1,819 research outputs found
Fixed point data of finite groups acting on 3-manifolds
We consider fully effective orientation-preserving smooth actions of a given
finite group G on smooth, closed, oriented 3-manifolds M. We investigate the
relations that necessarily hold between the numbers of fixed points of various
non-cyclic subgroups. In Section 2, we show that all such relations are in fact
equations mod 2, and we explain how the number of independent equations yields
information concerning low-dimensional equivariant cobordism groups. Moreover,
we restate a theorem of A. Szucs asserting that under the conditions imposed on
a smooth action of G on M as above, the number of G-orbits of points x in M
with non-cyclic stabilizer G_x is even, and we prove the result by using
arguments of G. Moussong. In Sections 3 and 4, we determine all the equations
for non-cyclic subgroups G of SO(3).Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-24.abs.htm
First-Come-First-Served for Online Slot Allocation and Huffman Coding
Can one choose a good Huffman code on the fly, without knowing the underlying
distribution? Online Slot Allocation (OSA) models this and similar problems:
There are n slots, each with a known cost. There are n items. Requests for
items are drawn i.i.d. from a fixed but hidden probability distribution p.
After each request, if the item, i, was not previously requested, then the
algorithm (knowing the slot costs and the requests so far, but not p) must
place the item in some vacant slot j(i). The goal is to minimize the sum, over
the items, of the probability of the item times the cost of its assigned slot.
The optimal offline algorithm is trivial: put the most probable item in the
cheapest slot, the second most probable item in the second cheapest slot, etc.
The optimal online algorithm is First Come First Served (FCFS): put the first
requested item in the cheapest slot, the second (distinct) requested item in
the second cheapest slot, etc. The optimal competitive ratios for any online
algorithm are 1+H(n-1) ~ ln n for general costs and 2 for concave costs. For
logarithmic costs, the ratio is, asymptotically, 1: FCFS gives cost opt + O(log
opt).
For Huffman coding, FCFS yields an online algorithm (one that allocates
codewords on demand, without knowing the underlying probability distribution)
that guarantees asymptotically optimal cost: at most opt + 2 log(1+opt) + 2.Comment: ACM-SIAM Symposium on Discrete Algorithms (SODA) 201
Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation
We obtain exact moving and stationary, spatially periodic and localized
solutions of a generalized discrete nonlinear Schr\"odinger equation. More
specifically, we find two different moving periodic wave solutions and a
localized moving pulse solution. We also address the problem of finding exact
stationary solutions and, for a particular case of the model when stationary
solutions can be expressed through the Jacobi elliptic functions, we present a
two-point map from which all possible stationary solutions can be found.
Numerically we demonstrate the generic stability of the stationary pulse
solutions and also the robustness of moving pulses in long-term dynamics.Comment: 22 pages, 7 figures, to appear in J. Phys.
Born-Infeld Chern-Simons Theory: Hamiltonian Embedding, Duality and Bosonization
In this paper we study in detail the equivalence of the recently introduced
Born-Infeld self dual model to the Abelian Born-Infeld-Chern-Simons model in
2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme,
to embed the Born-Infeld Self dual model to a gauge system and show that the
embedded model is equivalent to Abelian Born-Infeld-Chern-Simons theory. Next,
using Buscher's duality procedure, we demonstrate this equivalence in a
covariant Lagrangian formulation and also derive the mapping between the
n-point correlators of the (dual) field strength in Born-Infeld Chern-Simons
theory and of basic field in Born-Infeld Self dual model. Using this
equivalence, the bosonization of a massive Dirac theory with a non-polynomial
Thirring type current-current coupling, to leading order in (inverse) fermion
mass is also discussed. We also re-derive it using a master Lagrangian.
Finally, the operator equivalence between the fermionic current and (dual)
field strength of Born-Infeld Chern-Simons theory is deduced at the level of
correlators and using this the current-current commutators are obtained.Comment: 27 pages, One reference added, minor changes in presentation and
typos corrected. To appear in Nucl. Phys.
Chemical Enrichment at High Redshifts
We have tried to understand the recent observations related to metallicity in
Ly forest clouds in the framework of the two component model suggested
by Chiba & Nath (1997). We find that even if the mini-halos were chemically
enriched by an earlier generation of stars, to have [C/H] -2.5, the
number of C IV lines with column density , contributed by the
mini-halos, at the redshift of 3, would be only about 10% of the total number
of lines, for a chemical enrichment rate of in the galaxies.
