52,523 research outputs found
The spectra of finite 3-transposition groups
We calculate the spectrum of the diagram for each finite -transposition
group. Such graphs with a given minimal eigenvalue have occurred in the context
of compact Griess subalgebras of vertex operator algebras
Eigenvalue bounds for a class of singular potentials in N dimensions
The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963]
for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to
N-dimensions. In particular a simple formula is derived which bounds the
eigenvalues for the spiked harmonic oscillator potential V(x) = x^2 +
lambda/x^alpha, alpha > 0, lambda > 0, and is valid for all discrete
eigenvalues, arbitrary angular momentum ell, and spatial dimension N.Comment: 10 pages (plain tex with 2 ps figures). J.Phys.A:Math.Gen.(In Press
Primitive axial algebras of Jordan type
An axial algebra over the field is a commutative algebra
generated by idempotents whose adjoint action has multiplicity-free minimal
polynomial. For semisimple associative algebras this leads to sums of copies of
. Here we consider the first nonassociative case, where adjoint
minimal polynomials divide for fixed . Jordan
algebras arise when , but our motivating examples are certain
Griess algebras of vertex operator algebras and the related Majorana algebras.
We study a class of algebras, including these, for which axial automorphisms
like those defined by Miyamoto exist, and there classify the -generated
examples. For this implies that the Miyamoto
involutions are -transpositions, leading to a classification.Comment: 41 pages; comments welcom
On primitive axial algebras of Jordan type
In this note we give an overview of our knowledge regarding primitive axial
algebras of Jordan type half and connections between -transposition groups
and Matsuo algebras. We also show that primitive axial algebras of Jordan type
admit a Frobenius form, for any .Comment: 10 page
A low-loss wideband suspended coaxial transmission line\ud
This paper presents a transmission-line structure suitable \ud
for micromachining technology. The structure is an air-filled square coaxial cable, which is very low loss and has been designed in order to utilise current manufacturing processes. This transmission line demonstrates that such a structure can be designed to cover very wide bandwidth. \ud
As the cable is air filled, the centre conductor needs to be supported and this is accomplished by attaching quarter-wavelength stubs to the ground. The design method of such a cable is presented in detail and the results of an X-band component are presented
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