An expeditious construction of 9-membered rings

9-Membered rings are readily constructed through a radical addition-cyclisation sequence on a 1,6-dien-3-ol system followed by a Grob-type fragmentation.     

A divergent approach to highly substituted benzothiepinones and to 2,3-dihydrothieno[2,3-b]thiopyran-4-ones

The radical addition-transfer of S-(2-fluoro-phenacyl)xanthates can be used to construct rapidly benzothiepinones, including libraries of complex aza-bridged derivatives, and highly functionalized 2,3-dihydrothieno[2,3-b]thiopyran-4-ones.     

Membrane paradigm realized?

Are there any degrees of freedom on the black hole horizon? Using the ‘membrane paradigm’ we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need ‘real’ degrees of freedom at the horizon, which can modify Hawking’s evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.     

Stable numerical schemes for a partly convolutional partial integro-differential equation

A model partial integro-differential operator (PIDO) that contains both local and nonlocal diffusion operators is considered in this article. This type of operators come in modeling various scientific and financial engineering problems. In most cases, people use finite difference schemes to generate solutions of such model problems. We compare and analyze stability and accuracy of two such finite difference schemes. We first present a discrete analogue of the PIDO and then approximate the semi-discrete time dependent problem using two different one step methods and show the stability conditions and the accuracy of the schemes. We use the Fourier transforms throughout our analysis.     

Shear deformation plate continua of large double layered space structures

A simple method is presented to model large rigid-jointed lattice structures as continuous elastic media with couple stresses using energy equivalence. In our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a Taylor series about a suitable chosen origin. The strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua. Equivalent continua for single layered grids, double layered grids and three-dimensional lattices are then obtained.     

Generation of femtosecond pulses at 1350 nm by Cerenkov radiation in higher-order-mode fiber

We demonstrate a method of generating short pulses at 1350 nm by exciting Cerenkov radiation in a higher-order-mode fiber with a 1064 nm femtosecond fiber laser. We measure a 106 fs, 0.66 nJ output pulse. Cerenkov radiation in fibers allows for energy transfer between a soliton and a dispersive wave, providing an effective and engineerable platform to shift the wavelength of a femtosecond source. With appropriate design of the higher-order-mode fiber, this method of generating short pulses at 1350 nm can be extended to other wavelengths and to higher pulse energies.