1,214 research outputs found

    A Study on Set-Graphs

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    A \textit{primitive hole} of a graph GG is a cycle of length 33 in GG. The number of primitive holes in a given graph GG is called the primitive hole number of that graph GG. The primitive degree of a vertex vv of a given graph GG is the number of primitive holes incident on the vertex vv. In this paper, we introduce the notion of set-graphs and study the properties and characteristics of set-graphs. We also check the primitive hole number and primitive degree of set-graphs. Interesting introductory results on the nature of order of set-graphs, degree of the vertices corresponding to subsets of equal cardinality, the number of largest complete subgraphs in a set-graph etc. are discussed in this study. A recursive formula to determine the primitive hole number of a set-graph is also derived in this paper.Comment: 11 pages, 1 figure, submitte

    Forward scattering in two-beam laser interferometry

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    A fractional error as large as 25 pm mm(-1) at the zero optical-path difference has been observed in an optical interferometer measuring the displacement of an x-ray interferometer used to determine the lattice parameter of silicon. Detailed investigations have brought to light that the error was caused by light forward-scattered from the beam feeding the interferometer. This paper reports on the impact of forward-scattered light on the accuracy of two-beam optical interferometry applied to length metrology, and supplies a model capable of explaining the observed error

    Wavefront errors in a two-beam interferometer

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    This paper deals with the impact of wavefront errors, due to the optical aberrations of a two-beam interferometer, on the period of the travelling fringe observed by integrating the interference pattern. A Monte Carlo simulation of the interferometer operation showed that the fringe-period estimate is unbiased if evaluated on the basis of the angular spectrum of the beam entering the interferometer, but the wavefront errors increase the uncertainty

    Bayesian Probabilities and the Histories Algebra

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    We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200

    A New Approach for Analytic Amplitude Calculations

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    We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz scalars. The new approach renders the symbolic calculation of some complicated physical processes more feasible and easier, especially with the assistance of algebra manipulating codes for computer.Comment: LaTex, no figure, to appear in PR
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