261 research outputs found
Definition of the concept âvectorâ in set theoretic programming languages
AbstractA basic set of data types for a set theoretic programming language is presented. The emphasis is on a certain definition of vector in terms of sets. The definition is contrasted with other methods of defining vectors in terms of sets, such as Kuratowski's device
Automatic Abstraction for Congruences
One approach to verifying bit-twiddling algorithms is to derive invariants between the bits that constitute the variables of a program. Such invariants can often be described with systems of congruences where in each equation , (unknown variable m)\vec{c}\vec{x}$ is a vector of propositional variables (bits). Because of the low-level nature of these invariants and the large number of bits that are involved, it is important that the transfer functions can be derived automatically. We address this problem, showing how an analysis for bit-level congruence relationships can be decoupled into two parts: (1) a SAT-based abstraction (compilation) step which can be automated, and (2) an interpretation step that requires no SAT-solving. We exploit triangular matrix forms to derive transfer functions efficiently, even in the presence of large numbers of bits. Finally we propose program transformations that improve the analysis results
Extreme Ultra-Violet Spectroscopy of the Lower Solar Atmosphere During Solar Flares
The extreme ultraviolet portion of the solar spectrum contains a wealth of
diagnostic tools for probing the lower solar atmosphere in response to an
injection of energy, particularly during the impulsive phase of solar flares.
These include temperature and density sensitive line ratios, Doppler shifted
emission lines and nonthermal broadening, abundance measurements, differential
emission measure profiles, and continuum temperatures and energetics, among
others. In this paper I shall review some of the advances made in recent years
using these techniques, focusing primarily on studies that have utilized data
from Hinode/EIS and SDO/EVE, while also providing some historical background
and a summary of future spectroscopic instrumentation.Comment: 34 pages, 8 figures. Submitted to Solar Physics as part of the
Topical Issue on Solar and Stellar Flare
Hopf algebras and Markov chains: Two examples and a theory
The operation of squaring (coproduct followed by product) in a combinatorial
Hopf algebra is shown to induce a Markov chain in natural bases. Chains
constructed in this way include widely studied methods of card shuffling, a
natural "rock-breaking" process, and Markov chains on simplicial complexes.
Many of these chains can be explictly diagonalized using the primitive elements
of the algebra and the combinatorics of the free Lie algebra. For card
shuffling, this gives an explicit description of the eigenvectors. For
rock-breaking, an explicit description of the quasi-stationary distribution and
sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes
will only appear on the version on Amy Pang's website, the arXiv version will
not be updated.
Lambda Hyperons in 2 A*GeV Ni + Cu Collisions
A sample of Lambda's produced in 2 A*GeV Ni + Cu collisions has been obtained
with the EOS Time Projection Chamber at the Bevalac. Low background in the
invariant mass distribution allows for the unambiguous demonstration of Lambda
directed flow. The transverse mass spectrum at mid-rapidity has the
characteristic shoulder-arm shape of particles undergoing radial transverse
expansion. A linear dependence of Lambda multiplicity on impact parameter is
observed, from which a total Lambda + Sigma^0 production cross section of $112
+/- 24 mb is deduced. Detailed comparisons with the ARC and RVUU models are
made.Comment: Revised version accepted for publication in Phys. Lett.
An Observational Overview of Solar Flares
We present an overview of solar flares and associated phenomena, drawing upon
a wide range of observational data primarily from the RHESSI era. Following an
introductory discussion and overview of the status of observational
capabilities, the article is split into topical sections which deal with
different areas of flare phenomena (footpoints and ribbons, coronal sources,
relationship to coronal mass ejections) and their interconnections. We also
discuss flare soft X-ray spectroscopy and the energetics of the process. The
emphasis is to describe the observations from multiple points of view, while
bearing in mind the models that link them to each other and to theory. The
present theoretical and observational understanding of solar flares is far from
complete, so we conclude with a brief discussion of models, and a list of
missing but important observations.Comment: This is an article for a monograph on the physics of solar flares,
inspired by RHESSI observations. The individual articles are to appear in
Space Science Reviews (2011
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