Recently reported absence of heavy element lines associated with most of the Ly
lines with H I column density between and by Lu et al (1998), if correct, gives an upper limit on [C/H]=-3.7,
not only in the mini-halos, but also in the outer parts of galactic halos. This
is consistent with the results of numerical simulations, according to which,
the chemical elements associated with the Ly clouds are formed in situ
in clouds, rather than in an earlier generation of stars. However, the mean
value of for the column density ratio of C IV and H I,
determined by Cowie and Songaila (1998) for low Lyman alpha optical depths,
implies an abundance of [C/H] =-2.5 in mini-halos as well as in most of the
region in galactic halos, presumably enriched by an earlier generation of
stars. The redshift and column density distribution of C IV has been shown to
be in reasonable agreement with the observations.Comment: 23 pages, 6 figures, To appear in Astrophysical Journa
Generalized Pauli principle for particles with distinguishable traits
The s=3/2 Ising spin chain with uniform nearest-neighbor coupling, quadratic
single-site potential, and magnetic field is shown to be equivalent to a system
of 17 species of particles with internal structure. The same set of particles
(with different energies) is shown to generate the spectrum of the s=1/2 Ising
chain with dimerized nearest-neighbor coupling. The particles are free of
interaction energies even at high densities. The mutual exclusion statistics of
particles from all species is determined by their internal structure and
encoded in a generalized Pauli principle. The exact statistical mechanical
analysis can be performed for thermodynamically open or closed systems and with
arbitrary energies assigned to all particle species. Special circumstances make
it possible to merge two or more species into a single species. All traits that
distinguish the original species become ignorable. The particles from the
merged species are effectively indistinguishable and obey modified exclusion
statistics. Different mergers may yield the same endproduct, implying that the
inverse process (splitting any species into subspecies) is not unique. In a
macroscopic system of two merged species at thermal equilibrium, the
concentrations of the original species satisfy a functional relation governed
by their mutual statistical interaction. That relation is derivable from an
extremum principle. In the Ising context the system is open and the particle
energies depend on the Hamiltonian parameters. Simple models of polymerization
and solitonic paramagnetism each represent a closed system of two species that
can transform into each other. Here they represent distinguishable traits with
different energies of the same physical particle.Comment: 12 pages, 7 figures, 6 table
Optical constraints of kerogen from 0.15 to 40 microns: Comparison with meteoritic organics
Kerogens are dark, complex organic materials produced on the Earth primarily by geologic processing of biologic materials, but kerogens have chemical and spectral similarities to some classes of highly processed extraterrestrial organic materials. Kerogen-like solids were proposed as constitutents of the very dark reddish surfaces of some asteroids and are also spectrally similar to some carbonaceous organic residues and the Iapetus dark material. Kerogen can thus serve as a useful laboratory analog to very dark, spectrally red extraterrestrial materials; its optical constants can be used to investigate the effects of particle size, void space and mixing of bright and dark components in models of scattering by dark asteroidal, cometary, and satellite surfaces. Measurements of the optical constants of both Type 2 kerogen and of macromolecular organic residue from the Murchison carbonaceous chondrite via transmission and reflection measurements on thin films are reported. The real part of the refractive index, n, is determined by variable incidence-angle reflectance to be 1.60 + or - 0.05 from 0.4 to 2.0 micrometers wavelength. Work extending the measurement of n to longer wavelengths is in progress. The imaginary part of the refractive index, k, shows substantial structure from 0.15 to 40 micrometers. The values are accurate to + or - 20 percent in the UV and IR regions and to + or - 30 percent in the visible. The k values of organic residues were also measured from the Murchison meteorite. Comparison of the kerogen and Murchison data reveals that between 0.15 and 40 microns, Murchison has a similar structure but no bands as sharp as in kerogen, and that the k values for Murchison are significantly higher than those of kerogen
Category O over a deformation of the symplectic oscillator algebra
We discuss the representation theory of , which is a deformation of the
symplectic oscillator algebra , where is the
((2n+1)-dimensional) Heisenberg algebra. We first look at a more general setup,
involving an algebra with a triangular decomposition. Assuming the PBW theorem,
and one other hypothesis, we show that the BGG category is
abelian, finite length, and self-dual.
We decompose as a direct sum of blocks \calo(\la), and show
that each block is a highest weight category.
In the second part, we focus on the case for , where we prove all
these assumptions, as well as the PBW theorem.Comment: 42 pages, LaTeX, 11pt; Typos removed, references added, presentation
improved, minor corrections and additions, Section 16 modified, and Standing
Assumption added in Section 17; Final form, to appear in the Journal of Pure
and Applied Algebr
On Exactness Of The Supersymmetric WKB Approximation Scheme
Exactness of the lowest order supersymmetric WKB (SWKB) quantization
condition , for certain
potentials, is examined, using complex integration technique. Comparison of the
above scheme with a similar, but {\it exact} quantization condition, , originating from the quantum Hamilton-Jacobi
formalism reveals that, the locations and the residues of the poles that
contribute to these integrals match identically, for both of these cases. As
these poles completely determine the eigenvalues in these two cases, the
exactness of the SWKB for these potentials is accounted for. Three non-exact
cases are also analysed; the origin of this non-exactness is shown to be due
the presence of additional singularities in , like branch
cuts in the plane.Comment: 11 pages, latex, 1 figure available on reques
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