Hook Interpolations

The hook components of $V^{\otimes n}$ interpolate between the symmetric power \sym^n(V) and the exterior power $\wedge^n(V)$. When $V$ is the vector space of $k\times m$ matrices over \bbc, we decompose the hook components into irreducible GL_k(\bbc)\times GL_m(\bbc)-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over \bbc, a bivariate interpolation is presented and studied.Comment: 23 pages; small change

Thirty-five years of computerized cognitive assessment of aging — Where are we now?

Over the past 35 years, the proliferation of technology and the advent of the internet have resulted in many reliable and easy to administer batteries for assessing cognitive function. These approaches have great potential for affecting how the health care system monitors and screens for cognitive changes in the aging population. Here, we review these new technologies with a specific emphasis on what they offer over and above traditional ‘paper-and-pencil’ approaches to assessing cognitive function. Key advantages include fully automated administration and scoring, the interpretation of individual scores within the context of thousands of normative data points, the inclusion of ‘meaningful change’ and ‘validity’ indices based on these large norms, more efficient testing, increased sensitivity, and the possibility of characterising cognition in samples drawn from the general population that may contain hundreds of thousands of test scores. The relationship between these new computerized platforms and existing (and commonly used) paper-and-pencil tests is explored, with a particular emphasis on why computerized tests are particularly advantageous for assessing the cognitive changes associated with aging

Modulatory effect of fluoride and irradiation on rat molar rate of wear

The hypothesis was tested that fluoride (F-) modulates molar wear rate in the irradiated rat and that enamel solubility and dentin hardness are involved in this process. Seventy five 21 day-old rats were divided into 5 groups. Groups received either F-(25 ppm) in the drinking water or irradiation to the head (15 Gy in a single dose), or a combination of the two. The rate of occlusal wear was assessed by computerized planimetry.The amount of wear was significantly higher in the F- and irradiation monotreated rats, while under combined treatment it did nor differ significantly from the control values. Fluoridation or irradiation suppressed enamel solubility, as measured by calcium release in the etchant. Dentin microhardness, expressed in Vickers hardness number, was enhanced after either treatment, but remained unaffected when F- administration preceded irradiation. Enamel solubility and dentin microhardness did not correlate significantly with the rate of occlusal wear.L’hypothèse vérifiée dans cette recherche a été la modulation par le fluoré (F-) de l’usure des molaires du rat irradié et de l’éventuelle contribution de la solubilité de l’émail et de la dureté dentinaire dans ce processus. Soixante-dix rats âgés de 21 jours ont été divisés en 5 groupes. Les groupes ont reçu soit 25ppm F- dans l’eau de boisson, soit une dose unique d’irradiation (15 Gy) dans la sphère cranio-faciale, soit les deux traitements combinés. Le niveau d’usure occlusale des molaires a été déterminée par planimétrie computerisée.La quantité d’usure a été plus prononcée chez les animaux recevant uniquement du F- ou une irradiation tandis que les deux traitements combinés ont été suivis par des valeurs d’usure semblables a celles mesurées chez les témoins. La solubilité de l’émail, établie selon la quantité de calcium présente dans la solution corrosive et exprimée en mg/l Ca+ +, a été réduite par chacun des deux traitements. La dureté de la dentine, exprimée en unités Vickers, a été amplifiée par chaque traitement, restant toutefois inchangée uniquement chez les animaux recevant du F- avant l’irradiation. Les resultats de l’étude corrélative entre l’usure occlusale et la solubilité de l’émail ou la dureté dentinaire n’ont pas atteint des valeurs significatives

Numerical modelling of a dual-rotor marine current turbine in a rectilinear tidal flow

In this study, numerical simulation is used to investigate a counter-rotating dual-rotor marine current turbine (MCT) that is aligned for a rectilinear tidal current. Results of power and thrust coefficients and the mean wake axial velocity are compared with that of the blade element momentum (BEM) method coupled with the Park wake model. For a single-rotor MCT, small discrepancies are observed for front rotor, and larger discrepancies for rear rotor when comparing the CFD and BEM results. The mean axial wake velocity agrees better with the higher turbulence intensity (TI). CFD results shows that the power coefficient (CP ) of rear rotor depends on the ambient turbulence intensity. The maximum CP of dual-rotor turbine is 5% higher than that of just the front rotor. Streamlines show that a large vortex is formed behind the rear rotor. The numerical simulations give more credibility to the BEM Park model, but also points to its sensitivity to the incoming turbulence intensity

A numerical study on the influence of curvature ratio and vegetation density on a partially vegetated U-bend channel flow

Aquatic vegetation dramatically shifts the main flow, secondary flow and turbulent structures in a meandering channel. In this study, hydrodynamics in a bending channel with a vegetation patch (VP) has been numerically studied under the variation of curvature ratios (CRs=0.5, 1.0, 1.5, 2.0) and the vegetation density i.e. Solid Volume Fractions (SVF=1.13%, 4.86%). Both effects on vegetation shear flow, helical flow, bed shear stress and bulk drag coefficients are studied in twelve cases by using Ansys Fluent package. Unsteady Reynolds Averaging Navier-Stokes (URANS) framework coupled with the Reynolds Stress turbulence Model (RSM) and Volume Of Fluid (VOF) approach is successfully applied to predict the entire flow field including multi-circulation cells as well as the free surface. The conclusions are summarized as three points. Firstly, an increase of CR moves the main circulation cell and thalweg's location towards the outer bank, while decreasing the drag coefficients in streamwise and spanwise. However, the CR weakly affects the normalised shear flow velocity profiles and dominant eddy frequencies downstream of the VP. Secondly, the trend of the dominant shedding frequency to fall with the increase of SVF that has been known only for SVF<3.4% is extended up to 10.4%. Furthermore, an opposite trend is found between the frequency and SVF for 10.4%<SVF<20%. Thirdly, a newly proposed patch dimensionless frequency number, , links Stp and SVF, where N is the number of stems in the patch. This number stays almost constant for each case series regardless of the variation of SVF (for SVF<10.4%). We also conclude that is strongly determined by the patch shape factor, mildly influenced by the patch Reynolds number, but it excludes the influence of the SVF and N. The insights from the present study unveil the complicated eco-hydro-morphic interactions among the bio-mass density, turbulent flow and channel meanders’ variation. It provides a better understanding of natural bending river systems’ development and fundamentals for the recovery of urban channel ecosystems by vegetated re-meandering