293,913 research outputs found
Locally finite near-fields
A near-field is locally finite if every finite subset of it generates a finite sub-near-field. The main aim of this thesis is to give a coherent account of locally finite-near-fields, including finite ones. The well known results for finite near-fields are lised and proofs are given where appropriate. The results of Zassenhaus classify finite regular near-fields according to their order, pln, and the order of centres, pl, and Luneburg has determined the number of isomorphism types within each class. A polynomial h is given here which, together with the triple p, l, n, completely determines a finite regular near-field, up to isomorphism. The sub-near-field structure is determined in terms of these invariants and some results concerning near-field embeddings are included
A Monte Carlo study of surface critical phenomena: The special point
We study the special point in the phase diagram of a semi-infinite system,
where the bulk transition is in the three-dimensional Ising universality class.
To this end we perform a finite size scaling study of the improved Blume-Capel
model on the simple cubic lattice with two different types of surface
interactions. In order to check for the effect of leading bulk corrections we
have also simulated the spin-1/2 Ising model on the simple cubic lattice. We
have accurately estimated the surface enhancement coupling at the special point
of these models. We find and for the
surface renormalization group exponents of the special transitions. These
results are compared with previous ones obtained by using field theoretic
methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore we
study the behaviour of the surface transition near the special point and
finally we discuss films with special boundary conditions at one surface and
fixed ones at the other.Comment: 21 pages, 2 figures. figure 1 replaced, various typos correcte
On semi-finite hexagons of order containing a subhexagon
The research in this paper was motivated by one of the most important open
problems in the theory of generalized polygons, namely the existence problem
for semi-finite thick generalized polygons. We show here that no semi-finite
generalized hexagon of order can have a subhexagon of order .
Such a subhexagon is necessarily isomorphic to the split Cayley generalized
hexagon or its point-line dual . In fact, the employed
techniques allow us to prove a stronger result. We show that every near hexagon
of order which contains a generalized hexagon of
order as an isometrically embedded subgeometry must be finite. Moreover, if
then must also be a generalized hexagon, and
consequently isomorphic to either or the dual twisted triality hexagon
.Comment: 21 pages; new corrected proofs of Lemmas 4.6 and 4.7; earlier proofs
worked for generalized hexagons but not near hexagon
Curvature tensors on distorted Killing horizons and their algebraic classification
We consider generic static spacetimes with Killing horizons and study
properties of curvature tensors in the horizon limit. It is determined that the
Weyl, Ricci, Riemann and Einstein tensors are algebraically special and
mutually aligned on the horizon. It is also pointed out that results obtained
in the tetrad adjusted to a static observer in general differ from those
obtained in a free-falling frame. This is connected to the fact that a static
observer becomes null on the horizon.
It is also shown that finiteness of the Kretschmann scalar on the horizon is
compatible with the divergence of the Weyl component or
in the freely falling frame. Furthermore finiteness of is compatible
with divergence of curvature invariants constructed from second derivatives of
the Riemann tensor.
We call the objects with finite Krestschmann scalar but infinite
``truly naked black holes''. In the (ultra)extremal versions of these objects
the structure of the Einstein tensor on the horizon changes due to extra terms
as compared to the usual horizons, the null energy condition being violated at
some portions of the horizon surface. The demand to rule out such divergencies
leads to the constancy of the factor that governs the leading term in the
asymptotics of the lapse function and in this sense represents a formal analog
of the zeroth law of mechanics of non-extremal black holes. In doing so, all
extra terms in the Einstein tensor automatically vanish.Comment: 21 pages, To appear in Class. Quant. Gra
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