1,087 research outputs found
Boolean Dimension, Components and Blocks
We investigate the behavior of Boolean dimension with respect to components
and blocks. To put our results in context, we note that for Dushnik-Miller
dimension, we have that if for every component of a poset
, then ; also if for every block
of a poset , then . By way of constrast, local dimension is
well behaved with respect to components, but not for blocks: if
for every component of a poset , then
; however, for every , there exists a poset
with and for every block of . In this
paper we show that Boolean dimension behaves like Dushnik-Miller dimension with
respect to both components and blocks: if for every
component of , then ; also if
for every block of , then .Comment: 12 pages. arXiv admin note: text overlap with arXiv:1712.0609
Shattering-Extremal Set Systems of Small VC-Dimension
We say that a set system shatters a given set
if . The Sauer inequality
states that in general, a set system shatters at least
sets. Here we concentrate on the case of equality. A set system
is called shattering-extremal if it shatters exactly sets. We
characterize shattering extremal set systems of Vapnik-Chervonenkis dimension 1
in terms of their inclusion graphs. Also from the perspective of extremality,
we relate set systems of bounded Vapnik-Chervonenkis dimension to their
projections.Comment: 17 page
Exploring projective norm graphs
The projective norm graphs provide tight constructions for
the Tur\'an number of complete bipartite graphs with . In
this paper we determine their automorphism group and explore their small
subgraphs. To this end we give quite precise estimates on the number of
solutions of certain equation systems involving norms over finite fields. The
determination of the largest integer , such that the projective norm graph
contains for all large enough prime powers is
an important open question with far-reaching general consequences. The best
known bounds, , are far apart for . Here we
prove that does contain (many) for any prime power
not divisble by or . This greatly extends recent work of Grosu,
using a completely different approach. Along the way we also count the copies
of any fixed -degenerate subgraph, and find that projective norm graphs are
quasirandom with respect to this parameter. Some of these results also extend
the work of Alon and Shikhelman on generalized Tur\'an numbers. Finally we also
give a new, more elementary proof for the -freeness of
.Comment: 41 pages + 6 pages of Appendi
On the toughness of thermoplastic polymer nanocomposites as assessed by the essential work of fracture (EWF) approach
The essential work of fracture (EWF) approach is widely used to determine the plane stress fracture toughness of highly ductile polymers and related systems. To shed light on how the toughness is affected by nanofillers EWF-suited model polymers, viz. amorphous copolyester and polypropylene block copolymer were modified by multiwall carbon nanotube (MWCNT), graphene (GR), boehmite alumina (BA), and organoclay (MMT) in 1 wt% each. EWF tests were performed on deeply double-edge notched tensile-loaded specimens under quasistatic loading conditions. Data reduction occurred by energy partitioning between yielding and necking/tearing. The EWF prerequisites were not met with the nanocomposites containing MWCNT and GR by contrast to those with MMT and BA. Accordingly, the toughness of nanocomposites with homogeneously dispersed and low aspect ratio fillers may be properly determined using the EWF. Results indicated that incorporation of nanofillers may result in an adverse effect between the specific essential and non-essential EWF parameters
A Possible Explanation of the Radio Afterglow of GRB980519: The Dense Medium Effect
GRB{980519} is characterized by its rapidly declining optical and X-ray
afterglows. Explanations of this behavior include models invoking a dense
medium environment which makes the shock wave evolve quickly into the
sub-relativistic phase, a jet-like outflow, and a wind-shaped circumburst
medium environment. Recently, Frail {et al}. (1999a) found that the latter two
cases are consistent with the radio afterglow of this burst. Here, by
considering the trans-relativistic shock hydrodynamics, we show that the dense
medium model can also account for the radio light curve quite well. The
potential virtue of the dense medium model for GRB{980519} is that it implies a
smaller angular size of the afterglow, which is essential for interpreting the
strong modulation of the radio light curve. Optical extinction due to the dense
medium is not important if the prompt optical-UV flash accompanying the
-ray emission can destroy dust by sublimation out to an appreciable
distance. Comparisons with some other radio afterglows are also discussed.Comment: 5 pages, 1 figure, a few minor changes made and references up dated,
MNRAS, in pres
TeV Neutrinos from Successful and Choked Gamma-Ray Bursts
Core collapse of massive stars resulting in a relativistic fireball jet which
breaks through the stellar envelope is a widely discussed scenario for
gamma-ray burst production. For very extended or slow rotating stars, the
fireball may be unable to break through the envelope. Both penetrating and
choked jets will produce, by photo-meson interactions of accelerated protons, a
burst of neutrinos with energies in excess of 5 TeV while propagating in the
envelope. The predicted flux, from both penetrating and chocked fireballs,
should be easily detectable by planned cubic kilometer neutrino telescopes.Comment: Phys.Rev.Letters, in press, final version accepted 8/31/01 (orig.
3/17/01
The broad band spectral properties of galactic X-ray binary pulsars
BeppoSAX observed several galactic binary X-ray pulsars during the Science
Verification Phase and in the first year of the regular program. The complex
emission spectra of these sources are an ideal target for the BeppoSAX
instrumentation, that can measure the emission spectra in an unprecedented
broad energy band. Using this capability of BeppoSAX a detailed observational
work can be done on the galactic X-ray pulsars. In particular the 0.1-200 keV
energy band allows the shape of the continuum emission to be tightly
constrained. A better determination of the underlying continuum allows an
easier detection of features superimposed onto it, both at low energy (Fe K and
L, Ne lines) and at high energies (cyclotron features). We report on the
spectral properties of a sample of X-ray pulsars observed with BeppoSAX
comparing the obtained results. Some ideas of common properties are also
discussed and compared with our present understanding of the emission
mechanisms and processes.Comment: 6 pages, 2 figures. Uses espcrc2.sty (included).To appear in
Proceedings of "The Active X-ray Sky: Results from BeppoSAX and Rossi-XTE
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