146 research outputs found
Method of ordering the values of a linear function on a set of permutations.
The paper deals with a new method of solving a combinatorial problem with account for the properties
of the set of permutations and its structure. Using this method, the values of the linear objective
function are sequenced and the set of permutations is decomposed over hyperplanes, with account of
element recurrences. This makes it possible to develop an algorithm of finding the point (an element of
the set of permutations) at which the objective function attains a given value
Method of ordering the values of a linear function on a set of permutations.
The paper deals with a new method of solving a combinatorial problem with account for the properties
of the set of permutations and its structure. Using this method, the values of the linear objective
function are sequenced and the set of permutations is decomposed over hyperplanes, with account of
element recurrences. This makes it possible to develop an algorithm of finding the point (an element of
the set of permutations) at which the objective function attains a given value
N=4 supersymmetric Eguchi-Hanson sigma model in d=1
We show that it is possible to construct a supersymmetric mechanics with four
supercharges possessing not conformally flat target space. A general idea of
constructing such models is presented. A particular case with Eguchi--Hanson
target space is investigated in details: we present the standard and quotient
approaches to get the Eguchi--Hanson model, demonstrate their equivalence, give
a full set of nonlinear constraints, study their properties and give an
explicit expression for the target space metric.Comment: LaTeX, 9 page
Dilatonic Black Holes in Higher Curvature String Gravity
We give analytical arguments and demonstrate numerically the existence of
black hole solutions of the Effective Superstring Action in the presence
of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial
dilaton hair. The hair, however, is of ``secondary" type", in the sense that
the dilaton charge is expressed in terms of the black hole mass. Our solutions
are not covered by the assumptions of existing proofs of the ``no-hair"
theorem. We also find some alternative solutions with singular metric
behaviour, but finite energy. The absence of naked singularities in this system
is pointed out.Comment: 22 pages, Latex file, 7 Latex figures already include
Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations
We study both analytically and numerically a coupled system of spherically
symmetric SU(2) Yang-Mills-dilaton equation in 3+1 Minkowski space-time. It has
been found that the system admits a hidden scale invariance which becomes
transparent if a special ansatz for the dilaton field is used. This choice
corresponds to transition to a frame rotated in the plane at a
definite angle. We find an infinite countable family of self-similar solutions
which can be parametrized by the - the number of zeros of the relevant
Yang-Mills function. According to the performed linear perturbation analysis,
the lowest solution with N=0 only occurred to be stable. The Cauchy problem has
been solved numerically for a wide range of smooth finite energy initial data.
It has been found that if the initial data exceed some threshold, the resulting
solutions in a compact region shrinking to the origin, attain the lowest N=0
stable self-similar profile, which can pretend to be a global stable attractor
in the Cauchy problem. The solutions live a finite time in a self-similar
regime and then the unbounded growth of the second derivative of the YM
function at the origin indicates a singularity formation, which is in agreement
with the general expectations for the supercritical systems.Comment: 10 pages, 5 figure
Sequences of Einstein-Yang-Mills-Dilaton Black Holes
Einstein-Yang-Mills-dilaton theory possesses sequences of neutral static
spherically symmetric black hole solutions. The solutions depend on the dilaton
coupling constant and on the horizon. The SU(2) solutions are labelled
by the number of nodes of the single gauge field function, whereas the
SO(3) solutions are labelled by the nodes of both gauge field
functions. The SO(3) solutions form sequences characterized by the node
structure , where is fixed. The sequences of magnetically neutral
solutions tend to magnetically charged limiting solutions. For finite the
SO(3) sequences tend to magnetically charged Einstein-Yang-Mills-dilaton
solutions with nodes and charge . For and the SO(3) sequences tend to Einstein-Maxwell-dilaton solutions with
magnetic charges and , respectively. The latter also
represent the scaled limiting solutions of the SU(2) sequence. The convergence
of the global properties of the black hole solutions, such as mass, dilaton
charge and Hawking temperature, is exponential. The degree of convergence of
the matter and metric functions of the black hole solutions is related to the
relative location of the horizon to the nodes of the corresponding regular
solutions.Comment: 71 pages, Latex2e, 29 ps-figures include
Mixmaster Behavior in Inhomogeneous Cosmological Spacetimes
Numerical investigation of a class of inhomogeneous cosmological spacetimes
shows evidence that at a generic point in space the evolution toward the
initial singularity is asymptotically that of a spatially homogeneous spacetime
with Mixmaster behavior. This supports a long-standing conjecture due to
Belinskii et al. on the nature of the generic singularity in Einstein's
equations.Comment: 4 pages plus 4 figures. A sentence has been deleted. Accepted for
publication in PR
On the n=4 Supersymmetry for the FRW Model
In this work we have constructed the n=4 extended local conformal time
supersymmetry for the Friedmann-Robertson-Walker (FRW) cosmological models.
This is based on the superfield construction of the action, which is invariant
under wordline local n=4 supersymmetry with internal symmetry. It is shown that the supersymmetric action
has the form of the localized (or superconformal) version of the action for n=4
supersymmetric quantum mechanics. This superfield procedure provides a well
defined scheme for including supermatter.Comment: 8 pages. Accepted for publication in Phys. Rev
Sequences of globally regular and black hole solutions in SU(4) Einstein-Yang-Mills theory
SU(4) Einstein-Yang-Mills theory possesses sequences of static spherically
symmetric globally regular and black hole solutions. Considering solutions with
a purely magnetic gauge field, based on the 4-dimensional embedding of
in , these solutions are labelled by the node numbers of
the three gauge field functions , and . We classify the various
types of solutions in sequences and determine their limiting solutions. The
limiting solutions of the sequences of neutral solutions carry charge, and the
limiting solutions of the sequences of charged solutions carry higher charge.
For sequences of black hole solutions with node structure and
, several distinct branches of solutions exist up to critical values
of the horizon radius. We determine the critical behaviour for these sequences
of solutions. We also consider SU(4) Einstein-Yang-Mills-dilaton theory and
show that these sequences of solutions are analogous in most respects to the
corresponding SU(4) Einstein-Yang-Mills sequences of solutions.Comment: 40 pages, 5 tables, 19 Postscript figures, use revtex.st
- …