2,576,510 research outputs found

    Boundary smoothness of analytic functions

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    We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent α\alpha, with 0<α<10<\alpha<1, 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), α\alpha should have been 1−α1-\alpha. Also a misprint on page 14 in the formula for Ra−LaR_a-L_a. The validity of the argument is not affected and the result stand

    Boundary reconstruction for the broken ray transform

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    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

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    There exist logarithmic CFTs(LCFTs) such as the cp,1c_{p,1} 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 c=−2c=-2 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

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    Conformally invariant boundary conditions for minimal models on a cylinder are classified by pairs of Lie algebras (A,G)(A,G) 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 A⊗GA \otimes G 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 (A,A)(A,A), 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 (A,D)(A,D) and (A,E6)(A,E_6). 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

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    Written to the English (Calcutta) and Times of India (Bombay) by their special correspondent with the Mission

    Boundary Inflation

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    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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