3,143,726 research outputs found
On a connection between the switching separability of a graph and that of its subgraphs
A graph of order is called {switching separable} if its modulo-2 sum
with some complete bipartite graph on the same set of vertices is divided into
two mutually independent subgraphs, each having at least two vertices. We prove
the following: if removing any one or two vertices of a graph always results in
a switching separable subgraph, then the graph itself is switching separable.
On the other hand, for every odd order greater than 4, there is a graph that is
not switching separable, but removing any vertex always results in a switching
separable subgraph. We show a connection with similar facts on the separability
of Boolean functions and reducibility of -ary quasigroups. Keywords:
two-graph, reducibility, separability, graph switching, Seidel switching, graph
connectivity, -ary quasigroupComment: english: 9 pages; russian: 9 page
Some Observations on Non-covariant Gauges and the epsilon-term
We consider the Lagrangian path-integrals in Minkowski space for gauges with
a residual gauge-invariance. From rather elementary considerations, we
demonstrate the necessity of inclusion of an epsilon-term (even) in the formal
treatments, without which one may reach incorrect conclusions. We show,
further, that the epsilon-term can contribute to the BRST WT-identities in a
nontrivial way (even as epsilon-->0). We also show that the (expectation value
of the) correct epsilon-term satisfies an algebraic condition. We show by
considering (a commonly used) example of a simple local quadratic epsilon
-term, that they lead to additional constraints on Green's function that are
not normally taken into account in the BRST formalism that ignores the
epsilon-term, and that they are characteristic of the way the singularities in
propagators are handled. We argue that for a subclass of these gauges, the
Minkowski path-integral could not be obtained by a Wick rotation from a
Euclidean path-integral.Comment: 12 pages, LaTeX2
The Evolution of Adiabatic Supernova Remnants in a Turbulent, Magnetized Medium
(Abridged) We present the results of three dimensional calculations for the
MHD evolution of an adiabatic supernova remnant in both a uniform and turbulent
interstellar medium using the RIEMANN framework of Balsara. In the uniform
case, which contains an initially uniform magnetic field, the density structure
of the shell remains largely spherical, while the magnetic pressure and
synchrotron emissivity are enhanced along the plane perpendicular to the field
direction. This produces a bilateral or barrel-type morphology in synchrotron
emission for certain viewing angles. We then consider a case with a turbulent
external medium as in Balsara & Pouquet, characterized by .
Several important changes are found. First, despite the presence of a uniform
field, the overall synchrotron emissivity becomes approximately spherically
symmetric, on the whole, but is extremely patchy and time-variable, with
flickering on the order of a few computational time steps. We suggest that the
time and spatial variability of emission in early phase SNR evolution provides
information on the turbulent medium surrounding the remnant. The
shock-turbulence interaction is also shown to be a strong source of
helicity-generation and, therefore, has important consequences for magnetic
field generation. We compare our calculations to the Sedov-phase evolution, and
discuss how the emission characteristics of SNR may provide a diagnostic on the
nature of turbulence in the pre-supernova environment.Comment: ApJ, in press, 5 color figure
The identification of physical close galaxy pairs
A classification scheme for close pairs of galaxies is proposed. The scheme
is motivated by the fact that the majority of apparent close pairs are in fact
wide pairs in three-dimensional space. This is demonstrated by means of
numerical simulations of random samples of binary galaxies and the scrutiny of
the resulting projected and spatial separation distributions.
Observational strategies for classifying close pairs according to the scheme
are suggested. As a result, physical (i.e., bound and spatially) close pairs
are identified.Comment: 16 pages, 5 figures, accepted for publication in The Astronomical
Journal, added text corrections on proof
Triangular and Y-shaped hadrons with static sources
The structure of hadrons consisting of three static color sources in
fundamental (baryons) or adjoint (three-gluon glueballs) representations is
studied. The static potentials of glueballs as well as gluon field
distributions in glueballs and baryons are calculated in the framework of field
correlator method.Comment: 7 pages, 5 figures, talk at the NPD-2002 Conference, December 2-6,
ITEP, Moscow, reference adde
A superspace formulation of an "asymptotic" OSp(3,1|2) invariance of Yang-Mills theories
We formulate a superspace field theory which is shown to be equivalent to the
symmetric BRS/Anti-BRS invariant Yang-Mills action. The theory uses
a 6-dimensional superspace and one OSp(3,1|2) vector multiplet of unconstrained
superfields. We establish a superspace WT identity and show that the
formulation has an asymptotic OSp(3,1|2) invariance as the gauge parameter goes
to infinity. We give a physical interpretation of this asymptotic OSp(3,1|2)
invariance as a symmetry transformation among the longitudinal/time like
degrees of freedom of and the ghost degrees of freedom.Comment: Latex, 20pages, No fig
Optical diffraction of focused spots and subwavelength structures
We have developed a numerical diffraction tool for cases in which the incident field is a focused spot and the diffracting structure is a single structure or an aperiodic surface. Our approach uses the integral formulation to solve Maxwellâs equations and is different from previously published methods in its choice of basis function. We compared numerical results with experimental measurements of the far-field intensity for a focused spot incident on an aluminum grating, and the comparison was favorable. Finally, we predict the diffraction behavior of the proposed digital video disk format for the next generation of optical disk. Our analysis shows that the reflected signal for this format has a strong dependence on the polarization of the incident light
Spectral dimensions of hierarchical scale-free networks with shortcuts
The spectral dimension has been widely used to understand transport
properties on regular and fractal lattices. Nevertheless, it has been little
studied for complex networks such as scale-free and small world networks. Here
we study the spectral dimension and the return-to-origin probability of random
walks on hierarchical scale-free networks, which can be either fractals or
non-fractals depending on the weight of shortcuts. Applying the renormalization
group (RG) approach to the Gaussian model, we obtain the spectral dimension
exactly. While the spectral dimension varies between and for the
fractal case, it remains at , independent of the variation of network
structure for the non-fractal case. The crossover behavior between the two
cases is studied through the RG flow analysis. The analytic results are
confirmed by simulation results and their implications for the architecture of
complex systems are discussed.Comment: 10 pages, 3 figure
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