Results 1  10
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112
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
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 16 (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 11 (11 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 8 (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.
Limiting laws of linear eigenvalue statistics for unitary invariant matrix models
 J. Math. Phys
, 2006
"... We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n ×n Hermitian matrices as n → ∞. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogona ..."
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Cited by 6 (3 self)
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We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n ×n Hermitian matrices as n → ∞. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogonal polynomials with varying weights, we show first that if the support of the Density of States of the model consists of q ≥ 2 intervals, then in the global regime the variance of statistics is a quasiperiodic function of n as n → ∞ generically in the potential, determining the model. We show next that the exponent of the Laplace transform of the probability law is not in general 1/2 × variance, as it should be if the Central Limit Theorem would be valid, and we find the asymptotic form of the Laplace transform of the probability law in certain cases.
Amplitude equations for electrostatic waves: universal singular behavior in the limit of weak instability, Phys
 Plasmas
, 1995
"... An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the unstable manifold of the equilibrium F0(v). The mode eigenvalue arises from a simple zero of the dielectric ǫk(z); as the linear growth rate γ vanishes, the eigenvalue merges with the continuous ..."
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Cited by 5 (5 self)
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An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the unstable manifold of the equilibrium F0(v). The mode eigenvalue arises from a simple zero of the dielectric ǫk(z); as the linear growth rate γ vanishes, the eigenvalue merges with the continuous spectrum on the imaginary axis and disappears. The evolution of the mode amplitude ρ(t) is studied using an expansion in ρ. As γ → 0 +, the expansion coefficients diverge, but these singularities are absorbed by rescaling the amplitude: ρ(t) ≡ γ2 r(γt). This renders the theory finite and also indicates that the electric field exhibits trapping scaling E ∼ γ 2. These singularities and scalings are independent of the specific F0(v) considered. The asymptotic dynamics of r(τ) can depend on F0 only through exp iξ where dǫk/dz = ǫ ′ k exp −iξ/2. Similar results also hold for the electric field and distribution function.
The vector formfactor of the pion from unitariry and analyticity: a model independent approach
"... We study a model–independent parameterization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to √ s ≃ 1.2GeV and allows a model–independent determination of the mass of the ρ(770) resonance, Mρ = (775.1 ± 0.5)MeV. W ..."
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Cited by 5 (4 self)
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We study a model–independent parameterization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to √ s ≃ 1.2GeV and allows a model–independent determination of the mass of the ρ(770) resonance, Mρ = (775.1 ± 0.5)MeV. We analyse the experimental data on τ − → π−π0ντ, in this framework, and its consequences on the low–energy observables worked out by chiral perturbation theory. An evaluation of the two pion contribution to the anomalous magnetic moment of the muon, aµ, and to the fine structure constant, α(M2 Z), is also performed. The hadronic matrix elements of Quantum Chromodynamics (QCD) currents play a basic role in the understanding of electroweak processes at the low–energy regime (typically E ∼ 1 GeV). However our poor knowledge of the QCD dynamics at these energies introduces annoying and serious incertitudes in the description and prediction of the processes involved.
A Tandem Queueing Model with Coupled Processors
 Operations Research Letters
, 2003
"... We consider a tandem queue with coupled processors and analyze the twodimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this twodimensional process is derived and solved through the t ..."
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Cited by 4 (2 self)
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We consider a tandem queue with coupled processors and analyze the twodimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this twodimensional process is derived and solved through the theory of RiemannHilbert boundary value problems.
The GelfondSchnirelman Method In Prime Number Theory
 Canad. J. Math
"... The original GelfondSchnirelman method, proposed in 1936, uses polynomials with integer coe#cients and small norms on [0, 1] to give a Chebyshevtype lower bound in prime number theory. We study a generalization of this method for polynomials in many variables. Our main result is a lower bound for t ..."
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Cited by 4 (4 self)
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The original GelfondSchnirelman method, proposed in 1936, uses polynomials with integer coe#cients and small norms on [0, 1] to give a Chebyshevtype lower bound in prime number theory. We study a generalization of this method for polynomials in many variables. Our main result is a lower bound for the integral of Chebyshev's #function, expressed in terms of the weighted capacity. This extends previous work of Nair and Chudnovsky, and connects the subject to the potential theory with external fields generated by polynomialtype weights. We also solve the corresponding potential theoretic problem, by finding the extremal measure and its support. 1. Lower bounds for arithmetic functions Let #(x) be the number of primes not exceeding x. The celebrated Prime Number Theorem (PNT), suggested by Legendre and Gauss, states that ##.