Geometry projection method for optimizing photonic nanostructures

A geometry projection method for the design of photonic nanostructures is demonstrated and compared with a topology optimization method. By using a higher-dimensional surface to delineate the material interfaces, the projection method restricts the regions of intermediate dielectric properties to a narrow user-defined band and gives some implicit control over feature size. Topology optimization addresses these issues by using a penalization to avoid areas of intermediate dielectric and a filter to obtain implicit control over feature size. The directional emission from a photonic crystal waveguide termination is improved by both methods by generating a series of irregularly shaped dielectric posts. Results are presented, and the relative merits of each method are discussed.     

On sums of S-integers of bounded norm

We prove an asymptotic formula for the number of \(S\) -integers in a number field \(K\) that can be represented by a sum of \(n\) \(S\) -integers of bounded norm.     

An efficient and facile synthesis of highly substituted 2,6-dicyanoanilines

A one-pot procedure for the synthesis of substituted 2,6-dicyanoanilines starting from readily available ynones and malononitrile has been developed. For instance, penta-1,4-diyn-3-one is converted into the acetylene-substituted aniline derivative 1 in good yield. Upon photoexcitation, this chromophore shows a strong blue emission with a high quantum yield. The ground- and the excited-state geometries, charge distributions, and excitation energies of 1 have been evaluated by ab initio calculations.     

BSDEs in utility maximization with BMO market price of risk

This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary to the classical Itô representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a new dynamic exponential moments condition which is shown to be the minimal sufficient condition in a general filtration. The main results are complemented by several interesting examples which illustrate their sharpness as well as important properties of the utility maximization BSDE.