The free energies of the conformal field theories dual to charged adS and rotating adS black holes show Hawking-Page phase transition. We study the transition by constructing boundary free energies in terms of order parameters. This is done by employing Landau's phenomenological theory of first order phase transition. The Cardy-Verlinde formula is then showed to follow quite naturally. We furth...

A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, [Formula: see text] and [Formula: see text], play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error is calculated. This method is tested on three examples. The example...

Abstract. Given two unitary involutions σ1 and σ2 satisfying Gσi = −σiG on kerB on a compact manifold with cylindrical end, M. Lesch, K. Wojciechowski ([LW]) and W. Müller ([M]) established the formula describing the difference of two eta-invariants with the APS boundary conditions associated with σ1 and σ2. In this paper we establish the analogous formula for the zeta-determinants of Dirac Lap...

Alternating sign matrices with a U–turn boundary (UASMs) are a recent generalization of ordinary alternating sign matrices. Here we show that variations of these matrices are in bijective correspondence with certain symplectic shifted tableaux that were recently introduced in the context of a symplectic version of Tokuyama’s deformation of Weyl’s denominator formula. This bijection yields a for...

The paper is devoted to Schrödinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the Lax-Phillips scattering theory the asymptotic behaviour of the phase shift is investigated in detail and its relation to the spectral shift is discussed. In particular, the trace formula and the Birman-Krein formula are verified directly. The results ...

A rigorous proof for existence and uniqueness of solutions to a class of singular nonlinear boundary value problems arising in viscous flow and heat transfer behind a shock wave is made and a theoretical estimate formula for the skin friction coefficient is presented. The formula can be successfully applied to estimate the value of the skin friction coefficient. The correctness of the analytica...

Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over the transverse-electric and transverse-magnetic reflection coefficients associated with the surface, in analogy to the Lifshitz formula for the Casimir effect...

In this paper, we present a survey concerning unconstrained free boundary problems of type [Formula: see text] where B1 is the unit ball, Ω is an unknown open set, F(1) and F(2) are elliptic operators (admitting regular solutions), and [Formula: see text] is a functions space to be specified in each case. Our main objective is to discuss a unifying approach to the optimal regularity of solution...

In this paper we extend the results obtained in [9, 10] to manifolds with SpinC-structures defined, near the boundary, by an almost complex structure. We show that on such a manifold with a strictly pseudoconvex boundary, there are modified ∂̄-Neumann boundary conditions defined by projection operators, Reo + , which give subelliptic Fredholm problems for the SpinC-Dirac operator, ð eo + . We in...

Let X be a compact Kähler manifold with strictly pseudoconvex boundary, Y. In this setting, the SpinC Dirac operator is canonically identified with ∂̄ + ∂̄∗ : C∞(X ; Λ) → C∞(X ; Λ). We consider modifications of the classical ∂̄-Neumann conditions that define Fredholm problems for the SpinC Dirac operator. In part 2, [7], we use boundary layer methods to obtain subelliptic estimates for these bound...