18,623 research outputs found

    An Analysis of North American Archival Research Articles

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111827/1/J24 Conway Archival R&D 2013.pdfDescription of J24 Conway Archival R&D 2013.pdf : Main articl

    Systems of Hess-Appel'rot type

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    We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

    Semiclassical Analysis of the Wigner 12j12j Symbol with One Small Angular Momentum

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    We derive an asymptotic formula for the Wigner 12j12j symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the 12j12j symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner 9j9j symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave-functions to derive asymptotic formulas for the 9j9j symbol with small and large angular momenta. When applying the same technique to the 12j12j symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the 12j12j symbol is expressed in terms of the vector diagram for a 9j9j symbol. This illustrates a general geometric connection between asymptotic limits of the various 3nj3nj symbols. This work contributes the first known asymptotic formula for the 12j12j symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner 15j15j symbol with two small angular momenta.Comment: 15 pages, 14 figure

    The Physical State of the Intergalactic Medium or Can We Measure Y?

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    We present an argument for a {\it lower limit} to the Compton-yy parameter describing spectral distortions of the cosmic microwave background (CMB). The absence of a detectable Gunn-Peterson signal in the spectra of high redshift quasars demands a high ionization state of the intergalactic medium (IGM). Given an ionizing flux at the lower end of the range indicated by the proximity effect, an IGM representing a significant fraction of the nucleosynthesis-predicted baryon density must be heated by sources other than the photon flux to a temperature \go {\rm few} \times 10^5\, K. Such a gas at the redshift of the highest observed quasars, z∼5z\sim 5, will produce a y\go 10^{-6}. This lower limit on yy rises if the Universe is open, if there is a cosmological constant, or if one adopts an IGM with a density larger than the prediction of standard Big Bang nucleosynthesis.Comment: Proceedings of `Unveiling the Cosmic Infrared Background', April 23-25, 1995, Maryland. Self-unpacking uuencoded, compressed tar file with two figures include

    Asymptotic Limits of the Wigner 15J15J-Symbol with Small Quantum Numbers

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    We present new asymptotic formulas for the Wigner 15j15j-symbol with two, three, or four small quantum numbers, and provide numerical evidence of their validity. These formulas are of the WKB form and are of a similar nature as the Ponzano-Regge formula for the Wigner 6j6j-symbol. They are expressed in terms of edge lengths and angles of geometrical figures associated with angular momentum vectors. In particular, the formulas for the 15j15j-symbol with two, three, and four small quantum numbers are based on the geometric figures of the 9j9j-, 6j6j-, and 3j3j-symbols, respectively, The geometric nature of these new asymptotic formulas pave the way for further analysis of the semiclassical limits of vertex amplitudes in loop quantum gravity models.Comment: 13 pages, 8 figure

    Semiclassical Analysis of the Wigner 9J9J-Symbol with Small and Large Angular Momenta

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    We derive a new asymptotic formula for the Wigner 9j9j-symbol, in the limit of one small and eight large angular momenta, using a novel gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations. Our factorization eliminates the geometric phases completely, using gauge-invariant non-canonical coordinates, parallel transports of spinors, and quantum rotation matrices. Our derivation generalizes to higher 3nj3nj-symbols. We display without proof some new asymptotic formulas for the 12j12j-symbol and the 15j15j-symbol in the appendices. This work contributes a new asymptotic formula of the Wigner 9j9j-symbol to the quantum theory of angular momentum, and serves as an example of a new general method for deriving asymptotic formulas for 3nj3nj-symbols.Comment: 18 pages, 16 figures. To appear in Phys. Rev.

    The rigid body dynamics: classical and algebro-geometric integration

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    The basic notion for a motion of a heavy rigid body fixed at a point in three-dimensional space as well as its higher-dimensional generalizations are presented. On a basis of Lax representation, the algebro-geometric integration procedure for one of the classical cases of motion of three-dimensional rigid body - the Hess-Appel'rot system is given. The classical integration in Hess coordinates is presented also. For higher-dimensional generalizations, the special attention is paid in dimension four. The L-A pairs and the classical integration procedures for completely integrable four-dimensional rigid body so called the Lagrange bitop as well as for four-dimensional generalization of Hess-Appel'rot system are given. An nn-dimensional generalization of the Hess-Appel'rot system is also presented and its Lax representation is given. Starting from another Lax representation for the Hess-Appel'rot system, a family of dynamical systems on e(3)e(3) is constructed. For five cases from the family, the classical and algebro-geometric integration procedures are presented. The four-dimensional generalizations for the Kirchhoff and the Chaplygin cases of motion of rigid body in ideal fluid are defined. The results presented in the paper are part of results obtained in last decade.Comment: Zb. Rad.(Beogr.), 16(24), 2013 (accepted for publication); 43 page
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