46,913 research outputs found
Computing the Girth of a Planar Graph in Linear Time
The girth of a graph is the minimum weight of all simple cycles of the graph.
We study the problem of determining the girth of an n-node unweighted
undirected planar graph. The first non-trivial algorithm for the problem, given
by Djidjev, runs in O(n^{5/4} log n) time. Chalermsook, Fakcharoenphol, and
Nanongkai reduced the running time to O(n log^2 n). Weimann and Yuster further
reduced the running time to O(n log n). In this paper, we solve the problem in
O(n) time.Comment: 20 pages, 7 figures, accepted to SIAM Journal on Computin
Gauge Unification and Quark Masses in a Pati-Salam Model from Branes
We investigate the phase space of parameters in the Pati-Salam model derived
in the context of D-branes scenarios, requiring low energy string scale. We
find that a non-supersymmetric version complies with a string scale as low as
10 TeV, while in the supersymmetric version the string scale raises up to ~2 x
10^7 TeV. The limited energy region for RGE running demands a large tan(beta)
in order to have experimentally acceptable masses for the top and bottom
quarks.Comment: 11 pages, LaTeX, 7 figures include
Geometric CP Violation with Extra Dimensions
We discuss how CP symmetry can be broken geometrically through orbifold
projections in hidden extra dimensions in the context of D-brane models for
particle unifications. We present a few toy models to illustrate the idea and
suggest ways to incorporate this technique in the context of realistic models.Comment: 6 pages, one figure; references updated and a new model adde
On theories of random variables
We study theories of spaces of random variables: first, we consider random
variables with values in the interval , then with values in an arbitrary
metric structure, generalising Keisler's randomisation of classical structures.
We prove preservation and non-preservation results for model theoretic
properties under this construction: i) The randomisation of a stable structure
is stable. ii) The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type
Theory of magnetic excitons in the heavy-fermion superconductor
We analyze the influence of unconventional superconductivity on the magnetic
excitations in the heavy fermion compound UPdAl. We show that it leads
to the formation of a bound state at energies well below 2 at the
antiferromagnetic wave vector {\textbf Q}=. Its signature is a
resonance peak in the spectrum of magnetic excitations in good agreement with
results from inelastic neutron scattering. Furthermore we investigate the
influence of antiferromagnetic order on the formation of the resonance peak. We
find that its intensity is enhanced due to intraband transitions induced by the
reconstruction of Fermi surface sheets. We determine the dispersion of the
resonance peak near {\textbf Q} and show that it is dominated by the magnetic
exciton dispersion associated with local moments. We demonstrate by a
microscopic calculation that UPdAl is another example in which the
unconventional nature of the superconducting order parameter can be probed by
means of inelastic neutron scattering and determined unambiguously.Comment: 6 pages, 4 figure
Larkin-Ovchinnikov-Fulde-Ferrell phase in the superconductor (TMTSF)2ClO4: Theory versus experiment
We consider a formation of the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase
in a quasi-one-dimensional (Q1D) conductor in a magnetic field, parallel to its
conducting chains, where we take into account both the paramagnetic
spin-splitting and orbital destructive effects against superconductivity. We
show that, due to a relative weakness of the orbital effects in a Q1D case, the
LOFF phase appears in (TMTSF)ClO superconductor for real values of its
Q1D band parameters. We compare our theoretical calculations with the recent
experimental data by Y. Maeno's group [S. Yonezawa et al., Phys. Rev. Lett.
\textbf{100}, 117002 (2008)] and show that there is a good qualitative and
quantitative agreement between the theory and experimental data.Comment: 4 pages, 1 figur
Vacuum Energy Density and Cosmological Constant in dS Brane World
We discuss the vacuum energy density and the cosmological constant of dS
brane world with a dilaton field. It is shown that a stable AdS brane can
be constructed and gravity localization can be realized. An explicit relation
between the dS bulk cosmological constant and the brane cosmological constant
is obtained. The discrete mass spectrum of the massive scalar field in the
AdS brane is used to acquire the relationship between the brane
cosmological constant and the vacuum energy density. The vacuum energy density
in the brane gotten by this method is in agreement with astronomical
observations.Comment: 16 pages,4 figure
P and T Violation From Certain Dimension Eight Weinberg Operators
Dimension eight operators of the Weinberg type have been shown to give
important contributions to CP violating phenomena, such as the electric dipole
moment of the neutron. In this note we show how operators related to these (and
expected to occur on equal footing) can give rise to time-reversal violating
phenomena such as atomic electric dipole moments. We also estimate the induced
parity violating phenomena such as small ``wrong'' parity admixtures in atomic
states and find that they are negligible. Uses harvmac.tex and epsf.tex; one
figure submitted as a uuencoded, compressed EPS file.Comment: 6 pages, EFI-92-5
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