This paper is concerned with the first crossing of an order statistic point process through general moving boundaries. Our purpose is to determine exact boundary crossing probabilities in both one and two boundary cases. Simple recursive methods are obtained that exploit an underlying algebraic structure of polynomial type. This structure is a direct consequence of the order statistic property....

This paper proves sharp inequalities for the frequencies of vibration of strings and cylindrical membranes, under either fixed or fixed-free boundary conditions. We establish such inequalities also on the "generalized" cylinder, which is the cross-product of an interval with a homogeneous Riemannian manifold. The goal is to better understand the effect that inhomogeneities in the mass distribut...

Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.

We analyze Einstein’s vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions, which is constraint-preserving and sufficiently general to include recent proposals for reducing the amount of spurious reflections of gravitational radiation. In particular, our class comprises the boundary conditions recently ...

In quantum theory Hamilton operators with spininteractions have a long history [1 – 5]. Triple spin interaction have been studied by several authors [6 – 19]. Iglói [6] investigated an Ising model with three-spin interaction by finite-size scaling and applying free boundary conditions. Vanderzande and Iglói [7] studied the critical behaviour and logarithmic corrections of a quantum model with t...

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian primary constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a new feature in the context of constrained systems. We discuss the Dirac brackets and the reduced phase space structure for different boundary conditio...

Generic classically integrable boundary conditions for the A (1) n affine Toda field theories (ATFT) are investigated. The present analysis relies primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the A (1) 2 ATFT, however our results may be generalized for any A (1) n...

Generic classically integrable boundary conditions for the A (1) n affine Toda field theories (ATFT) are investigated. The present analysis rests primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the A (1) 2 ATFT, however our results may be generalized for any A (1) n ...

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian primary constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a new feature in the context of constrained systems. We discuss the Dirac brackets and the reduced phase space structure for different boundary conditio...

This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the strong curvature regime by means of CFT on surfaces with boundary.