3,600 research outputs found
Reflectionless measures and the Mattila-Melnikov-Verdera uniform rectifiability theorem
A new proof is given of the Mattila-Melnikov-Verdera theorem on the uniform
rectifiability of an Ahlfors-David regular measure whose associated Cauchy
transform operator is bounded.Comment: 31 pages, 5 figure
Supernovae in the nuclear regions of starburst galaxies
The feasibility of using near-infrared observations to discover supernovae in
the nuclear and circumnuclear regions of nearby starburst galaxies is
investigated. We provide updated estimates of the intrinsic core-collapse
supernova rates in these regions. We discuss the problem of extinction, and
present new estimates of the extinction towards 33 supernova remnants in the
starburst galaxy M 82. This is done using H I and H_2 column density
measurements. We estimate the molecular to atomic hydrogen mass ratio to be 7.4
+- 1.0 in M 82. We have assembled near-infrared photometric data for a total of
13 core-collapse supernovae, some unpublished hitherto. This constitutes the
largest database of IR light curves for such events. We show that the IR light
curves fall into two classes, ``ordinary'' and ``slow-declining''. Template
JHKL light curves are derived for both classes. For ordinary core-collapse
supernovae, the average peak JHKL absolute magnitudes are -18.4, -18.6, -18.6,
and -19.0 respectively. The slow-declining core-collapse SNe are found to be
significantly more luminous than the ordinary events, even at early times,
having average peak JHKL absolute magnitudes of -19.9, -20.0, -20.0, and -20.4
respectively. We investigate the efficiency of a computerised image subtraction
method in supernova detection. We then carry out a Monte Carlo simulation of a
supernova search using K-band images of NGC 5962. The effects of extinction and
observing strategy are discussed. We conclude that a modest observational
programme will be able to discover a number of nuclear supernovae.Comment: 19 pages, 7 figures; accepted in MNRA
Slicing Sets and Measures, and the Dimension of Exceptional Parameters
We consider the problem of slicing a compact metric space \Omega with sets of
the form \pi_{\lambda}^{-1}\{t\}, where the mappings \pi_{\lambda} \colon
\Omega \to \R, \lambda \in \R, are \emph{generalized projections}, introduced
by Yuval Peres and Wilhelm Schlag in 2000. The basic question is: assuming that
\Omega has Hausdorff dimension strictly greater than one, what is the dimension
of the 'typical' slice \pi_{\lambda}^{-1}{t}, as the parameters \lambda and t
vary. In the special case of the mappings \pi_{\lambda} being orthogonal
projections restricted to a compact set \Omega \subset \R^{2}, the problem
dates back to a 1954 paper by Marstrand: he proved that for almost every
\lambda there exist positively many such that \dim
\pi_{\lambda}^{-1}{t} = \dim \Omega - 1. For generalized projections, the same
result was obtained 50 years later by J\"arvenp\"a\"a, J\"arvenp\"a\"a and
Niemel\"a. In this paper, we improve the previously existing estimates by
replacing the phrase 'almost all \lambda' with a sharp bound for the dimension
of the exceptional parameters.Comment: 31 pages, three figures; several typos corrected and large parts of
the third section rewritten in v3; to appear in J. Geom. Ana
Singular integrals and rectifiability
We shall discuss singular integrals on lower dimensional subsets of . A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey on some newer results and open problems. In the second part we prove some results on the Riesz kernels in . As far I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods
Super star clusters and Supernovae in interacting LIRGs unmasked by NIR adaptive optics
We report on an on-going near-IR adaptive optics survey targeting interacting
luminous IR galaxies. High-spatial resolution NIR data are crucial to enable
interpretation of kinematic, dynamical and star formation (SF) properties of
these very dusty objects. Whole progenitor nuclei in the interactions can be
missed if only optical HST imaging is used. Here we specifically present the
latest results regarding core-collapse supernovae found within the highly
extincted nuclear regions of these galaxies. Direct detection and study of such
highly obscured CCSNe is crucial for revising the optically-derived SN rates
used for providing an independent measurement of the SF history of the
Universe. We also present thus-far the first NIR luminosity functions of super
star cluster (SSC) candidates. The LFs can then be used to constrain the
formation and evolution of SSCs via constraints based on initial mass functions
and cluster disruption models.Comment: 6 pages. To appear in proceedings of 'Galaxies and their Masks'
(Namibia, April 2010), published by Springer, New York, eds. D.L. Block, K.C.
Freeman, I. Puerar
Filopodia: molecular architecture and cellular functions
Filopodia are thin, actin-rich plasma-membrane protrusions that function as antennae for cells to probe their environment. Consequently, filopodia have an important role in cell migration, neurite outgrowth and wound healing and serve as precursors for dendritic spines in neurons. The initiation and elongation of filopodia depend on the precisely regulated polymerization, convergence and crosslinking of actin filaments. The increased understanding of the functions of various actin-associated proteins during the initiation and elongation of filopodia has provided new information on the mechanisms of filopodia formation in distinct cell types
Porosities and dimensions of measures
We introduce a concept of porosity for measures and study relations between
dimensions and porosities for two classes of measures: measures on which
satisfy the doubling condition and strongly porous measures on .Comment: Jarvenpaa = J\"arvenp\"a\"
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