329,736 research outputs found
Representing a P-complete problem by small trellis automata
A restricted case of the Circuit Value Problem known as the Sequential NOR
Circuit Value Problem was recently used to obtain very succinct examples of
conjunctive grammars, Boolean grammars and language equations representing
P-complete languages (Okhotin, http://dx.doi.org/10.1007/978-3-540-74593-8_23
"A simple P-complete problem and its representations by language equations",
MCU 2007). In this paper, a new encoding of the same problem is proposed, and a
trellis automaton (one-way real-time cellular automaton) with 11 states solving
this problem is constructed
Marshall system for aerospace simulation (MARSYAS)
System is simple flexible language which can be coded by users unfamiliar with computer programming. It is designed for engineers with little experience in simulation, who desire to simulate large physical systems. User has ability to mix differential equations with diagrams in his model. With few exceptions, there is no rigid statement-operator structure within given module
On equations over sets of integers
Systems of equations with sets of integers as unknowns are considered. It is
shown that the class of sets representable by unique solutions of equations
using the operations of union and addition S+T=\makeset{m+n}{m \in S, \: n \in
T} and with ultimately periodic constants is exactly the class of
hyper-arithmetical sets. Equations using addition only can represent every
hyper-arithmetical set under a simple encoding. All hyper-arithmetical sets can
also be represented by equations over sets of natural numbers equipped with
union, addition and subtraction S \dotminus T=\makeset{m-n}{m \in S, \: n \in
T, \: m \geqslant n}. Testing whether a given system has a solution is
-complete for each model. These results, in particular, settle the
expressive power of the most general types of language equations, as well as
equations over subsets of free groups.Comment: 12 apges, 0 figure
Gaudin Model, Bethe Ansatz and Critical Level
We propose a new method of diagonalization of hamiltonians of the Gaudin
model associated to an arbitrary simple Lie algebra, which is based on Wakimoto
modules over affine algebras at the critical level. We construct eigenvectors
of these hamiltonians by restricting certain invariant functionals on tensor
products of Wakimoto modules. In conformal field theory language, the
eigenvectors are given by certain bosonic correlation functions. Analogues of
Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the
existence of certain singular vectors in Wakimoto modules. We use this
construction to expalain a connection between Gaudin's model and correlation
functions of WZNW models.Comment: 40 pages, postscript-file (references added and corrected
Computing Accurate Age and Distance Factors in Cosmology
As the universe expands astronomical observables such as brightness and
angular size on the sky change in ways that differ from our simple Cartesian
expectation. We show how observed quantities depend on the expansion of space
and demonstrate how to calculate such quantities using the Friedmann equations.
The general solution to the Friedmann equations requires a numerical solution
which is easily coded in any computing language (including EXCEL). We use these
numerical calculations in four student projects that help to build their
understanding of high-redshift phenomena and cosmology. Instructions for these
projects are available as supplementary materials.Comment: accepted for publication in the American Journal of Physic
Transport Equations for Oscillating Neutrinos
We derive a suite of generalized Boltzmann equations, based on the
density-matrix formalism, that incorporates the physics of neutrino
oscillations for two- and three-flavor oscillations, matter refraction, and
self-refraction. The resulting equations are straightforward extensions of the
classical transport equations that nevertheless contain the full physics of
quantum oscillation phenomena. In this way, our broadened formalism provides a
bridge between the familiar neutrino transport algorithms employed by supernova
modelers and the more quantum-heavy approaches frequently employed to
illuminate the various neutrino oscillation effects. We also provide the
corresponding angular-moment versions of this generalized equation set. Our
goal is to make it easier for astrophysicists to address oscillation phenomena
in a language with which they are familiar. The equations we derive are simple
and practical, and are intended to facilitate progress concerning oscillation
phenomena in the context of core-collapse supernova theory.Comment: 13 pages; Submitted to Physical Review
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