Symmetric groups and conjugacy classes

Let S_n be the symmetric group on n-letters. Fix n>5. Given any nontrivial $\alpha,\beta\in S_n$, we prove that the product $\alpha^{S_n}\beta^{S_n}$ of the conjugacy classes $\alpha^{S_n}$ and $\beta^{S_n}$ is never a conjugacy class. Furthermore, if n is not even and $n$ is not a multiple of three, then $\alpha^{S_n}\beta^{S_n}$ is the union of at least three distinct conjugacy classes. We also describe the elements $\alpha,\beta\in S_n$ in the case when $\alpha^{S_n}\beta^{S_n}$ is the union of exactly two distinct conjugacy classes.Comment: 7 page

Spring wheat yield assessment under drought conditions using vegetation health index: case of Canadian prairies

Non-Peer ReviewedAgricultural drought is a major climate concern which occurs frequently on Canadian prairies. It acts negatively on crop production, which directly affects the Canadian economy. The Normalized Difference Vegetation Index (NDVI) has been widely used to assess crop yield losses related to drought events. However, this index suffers from some shortcomings such as the apparent time lag between drought impact due to rainfall deficit and NDVI response. This study was undertaken to investigate the effectiveness of the integrated Vegetation Health Index (iVHI) for the assessment of spring wheat yield across Canadian prairies. A time series of five years from the Advanced Very High Resolution Radiometer (AVHRR) sensor were used to develop a spring wheat yield model for three agroclimatic regions: subarid, semiarid and subhumid. The results demonstrated that spring wheat yield assessment is feasible through the use of iVHI, especially in subarid and semiarid regions where it reached a correlation coefficient of 0.75 and 0.61, respectively. This finding shows that iVHI can be used to estimate spring wheat yield losses due to agricultural drought across the Canadian prairies. However, in subhumid regions where spring wheat growing conditions are favourable because of adequate water supply, the integrated NDVI (iNDVI) outperforms iVHI with a correlation coefficient of 0.44 compared to 0.34. Consequently, to develop an efficient tool, it suggested coupling the iVHI with iNDVI to better estimate spring wheat yield in the Canadian prairies

Diffusion of hydrogen in crystalline silicon

The coefficient of diffusion of hydrogen in crystalline silicon is calculated using tight-binding molecular dynamics. Our results are in good quantitative agreement with an earlier study by Panzarini and Colombo [Phys. Rev. Lett. 73, 1636 (1994)]. However, while our calculations indicate that long jumps dominate over single hops at high temperatures, no abrupt change in the diffusion coefficient can be observed with decreasing temperature. The (classical) Arrhenius diffusion parameters, as a consequence, should extrapolate to low temperatures.Comment: 4 pages, including 5 postscript figures; submitted to Phys. Rev. B Brief Repor

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

An adverbial approach for the formal specification of topological constraints involving regions with broad boundaries

Topological integrity constraints control the topological properties of spatial objects and the validity of their topological relationships in spatial databases. These constraints can be specified by using formal languages such as the spatial extension of the Object Constraint Language (OCL). Spatial OCL allows the expression of topological constraints involving crisp spatial objects. However, topological constraints involving spatial objects with vague shapes (e.g., regions with broad boundaries) are not supported by this language. Shape vagueness requires using appropriate topological operators (e.g., strongly Disjoint, fairly Meet) to specify valid relations between these objects; otherwise, the constraints cannot be respected. This paper addresses the problem of the lack of terminology to express topological constraints involving regions with broad boundaries. We propose an extension of Spatial OCL based on a geometric model for objects with vague shapes and an adverbial approach for topological relations between regions with broad boundaries. This extension of Spatial OCL is then tested on an agricultural database

Virtual prototyping of a semi-active transfemoral prosthetic leg

This article presents a virtual prototyping study of a semi-active lower limb prosthesis to improve the functionality of an amputee during prosthesis–environment interaction for level ground walking. Articulated ankle–foot prosthesis and a single-axis semi-active prosthetic knee with active and passive operating modes were considered. Data for level ground walking were collected using a photogrammetric method in order to develop a base-line simulation model and with the hip kinematics input to verify the proposed design. The simulated results show that the semi-active lower limb prosthesis is able to move efficiently in passive mode, and the activation time of the knee actuator can be reduced by approximately 50%. Therefore, this semi-active system has the potential to reduce the energy consumption of the actuators required during level ground walking and requires less compensation from the amputee due to lower deviation of the vertical excursion of body centre of mass

Spreading continents kick-started plate tectonics

International audienceStresses acting on cold, thick and negatively buoyant oceanic litho- sphere are thought to be crucial to the initiation of subduction and the operation of plate tectonics, which characterizes the present- day geodynamics of the Earth. Because the Earth’s interior was hotter in the Archaean eon, the oceanic crust may have been thicker, thereby making the oceanic lithosphere more buoyant than at present, and whether subduction and plate tectonics occurred during this time is ambiguous, both in the geological record and in geodynamic models. Here we show that because the oceanic crust was thick and buoyant5, early continents may have produced intra-lithospheric gravitational stresses large enough to drive their gravitational spreading, to initiate subduction at their margins and to trigger episodes of subduction. Our model predicts the co-occurrence of deep to progressively shallower mafic volcanics and arc magmatism within continents in a self-consistent geodynamic framework, explaining the enigmatic multimodal volcanism and tectonic record of Archaean cratons. Moreover, our model predicts a petrological stratification and tectonic structure of the sub-continental lithospheric mantle, two predictions that are consistent with xenolith and seismic studies, respectively, and consistent with the existence of a mid-lithospheric seismic discontinuity. The slow gravitational collapse of early continents could have kick-started transient episodes of plate tectonics until, as the Earth’s interior cooled and oceanic lithosphere became heavier, plate tectonics became self-sustaining

The clinical utility of the continuous performance test and objective measures of activity for diagnosing and monitoring ADHD in children: a systematic review

Attention deficit hyperactivity disorder (ADHD) is typically diagnosed using clinical observation and subjective informant reports. Once children commence ADHD medication, robust monitoring is required to detect partial or non-responses. The extent to which neuropsychological continuous performance tests (CPTs) and objective measures of activity can clinically aid the assessment and titration process in ADHD is not fully understood. This review describes the current evidence base for the use of CPTs and objectively measured activity to support the diagnostic procedure and medication management for children with ADHD. Four databases (PsycINFO, Medline, Allied and Complementary Medicine (AMED) and PsycARTICLES) were systematically searched to understand the current evidence base for: (1) the use of CPTs to aid clinical assessment of ADHD; (2) the use of CPTs to aid medication management; (3) the clinical utility of objective measures of activity in ADHD. Sixty relevant articles were identified. The search revealed six commercially available CPTs that had been reported on for their clinical use. There were mixed findings with regard to the use of CPTs to assess and manage medication, with contrasting evidence on their ability to support clinical decision making. There was a strong evidence base for the use of objective measures of activity to aid ADHD/non-ADHD group differentiation, which appears sensitive to medication effects and would also benefit from further research on their clinical utility. The findings suggest that combining CPTs and an objective measure of activity may be particularly useful as a clinical tool and worthy of further pursuit