Vector bundles on the projective line and finite domination of chain complexes

We present an algebro-geometric approach to a theorem on finite domination of chain complexes over a Laurent polynomial ring. The approach uses extension of chain complexes to sheaves on the projective line, which is governed by a K-theoretical obstruction.

Efficient FPGA Hardware Development: A Multi-Language Approach

This paper presents a multi-language framework to FPGA hardware development which aims to satisfy the dual requirement of high-level hardware design and efficient hardware implementation. The central idea of this framework is the integration of different hardware languages in a way that harnesses the best features of each language. This is illustrated in this paper by the integration of two hardware languages in the form of HIDE: a structured hardware language which provides more abstract and elegant hardware descriptions and compositions than are possible in traditional hardware description languages such as VHDL or Verilog, and Handel-C: an ANSI C-like hardware language which allows software and hardware engineers alike to target FPGAs from high-level algorithmic descriptions. On the one hand, HIDE has proven to be very successful in the description and generation of highly optimised parameterisable FPGA circuits from geometric descriptions. On the other hand, Handel-C has also proven to be very successful in the rapid design and prototyping of FPGA circuits from algorithmic application descriptions. The proposed integrated framework hence harnesses HIDE for the generation of highly optimised circuits for regular parts of algorithms, while Handel-C is used as a top-level design language from which HIDE functionality is dynamically invoked. The overall message of this paper posits that there need not be an exclusive choice between different hardware design flows. Rather, an integrated framework where different design flows can seamlessly interoperate should be adopted. Although the idea might seem simple prima facie, it could have serious implications on the design of future generations of hardware languages.

Geometric bonding effects in the X2A1, A2∑+u, and B2IIg states of Li2F

Published ab-initio and pseudopotential calculations for the dialkali halide systems suggest that the preferred co-linear geometry is for the metal to approach the metal end of the alkali halide. Here, ab-initio calculations on the Li2F system reveal that the well depth on the halide side in this radical is much deeper and is a local saddle-point associated with the ionic non-linear global minima. Although many features of the pseudopotential surfaces are confirmed, significant differences are apparent including the existence of a linear excited state instead of a triangular one, a considerably deeper global minimum some 50% lower in energy and a close approach between the X2A1 and the states, with the minimum 87 kJ mol-1 below the ground state asymptote. All the results can be rationalised as the avoided crossings between a long range, covalent potential dominant within the LiLiF geometry and an ionic state that forms the global minimum. Calculations on the 3rd 2A' potential indicate that even for Li + LiF collisions at ultracold temperatures the collision dynamics could involve as many as three electronic states.

Modeling the geometric characteristics of five-dimensionally woven composites

An analytical modeling approach for the prediction of the geometric characteristics of five-dimensional (5D) woven composites has been formulated. The model is driven by readily available data including the weaving parameters and constituent material properties. The new model calculates the individual proportions of fiber in each direction, areal density, overall fiber volume fraction, and laminate thickness. This information is useful for the engineer in the design and manufacture of 5D woven composites. In addition the present model outputs the mathematical definition of the 5D woven composite unit cell, which could be implemented as the geometric input for a downstream analytical model that is capable of predicting the elastic stiffness of 5D woven composites. Input parameters have been sourced from existing published work and the subsequent predictions made by the model are compared with the available experimental data on 5D woven composites.

Spontaneous spin polarization and charge localization in metal nanowires: the role of a geometric constriction

An idealized jellium model of conducting nanowires with a geometric constriction is investigated by density functional theory (DFT) in the local spin density (LSD) approximation. The results reveal a fascinating variety of spin and charge patterns arising in wires of sufficiently low (r(s) >= 15) average electron density, pinned at the indentation by an apparent attractive interaction with the constriction. The spin-resolved frequency-dependent conductivity shows a marked asymmetry in the two spin channels, reflecting the spontaneous spin polarization around the wire neck. The relevance of the computational results is discussed in relation to the so-called 0.7 anomaly found by experiments in the low-frequency conductivity of nanowires at near-breaking conditions (see 2008 J. Phys.: Condens Matter 20, special issue on the 0.7 anomaly). Although our mean-field approach cannot account for the intrinsic many-body effects underlying the 0.7 anomaly, it still provides a diagnostic tool to predict impending transitions in the electronic structure.

Validation of a passive stereophotogrammetry system for imaging of the breast: A geometric analysis

The overall aim of this study was to assess the accuracy, reproducibility and stability of a high resolution passive stereophotogrammetry system to image a female mannequin torso, to validate measurements made on the textured virtual surface compared with those obtained using manual techniques and to develop an approach to make objective measurements of the female breast. 3D surface imaging was carried out on a textured female torso and measurements made in accordance with the system of mammometrics. Linear errors in measurements were less than 0.5 mm, system calibration produced errors of less than 1.0 mm over 94% over the surface and intra-rater reliability measured by ICC = 0.999. The mean difference between manual and digital curved surface distances was 1.36 mm with maximum and minimum differences of 3.15 mm and 0.02 mm, respectively. The stereophotogrammetry system has been demonstrated to perform accurately and reliably with specific reference to breast assessment. (C) 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

Principal Component Analysis of Wide Area Phasor Measurements for Islanding Detection – A Geometric View

This paper presents a new technique for the detectionof islanding conditions in electrical power systems. This problem isespecially prevalent in systems with significant penetrations of distributedrenewable generation. The proposed technique is based onthe application of principal component analysis (PCA) to data setsof wide-area frequency measurements, recorded by phasor measurementunits. The PCA approach was able to detect islandingaccurately and quickly when compared with conventional RoCoFtechniques, as well as with the frequency difference and change-ofangledifference methods recently proposed in the literature. Thereliability and accuracy of the proposed PCA approach is demonstratedby using a number of test cases, which consider islandingand nonislanding events. The test cases are based on real data,recorded from several phasor measurement units located in theU.K. power system.