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Flow of the Rio Grande and Related Data: From Elephant Butte Dam, New Mexico to the Gulf of Mexico 1979
Boundary smoothness of analytic functions
We consider the behaviour of holomorphic functions on a bounded open subset
of the plane, satisfying a Lipschitz condition with exponent , with
, in the vicinity of an exceptional boundary point where all such
functions exhibit some kind of smoothness. Specifically, we consider the
relation between the abstract idea of a bounded point derivation on the algebra
of such functions and the classical complex derivative evaluated as a limit of
difference quotients. We obtain a result which applies, for example, when the
open set admits an interior cone at the special boundary point.Comment: 14 pages. This revision corrects a misprint on p.12: In equation (3),
should have been . Also a misprint on page 14 in the
formula for . The validity of the argument is not affected and the
result stand
Boundary reconstruction for the broken ray transform
We reduce boundary determination of an unknown function and its normal
derivatives from the (possibly weighted and attenuated) broken ray data to the
injectivity of certain geodesic ray transforms on the boundary. For
determination of the values of the function itself we obtain the usual geodesic
ray transform, but for derivatives this transform has to be weighted by powers
of the second fundamental form. The problem studied here is related to
Calder\'on's problem with partial data.Comment: 23 pages, 1 figure; final versio
Boundary states in boundary logarithmic CFT
There exist logarithmic CFTs(LCFTs) such as the models. It is also
well known that it generally contains Jordan cell structure. In this paper, we
obtain the boundary Ishibashi state for a rank-2 Jordan cell structure and,
with these states in rational LCFT, we derive boundary states in the
closed string picture, which correspond to boundary conditions in the open
string picture. We also discuss the Verlinde formula for LCFT and possible
applications to string theory.Comment: LaTeX, 21 pages; a reference adde
Symmetric boundary conditions in boundary critical phenomena
Conformally invariant boundary conditions for minimal models on a cylinder
are classified by pairs of Lie algebras of ADE type. For each model, we
consider the action of its (discrete) symmetry group on the boundary
conditions. We find that the invariant ones correspond to the nodes in the
product graph that are fixed by some automorphism. We proceed to
determine the charges of the fields in the various Hilbert spaces, but, in a
general minimal model, many consistent solutions occur. In the unitary models
, we show that there is a unique solution with the property that the
ground state in each sector of boundary conditions is invariant under the
symmetry group. In contrast, a solution with this property does not exist in
the unitary models of the series and . A possible
interpretation of this fact is that a certain (large) number of invariant
boundary conditions have unphysical (negative) classical boundary Boltzmann
weights. We give a tentative characterization of the problematic boundary
conditions.Comment: 13 pages, REVTeX; reorganized and expanded version; includes a new
section on unitary minimal models; conjectures reformulated, pointing to the
generic existence of negative boundary Boltzmann weights in unitary model
\u3ci\u3eLetters on the Baluch-Afghan Boundary Commission of 1896 (1909)\u3c/i\u3e
Written to the English (Calcutta) and Times of India (Bombay) by their special correspondent with the Mission
Boundary Inflation
Inflationary solutions are constructed in a specific five-dimensional model
with boundaries motivated by heterotic M-theory. We concentrate on the case
where the vacuum energy is provided by potentials on those boundaries. It is
pointed out that the presence of such potentials necessarily excites bulk
Kaluza-Klein modes. We distinguish a linear and a non-linear regime for those
modes. In the linear regime, inflation can be discussed in an effective
four-dimensional theory in the conventional way. We lift a four-dimensional
inflating solution up to five dimensions where it represents an inflating
domain wall pair. This shows explicitly the inhomogeneity in the fifth
dimension. We also demonstrate the existence of inflating solutions with
unconventional properties in the non-linear regime. Specifically, we find
solutions with and without an horizon between the two boundaries. These
solutions have certain problems associated with the stability of the additional
dimension and the persistence of initial excitations of the Kaluza-Klein modes.Comment: 35 pages, Latex, one eps-figur
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