3,009 research outputs found
The Elementary Divisors of the Incidence Matrix of Skew Lines in PG(3,q)
The elementary divisors of the incidence matrix of lines in PG(3,q) are
computed, where two lines are incident if and only if they are skew.Comment: 13 pages. The results of this paper supersede those in the paper
arXiv:math/1001.2551 V2. Minor correction
A Gravity Dual of RHIC Collisions
In the context of the AdS/CFT correspondence we discuss the gravity dual of a
heavy-ion-like collision in a variant of SYM. We provide a gravity
dual picture of the entire process using a model where the scattering process
creates initially a holographic shower in bulk AdS. The subsequent
gravitational fall leads to a moving black hole that is gravity dual to the
expanding and cooling heavy-ion fireball. The front of the fireball cools at
the rate of , while the core cools as from a
cosmological-like argument. The cooling is faster than Bjorken cooling. The
fireball freezes when the dual black hole background is replaced by a confining
background through the Hawking-Page transition.Comment: 25 pages, 8 figures, Added references, Falling picture elucidate
Spectral Theory of Discrete Processes
We offer a spectral analysis for a class of transfer operators. These
transfer operators arise for a wide range of stochastic processes, ranging from
random walks on infinite graphs to the processes that govern signals and
recursive wavelet algorithms; even spectral theory for fractal measures. In
each case, there is an associated class of harmonic functions which we study.
And in addition, we study three questions in depth:
In specific applications, and for a specific stochastic process, how do we
realize the transfer operator as an operator in a suitable Hilbert space?
And how to spectral analyze once the right Hilbert space has
been selected? Finally we characterize the stochastic processes that are
governed by a single transfer operator.
In our applications, the particular stochastic process will live on an
infinite path-space which is realized in turn on a state space . In the case
of random walk on graphs , will be the set of vertices of . The
Hilbert space on which the transfer operator acts will then
be an space on , or a Hilbert space defined from an energy-quadratic
form.
This circle of problems is both interesting and non-trivial as it turns out
that may often be an unbounded linear operator in ; but even
if it is bounded, it is a non-normal operator, so its spectral theory is not
amenable to an analysis with the use of von Neumann's spectral theorem. While
we offer a number of applications, we believe that our spectral analysis will
have intrinsic interest for the theory of operators in Hilbert space.Comment: 34 pages with figures removed, for the full version with all the
figures please go to http://www.siue.edu/~msong/Research/spectrum.pd
The critical group of the Kneser graph on -subsets of an -element set
In this paper we compute the critical group of the Kneser graph .
This is equivalent to computing the Smith normal form of a Laplacian matrix of
this graph.Comment: 16 pages, minor change
Supersymmetric three family chiral SU(6) grand unification model from F-theory
We obtain a supersymmetric three family chiral SU(6) grand unification model
with the global family symmetry SU(3)[family] from F-theory. This model has
nice features such as all the fermion masses are reasonably generated and there
results only one pair of Higgs doublets, realizing the doublet-triplet
splitting from the family symmetry SU(3)[family]. The proton hexality is
realized toward the proton stability problem. There is a room to fit the three
gauge couplings using the F-theory flux idea and we obtain the proton lifetime
in the 10^{36-37} yr region.Comment: 5 pages, to be published in Phys. Rev.
Hairs of discrete symmetries and gravity
Gauge symmetries are known to be respected by gravity because gauge charges
carry flux lines, but global charges do not carry flux lines and are not
conserved by gravitational interaction. For discrete symmetries, they are
spontaneously broken in the Universe, forming domain walls. Since the
realization of discrete symmetries in the Universe must involve the vacuum
expectation values of Higgs fields, a string-like configuration (hair) at the
intersection of domain walls in the Higgs vacua can be realized. Therefore, we
argue that discrete charges are also respected by gravity.Comment: 9 pages,9 figure
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