18,623 research outputs found
An Analysis of North American Archival Research Articles
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
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 Symbol with One Small Angular Momentum
We derive an asymptotic formula for the Wigner symbol, in the limit of
one small and 11 large angular momenta. There are two kinds of asymptotic
formulas for the 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 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 symbol with small and large angular momenta. When applying the same
technique to the 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
symbol is expressed in terms of the vector diagram for a symbol. This
illustrates a general geometric connection between asymptotic limits of the
various symbols. This work contributes the first known asymptotic formula
for the symbol to the quantum theory of angular momentum, and serves as a
basis for finding asymptotic formulas for the Wigner symbol with two
small angular momenta.Comment: 15 pages, 14 figure
The Physical State of the Intergalactic Medium or Can We Measure Y?
We present an argument for a {\it lower limit} to the Compton- 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, , will produce a y\go
10^{-6}. This lower limit on 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 -Symbol with Small Quantum Numbers
We present new asymptotic formulas for the Wigner -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 -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 -symbol with two,
three, and four small quantum numbers are based on the geometric figures of the
-, -, and -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 -Symbol with Small and Large Angular Momenta
We derive a new asymptotic formula for the Wigner -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 -symbols.
We display without proof some new asymptotic formulas for the -symbol and
the -symbol in the appendices. This work contributes a new asymptotic
formula of the Wigner -symbol to the quantum theory of angular momentum,
and serves as an example of a new general method for deriving asymptotic
formulas for -symbols.Comment: 18 pages, 16 figures. To appear in Phys. Rev.
The rigid body dynamics: classical and algebro-geometric integration
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 -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 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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