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201
Boundary Integral Equations
"... Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. The later has become one of the most popular numerical schemes in recent years. In this expository paper, we ..."
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Cited by 53 (3 self)
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Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. The later has become one of the most popular numerical schemes in recent years. In this expository paper, we discuss some of the essential features of the methods, their intimate relations with the variational formulations of the corresponding partial differential equations and recent developments with respect to applications in domain composition from both mathematical and numerical points of view. 1 Variational Formulations
Solving open string field theory with special projectors,” hepth/0606131
"... Schnabl recently found an analytic expression for the string field tachyon condensate using a gauge condition adapted to the conformal frame of the sliver projector. We propose that this construction is more general. The sliver is an example of a special projector, a projector such that the Virasoro ..."
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Cited by 43 (5 self)
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Schnabl recently found an analytic expression for the string field tachyon condensate using a gauge condition adapted to the conformal frame of the sliver projector. We propose that this construction is more general. The sliver is an example of a special projector, a projector such that the Virasoro operator L0 and its BPZ adjoint L ⋆ 0 obey the algebra [L0, L ⋆ 0] = s(L0 + L ⋆ 0), with s a positive real constant. All special projectors provide abelian subalgebras of string fields, closed under both the ∗product and the action of L0. This structure guarantees exact solvability of a ghost number zero string field equation. We recast this infinite recursive set of equations as an ordinary differential equation that is easily solved. The classification of special projectors is reduced to a version of the RiemannHilbert problem, with piecewise constant data on the boundary of a disk.
The Hagedorn transition, deconfinement and N = 4 SYM theory,” Nucl. Phys
 B
, 2001
"... N = 4 Super YangMills theory supplies us with a nonAbelian 4D gauge theory with a meaningful perturbation expansion, both in the UV and in the IR. We calculate the free energy on a 3sphere and observe a deconfinement transition for large N at zero coupling. The same thermodynamic behaviour is fou ..."
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Cited by 24 (0 self)
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N = 4 Super YangMills theory supplies us with a nonAbelian 4D gauge theory with a meaningful perturbation expansion, both in the UV and in the IR. We calculate the free energy on a 3sphere and observe a deconfinement transition for large N at zero coupling. The same thermodynamic behaviour is found for a wide class of toy models, possibly also including the case of nonzero coupling. Below the transition we also find Hagedorn behaviour, which is identified with fluctuations signalling the approach to the deconfined phase. The Hagedorn and the deconfinement temperatures are identical. Application of the AdS/CFT correspondence gives a connection between string Hagedorn behaviour and black holes. 1
The effect of cavitation on glacier sliding
, 2005
"... Basal sliding is one of the most important components in the dynamics of fastflowing glaciers, but remains poorly understood on a theoretical level. In this paper, the problem of glacier sliding with cavitation over hard beds is addressed in detail. First, a bound on drag generated by the bed is de ..."
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Cited by 19 (2 self)
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Basal sliding is one of the most important components in the dynamics of fastflowing glaciers, but remains poorly understood on a theoretical level. In this paper, the problem of glacier sliding with cavitation over hard beds is addressed in detail. First, a bound on drag generated by the bed is derived for arbitrary bed geometries. This bound shows that the commonly used sliding law, τb = Cumb N n, cannot apply to beds with bounded slopes. In order to resolve the issue of a realistic sliding law, we consider the classical Nye–Kamb sliding problem, extended to cover the case of cavitation but neglecting regelation. Based on an analogy with contact problems in elasticity, we develop a method which allows solutions to be constructed for any finite number of cavities per bed period. The method is then used to find sliding laws for irregular hard beds, and to test previously developed theories for calculating the drag generated by beds on which obstacles of many different sizes are present. It is found that the maximum drag attained is controlled by those bed obstacles which have the steepest slopes.
Hilbert analysis for orthogonal polynomials
 Orthogonal Polynomials and Special Functions (E. Koelink and W. Van Assche eds.) Lecture Notes in Mathematics 1817 (2003
"... Summary. This is an introduction to the asymptotic analysis of orthogonal polynomials based on the steepest descent method for RiemannHilbert problems of Deift and Zhou. We consider in detail the polynomials that are orthogonal with respect to the modified Jacobi weight (1 − x) α (1 + x) β h(x) on ..."
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Cited by 19 (8 self)
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Summary. This is an introduction to the asymptotic analysis of orthogonal polynomials based on the steepest descent method for RiemannHilbert problems of Deift and Zhou. We consider in detail the polynomials that are orthogonal with respect to the modified Jacobi weight (1 − x) α (1 + x) β h(x) on [−1, 1] where α, β> −1 and h is real analytic and positive on [−1, 1]. These notes are based on joint work with
Inverse Scattering theory for onedimensional Schrödinger operators with steplike finitegap potentials
, 2008
"... We develop direct and inverse scattering theory for onedimensional Schrödinger operators with steplike potentials which are asymptotically close to different finitegap potentials on different halfaxes. We give a complete characterization of the scattering data, which allow unique solvability of t ..."
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Cited by 14 (12 self)
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We develop direct and inverse scattering theory for onedimensional Schrödinger operators with steplike potentials which are asymptotically close to different finitegap potentials on different halfaxes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.
The attenuated xray transform: Recent developments
 Inside Out: Inverse Problems and Applications
, 2003
"... Abstract. We survey recent work on the attenuated xray transform, concentrating especially on the inversion formulas found in the last few years. 1. ..."
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Cited by 14 (0 self)
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Abstract. We survey recent work on the attenuated xray transform, concentrating especially on the inversion formulas found in the last few years. 1.
Equilibrium problems associated with fast decreasing polynomials
 Proc. Amer. Math. Soc
, 1999
"... Abstract. The determination of the support of the equilibrium measure in the presence of an external field is important in the theory of weighted polynomials on the real line. Here we present a general condition guaranteeing that the support consists of at most two intervals. Applying this to the ex ..."
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Cited by 13 (9 self)
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Abstract. The determination of the support of the equilibrium measure in the presence of an external field is important in the theory of weighted polynomials on the real line. Here we present a general condition guaranteeing that the support consists of at most two intervals. Applying this to the external fields associated with fast decreasing polynomials, we extend previous results of Totik and KuijlaarsVan Assche. In the proof we use the iterated balayage algorithm which was first studied by Dragnev.
Singular integral equations in the Lebesgue spaces with variable exponent
 Proc. A. Razmadze Math. Inst
"... For the singular integral operators with piecewise continuous coefficients there is proved the criterion of Fredholmness and formula for index in the generalized Lebesgue spaces Lp(·)(Γ) on a finite closed Lyapunov curve Γ or a curve of bounded rotation. The obtained criterion shows that Fredholmnes ..."
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Cited by 13 (8 self)
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For the singular integral operators with piecewise continuous coefficients there is proved the criterion of Fredholmness and formula for index in the generalized Lebesgue spaces Lp(·)(Γ) on a finite closed Lyapunov curve Γ or a curve of bounded rotation. The obtained criterion shows that Fredholmness in this space and the index depend on values of the function p(t) at the discontinuity points of the coefficients of the operator, but do not depend on values of p(t) at points of their continuity.