We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength H is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the...

Abstract. Let A be an n by n symmetric matrix with real entries. Using the l1-norm for vectors and letting S 1 = {x ∈ R|||x||1 = 1, x ≥ 0}, the matrix A is said to be interior if the quadratic form x Ax achieves its minimum on S 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not th...

We apply an integrated and interdisciplinary conceptual framework to assess the potential for uptake of bycatch reduction measures by small-scale fisheries along the Andaman coast and eastern Gulf of Thailand, and in Sabah, Malaysia. Specifically, we characterize the current governance, socio-economic, ecological, and scientific context for marine megafauna bycatch, and identify the enabling an...

We formulate and exploit a computational inverse-design method based on topology optimization to demonstrate photonic crystal structures supporting complex spectral degeneracies. In particular, we discover photonic crystals exhibiting third-order Dirac points formed by the accidental degeneracy of monopolar, dipolar, and quadrupolar modes. We show that, under suitable conditions, these modes ca...

The generalized Schrr odinger equation d 2 =dx 2 + F (k) = ikP (x) + Q(x)] is considered, where P and Q are integrable potentials with nite rst moments and F satisses certain conditions. The behavior of the scattering coeecients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coeecients at a zero of F may be aaected by P (x): The loc...

Exception handling is a powerful abstraction that can be used to help manage errors and support the construction of reliable operating systems. Using exceptions to notify system components about exceptional conditions also reduces coupling of error handling code and increases the modularity of the system. We explore the benefits of incorporating exception handling into the Choices operating sys...

We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the ‘blob’ algebra (the reason for the name will become obvious shortly!). We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the period...

Let A be an n by n symmetric matrix with real entries. Using the l1-norm for vectors and letting S 1 = {x ∈ Rn|||x||1 = 1, x ≥ 0}, the matrix A is said to be interior if the quadratic form xT Ax achieves its minimum on S 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not the sum of...