Left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions are studied. A characterization is given in terms of right-definite problems, a concrete and “natural” indexing scheme for the eigenvalues is proposed. Pruefer transformation techniques can be used to establish the existence of and to give a characterization for the eigenvalues in the case...

In N = 4 super Yang-Mills spin chain, we compute reflection amplitudes of magnon bound-state off giant graviton. We first compute the reflection amplitude off Y = 0 brane boundary and compare it with the scattering amplitude between two magnon bound-states in the bulk. We find that analytic structure of the two amplitudes are intimately related each other: the boundary reflection amplitude is a...

Abstract Based on the insight gained by many authors over years structure of Einstein–Hilbert, Gauss–Bonnet and Lovelock gravity Lagrangians, we show how to derive-in an elementary fashion-their first-order, generalized ‘Arnowitt–Deser–Misner’ Lagrangian associated Hamiltonian. To do so, start from supplemented with Myers boundary term, which guarantees a Dirichlet variational principle surface...

In this paper, we are concerned with the asymptotic behavior of solutions to Cauchy problem (or initial-boundary value problem) one-dimensional Keller–Segel model. For problem, prove that time-asymptotically converge nonlinear diffusion wave whose profile is self-similar solution corresponding parabolic equation, which derived by Darcy's law. consider two cases: Dirichlet boundary condition and...

Four classes of models of the lightning return stroke are reviewed. These four classes are: 1) the gas dynamic models; 2) the electromagnetic models; 3) the distributed-circuit models; and 4) the “engineering” models. Validation of the reviewed models is discussed. For the gas dynamic models, validation is based on observations of the optical power and spectral output from natural lightning. Th...

It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying algebra, a semisimple commutative associative complex algebra. We show how this algebra arises naturally from the three-dimensional geometry of factorization ...

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one can not go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the contro...

We obtain the reflection matrices for the scattering of elementary magnons from certain open boundaries, corresponding to open strings ending on D7 and D5 branes in AdS5 × S. In each case we consider two possible orientations for the vacuum state. We show that symmetry arguments are sufficient to determine the reflection matrices up to at most two unknown functions. The D7 reflection matrices o...

This work deals with trace theorems for a class of ramified bidimensional domains Ω with a self-similar fractal boundary Γ. The fractal boundary Γ is supplied with a probability measure μ called the self-similar measure. Emphasis is put on the case when the domain is not a − δ domain as defined by Jones and the fractal set is not totally disconnected. In this case, the classical trace results c...