156,364 research outputs found
Sequences, modular forms and cellular integrals
It is well-known that the Ap\'ery sequences which arise in the irrationality
proofs for and satisfy many intriguing arithmetic
properties and are related to the th Fourier coefficients of modular forms.
In this paper, we prove that the connection to modular forms persists for
sequences associated to Brown's cellular integrals and state a general
conjecture concerning supercongruences.Comment: 26 pages, to appear in Mathematical Proceedings of the Cambridge
Philosophical Societ
[Book Review of] \u3cem\u3eReasoning in Medicine: An Introduction to Clinical Inference\u3c/em\u3e, by Daniel A. Albert, Ronald Munson, and Michael D. Resnik
Vectorized Monte Carlo methods for reactor lattice analysis
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed
Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle
In this paper we shall re-visit the well-known Schr\"odinger and Lindblad
dynamics of quantum mechanics. However, these equations may be realized as the
consequence of a more general, underlying dynamical process. In both cases we
shall see that the evolution of a quantum state has the not
so well-known pseudo-quadratic form
where
is a vector operator in a complex Minkowski space and the pseudo-adjoint
is induced by the Minkowski metric . The
interesting thing about this formalism is that its derivation has very deep
roots in a new understanding of the differential calculus of time. This
Minkowski-Hilbert representation of quantum dynamics is called the
\emph{Belavkin Formalism}; a beautiful, but not well understood theory of
mathematical physics that understands that both deterministic and stochastic
dynamics may be `unraveled' in a second-quantized Minkowski space. Working in
such a space provided the author with the means to construct a QS (quantum
stochastic) Duhamel principle and known applications to a Schr\"odinger
dynamics perturbed by a continual measurement process are considered. What is
not known, but presented here, is the role of the Lorentz transform in quantum
measurement, and the appearance of Riemannian geometry in quantum measurement
is also discussed
The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time
Here it is shown that the unitary dynamics of a quantum object may be
obtained as the conditional expectation of a counting process of object-clock
interactions. Such a stochastic process arises from the quantization of the
clock, and this is derived naturally from the matrix-algebra representation of
the nilpotent Newton-Leibniz time differential [Belavkin]. It is observed that
this condition expectation is a rigorous formulation of the Feynman Path
Integral.Comment: 21 page
Hypercubes, Leonard triples and the anticommutator spin algebra
This paper is about three classes of objects: Leonard triples,
distance-regular graphs and the modules for the anticommutator spin algebra.
Let \K denote an algebraically closed field of characteristic zero. Let
denote a vector space over \K with finite positive dimension. A Leonard
triple on is an ordered triple of linear transformations in
such that for each of these transformations there exists a
basis for with respect to which the matrix representing that transformation
is diagonal and the matrices representing the other two transformations are
irreducible tridiagonal. The Leonard triples of interest to us are said to be
totally B/AB and of Bannai/Ito type.
Totally B/AB Leonard triples of Bannai/Ito type arise in conjunction with the
anticommutator spin algebra , the unital associative \K-algebra
defined by generators and relations
Let denote an integer, let denote the hypercube of diameter
and let denote the antipodal quotient. Let (resp.
) denote the Terwilliger algebra for (resp.
).
We obtain the following. When is even (resp. odd), we show that there
exists a unique -module structure on (resp.
) such that act as the adjacency and dual adjacency
matrices respectively. We classify the resulting irreducible
-modules up to isomorphism. We introduce weighted adjacency
matrices for , . When is even (resp. odd) we show
that actions of the adjacency, dual adjacency and weighted adjacency matrices
for (resp. ) on any irreducible -module (resp.
-module) form a totally bipartite (resp. almost bipartite) Leonard
triple of Bannai/Ito type and classify the Leonard triple up to isomorphism.Comment: arXiv admin note: text overlap with arXiv:0705.0518 by other author
Discrimination between the effect on soils of 4 tree species in pure and mixed stands using cotton strip assay
An analytical and experimental assessment of flexible road ironwork support structures
This paper describes work undertaken to investigate the mechanical performance of road ironwork installations in highways, concentrating on the chamber construction. The principal aim was to provide the background research which would allow improved designs to be developed to reduce the incidence of failures through improvements to the structural continuity between the installation and the surrounding pavement. In doing this, recycled polymeric construction materials (Jig Brix) were studied with a view to including them in future designs and specifications. This paper concentrates on the Finite Element (FE) analysis of traditional (masonry) and flexible road ironwork structures incorporating Jig Brix. The global and local buckling capacity of the Jig Brix elements was investigated and results compared well with laboratory measurements. FE models have also been developed for full-scale traditional (masonry) and flexible installations in a surrounding flexible (asphalt) pavement structure. Predictions of response to wheel loading were compared with full-scale laboratory measurements. Good agreement was achieved with the traditional (masonry) construction but poorer agreement for the flexible construction. Predictions from the FE model indicated that the use of flexible elements significantly reduces the tensile horizontal strain on the surface of the surrounding asphaltic material which is likely to reduce the incidence of surface cracking
Solving the electrical control of magnetic coercive field paradox
The ability to tune magnetic properties of solids via electric voltages instead of external magnetic fields is a physics curiosity of great scientific and technological importance. Today, there is strong published experimental evidence of electrical control of magnetic coercive fields in composite multiferroic solids. Unfortunately, the literature indicates highly contradictory results. In some studies, an applied voltage increases the magnetic coercive field and in other studies the applied voltage decreases the coercive field of composite multiferroics. Here, we provide an elegant explanation to this paradox and we demonstrate why all reported results are in fact correct. It is shown that for a given polarity of the applied voltage, the magnetic coercive field depends on the sign of two tensor components of the multiferroic solid: magnetostrictive and piezoelectric coefficient. For a negative applied voltage, the magnetic coercive field decreases when the two material parameters have the same sign and increases when they have opposite signs, respectively. The effect of the material parameters is reversed when the same multiferroic solid is subjected to a positive applied voltage
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