha, a major city in South East Nigeria.Objectives: The study was aimed at determining the nutritional status and evaluating the effect of certain sociodemographic factors on the nutritional status of ‘urban poor’ public primary school children in Onitsha, South East NigeriaMethod: This was a cross sectional study of 788 children aged 6 to 12 years, randomly selected from 12 public primary schools in Onitsha metropolis. Their anthropometric measures were used to determine their nutritional status. Data on their sociodemographic characteristics was  obtained from their parents or caregivers using interviewer administered standardized questionnaires. Analysis was done using Microsoft Office Excel2007, SPSS version 17 and Epiinfo version 3.5.1 software packagesResults: Stunting was the predominant form of under nutrition with ahigher prevalence in the slum resident children. Greater than 60% ofall the children studied were from large families with more than 4 children. Family size, however, age and gender were not significantly associated with the nutritional status of the children. Relatively though, a greater  percentage of the stunted children were from large families.Conclusion: The nutritional status of ‘urban poor’ school children especially in slums in Onitsha is suboptimal compared with their counterparts in developed countries of the world. There is need for regional studies of children with similar characteristics who should be considered when  favourable health policies are being made for children

Ladder operators and endomorphisms in combinatorial Physics

Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of Combinatorics. These may be expressed in terms of infinite, but row-finite, matrices, which may also be considered as endomorphisms of C[x]. This leads us to consider endomorphisms in more general spaces, and these in turn may be expressed in terms of generalizations of the ladder-operators familiar in physics