An alternative proof of the extended Saalschütz summation theorem for the _{r + 3}F_{r + 2}(1) series with applications

A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 2(1) hypergeometric series for the case when r pairs of numeratorial and denominatorial parameters differ by positive integers. This formula represents an extension of the well-known Saalschütz summation formula for a 3F2(1) series. Two applications of this extended summation formula are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde–Chu summation theorem for the 2F1 series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijović & Miller

Higher dimensional quantum communication in a curved spacetime: an efficient simulation of the propagation of the wavefront of a photon

A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channel\~Os tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the propagation photon with an arbitrary complex wavefront in a material with an isotropic but inhomogeneous index of refraction. We simulate the waveform propagation of an optical vortex in a volume holographic element in the paraxial approximation using an operator splitting method. We use this code to analyze an OAM volume-holographic sorter. Furthermore, there are analogue models of the evolution of a wavefront in the curved spacetime environs of the Earth that can be constructed using an optical medium with a given index of refraction. This can lead to a work-bench realization of a satellite HD-QKD system.Comment: 20 pages, 7 figure

Medicine is not science

ABSTRACT: Abstract Most modern knowledge is not science. The physical sciences have successfully validated theories to infer they can be used universally to predict in previously unexperienced circumstances. According to the conventional conception of science such inferences are falsified by a single irregular outcome. And verification is by the scientific method which requires strict regularity of outcome and establishes cause and effect. Medicine, medical research and many “soft” sciences are concerned with individual people in complex heterogeneous populations. These populations cannot be tested to demonstrate strict regularity of outcome in every individual. Neither randomised controlled trials nor observational studies in medicine are science in the conventional conception. Establishing and using medical and other “soft science” theories cannot be scientific. It requires conceptually different means: requiring expert judgement applying all available evidence in the relevant available factual matrix. The practice of medicine is observational. Prediction of outcomes for the individual requires professional expertise applying available medical knowledge and evidence. Expertise in any profession can only be acquired through experience. Prior cases are the fundament of knowledge and expertise in medicine. Case histories, studies and series can provide knowledge of extremely high reliability applicable to establishing reliable general theories and falsifying others. Their collation, study and analysis should be a priority in medicine. Their devaluation as evidence, the failure to apply their lessons, the devaluation of expert professional judgement and the attempt to emulate the scientific method are all historic errors in the theory and practice of modern medicine

Strategies for Parallel Markup

Cross-referenced parallel markup for mathematics allows the combination of both presentation and content representations while associating the components of each. Interesting applications are enabled by such an arrangement, such as interaction with parts of the presentation to manipulate and querying the corresponding content, and enhanced search indexing. Although the idea of such markup is hardly new, effective techniques for creating and manipulating it are more difficult than it appears. Since the structures and tokens in the two formats often do not correspond one-to-one, decisions and heuristics must be developed to determine in which way each component refers to and is referred to by components of the other representation. Conversion between fine and coarse grained parallel markup complicates ID assignments. In this paper, we will describe the techniques developed for \LaTeXML, a \TeX/\LaTeX to XML converter, to create cross-referenced parallel MathML. While we do not yet consider \LaTeXML's content MathML to be useful, the current effort is a step towards that continuing goal

Nuclear Physics on the Light Front

High energy scattering experiments involving nuclei are typically analyzed in terms of light front variables. The desire to provide realistic, relativistic wave functions expressed in terms of these variables led me to try to use light front dynamics to compute nuclear wave functions. The progress is summarized here.Comment: 4 pages, text of presentation made at PANIC9

Propaganda managed democracy: the UK and the lessons of Iraq

How does power shape ideas and ideologies today? Who controls the information on which public discussion rests? How is power used to exclude critical thought in politics, the media, universities, state policy-making? Has neo-liberal globalisation introduced a new era of state duplicity, corporate manipulation of truth and intellectual conformity? Are we entering a new age of unreason? The Socialist Register 2006 examines contemporary public debate and policy-making, scientific and social scientific research, statistics, the media, the business 'community', the World Bank, humanitarian 'aid', the role of the theatre. What standards of intellectual integrity exist today? After postmodernism, is it still possible for truth to prevail over half-truths and lies

Taking the tax temperature in our universities

Results of a comprehensive survey of tax teaching in UK univerisities undertaken for the Chartered Institute of Taxatio