Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.Comment: V1: 25 pages, 6 figures; V2: 22 pages, 5 figures. The revised version is shortened and the arguments streamlined. Minor changes in notation and figures. This version matches the published versio

Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input

PROBLEM OF NESTERENKO AND METHOD OF BERNIK

In this article we prove that, if integer polynomial Psatisfies |P(w)|p< H−w, then for w > 2n− 2 and sufficiently large H the root belongs to the field of p-adic numbers.In this article we prove that, if integer polynomial Psatisfies |P(w)|p< H−w, then for  > 2n− 2 and sufficiently large H the root belongs to the field of p-adic numbers

Fluoride-containing bioactive glasses: Effect of glass design and structure on degradation, pH and apatite formation in simulated body fluid

NOTICE: this is the author’s version of a work that was accepted for publication in Acta Biomaterialia. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Acta Biomaterialia, [VOL 6, ISSUE 8, (2010)] DOI: 10.1016/j.actbio.2010.01.04

Different Approaches to Managerial Support for Flexible Working: Implications for Public Sector Employee Well-Being

Improving well-being is an important human resource management issue within public sector organizations as it is linked with improved employee and organizational outcomes. A key antecedent to employee well-being is work–life balance, which can be supported or impeded by flexible working. The extent to which flexible working supports work–life balance and, ultimately, well-being depends on how flexible working is implemented, where managers play a central role. Managers can enable work–life balance by providing employees with work-family-specific support, which incorporates a range of behaviors, including facilitating access to flexible working. However, research to date says little about how and why managers engage in these behaviors and whether this differs within the same organizational context. This article addresses this gap, presenting four approaches to managerial support for flexible working: unconditional support, performance contingent support, no support, and support based upon the approval of others (transfer responsibility). It explores the reasons for each approach through the lens of Conservation of Resources (COR) theory. It suggests that different approaches create the potential for employee well-being to vary considerably within the same organizational and team context. These findings inform how to support and manage flexible working arrangements in ways that optimize well-being in the public sector

Charm and Bottom Semileptonic Decays

We review the present status of theoretical attempts to calculate the semileptonic charm and bottom decays and then present a calculation of these decays in the light--front frame at the kinematic point $q^2=0$. This allows us to evaluate the form factors at the same value of $q^2$, even though the allowed kinematic ranges for charm and bottom decays are very different. Also, at this kinematic point the decay is given in terms of only one form factor $A_{0}(0)$. For the ratio of the decay rates given by the E653 collaboration we show that the determination of the ratio of the Cabibbo--Kobayashi--Maskawa (CKM) matrix elements is consistent with that obtained from the unitarity constraint. At present, though, the unitarity method still has greater accuracy. Since comparisons of the semileptonic decays into $\rho$ and either electrons or muons will be available soon from the E791 Fermilab experiment, we also look at the massive muon case. We show that for a range of $q^2$ the $SU(3)_F$ symmetry breaking is small even though the contributions of the various helicity amplitudes becomes more complicated. For $B$ decays, the decay $B \rightarrow K^{*} \ell \bar{\ell}$ at $q^2=0$ involves an extra form factor coming from the photon contribution and so is not amenable to the same kind of analysis, leaving only the decay $B \rightarrow K^{*}\nu \bar{\nu}$ as a possibility. As the mass of the decaying particle increases we note that the $SU(3)$ symmetry becomes badly broken at $q^2=0$.Comment: Latex, 19 pages, two figures are attached, a minor change in the manuscript related to thi

Optical energies of AllnN epilayers

Optical energy gaps are measured for high-quality Al1−xInxN-on-GaN epilayers with a range of compositions around the lattice match point using photoluminescence and photoluminescence excitation spectroscopy. These data are combined with structural data to determine the compositional dependence of emission and absorption energies. The trend indicates a very large bowing parameter of 6 eV and differences with earlier reports are discussed. Very large Stokes' shifts of 0.4-0.8 eV are observed in the composition range 0.13<x<0.24, increasing approximately linearly with InN fraction despite the change of sign of the piezoelectric fiel

Improving bank erosion modelling at catchment scale by incorporating temporal and spatial variability

Bank erosion can contribute a significant portion of the sediment budget within temperate catchments, yet few catchment scale models include an explicit representation of bank erosion processes. Furthermore, representation is often simplistic resulting in an inability to capture realistic spatial and temporal variability in simulated bank erosion. In this study, the sediment component of the catchment scale model SHETRAN is developed to incorporate key factors influencing the spatio-temporal rate of bank erosion, due to the effects of channel sinuosity and channel bank vegetation. The model is applied to the Eden catchment, north-west England, and validated using data derived from a GIS methodology. The developed model simulates magnitudes of total catchment annual bank erosion (617 - 4063 t yr-1) within the range of observed values (211 - 4426 t yr-1). Additionally the model provides both greater inter-annual and spatial variability of bank eroded sediment generation when compared with the basic model, and indicates a potential 61% increase of bank eroded sediment as a result of temporal flood clustering. The approach developed within this study can be used within a number of distributed hydrologic models and has general applicability to temperate catchments, yet further development of model representation of bank erosion processes is required