132,327 research outputs found
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
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
The importance of social worlds: an investigation of peer relationships [Wider Benefits of Learning Research Report No. 29]
In the following report, we investigate the developing social worlds in late primary school, exploring the patterns in childrenâs general peer relationships, their closer and more significant friendships and bullying behaviours. Using cluster analysis, we identify unique groups of children characterized not only by their experiences of bullying and victimization, but the support and satisfaction they receive from their friendships and interactions between the ages of 8 and 10. We also expand past research by examining how childrenâs early development (ages 3 to 4) may predict their later designation as bullies and/or victims, and whether peer clusters relate to childrenâs contemporaneous and later adjustment
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
The reduced Lefschetz number, that is, the Lefschetz number minus 1, is
proved to be the unique integer-valued function L on selfmaps of compact
polyhedra which is constant on homotopy classes such that (1) L(fg) = L(gf),
for f:X -->Y and g:Y -->X; (2) if (f_1, f_2, f_3) is a map of a cofiber
sequence into itself, then L(f_2) = L(f_1) + L(f_3); (3) L(f) = - (degree(p_1 f
e_1) + ... + degree(p_k f e_k)), where f is a map of a wedge of k circles, e_r
is the inclusion of a circle into the rth summand and p_r is the projection
onto the rth summand. If f:X -->X is a selfmap of a polyhedron and I(f) is the
fixed point index of f on all of X, then we show that I minus 1 satisfies the
above axioms. This gives a new proof of the Normalization Theorem: If f:X -->X
is a selfmap of a polyhedron, then I(f) equals the Lefschetz number of f. This
result is equivalent to the Lefschetz-Hopf Theorem: If f: X -->X is a selfmap
of a finite simplicial complex with a finite number of fixed points, each lying
in a maximal simplex, then the Lefschetz number of f is the sum of the indices
of all the fixed points of f.Comment: 9 page
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