Three-dimensional Schwarzschild spacetimes

In the following we find all of the three-dimensional flat spacetimes which are static and rotationally symmetric.     

A Tin(IV) Porphyrin with Two Axial Organometallic NCN‐Pincer Platinum Units

A tin(IV) porphyrin was combined with two axial NCN‐pincer platinum(II) fragments by utilizing the oxophilicity of the apical positions on the tin atom and the acidic nature of the NCN‐pincer platinum derived benzoic acid. The solid‐state structure determined by X‐ray crystallography revealed some close contacts between the pincer complexes and the meso‐p‐tolyl subsitutents of the porphyrin. It was shown by ¹H NMR spectroscopy that these close contacts were not present in solution and that this compound can potentially act as a novel building block for supramolecular architectures.     

Time-marching numerical schemes for the electric field integral equation on a straight thin wire

We derive and analyse four algorithms for computing the current induced on a thin straight wire by a transient electric field. They all involve solving the thin wire electric field integral equations (EFIEs) and consist of a very accurate differential equations solver together with various schemes to approximate the vector potential integral equation. We carry out a rigorous numerical stability analysis of each of these methods. This has not previously been done for solution schemes for the thin wire EFIEs. Each scheme is shown to be stable and convergent provided the radius of the wire is small enough for the thin wire equations to be a valid model.     

Ring resonators with N × M couplers

Multiple-zero multiple-pole optical filter transfer functions may be implemented more efficiently in an integrated optics architecture if higher order N × M optical couplers are utilized. For example, a coherent ring resonator made from two 3×3 couplers offers some advantages over the three mirror Fabry-Perot etalon, which is its analog. To this end we develop the formalism for obtaining the transfer functions and scattering matrices of ring resonators made from two N × M couplers. We then present a methodology for analyzing serial and parallel systems of N × M optical coupler ring resonators.     

Quantized enveloping algebras for Borcherds superalgebras

We construct quantum deformations of enveloping algebras of Borcherds superalgebras, their Verma modules, and their irreducible highest weight modules.

     

Reactions of siliranes with elemental sulfur and with t-butyl mercaptan. Preparation of the 2,3-dithia-1-silacyclopentane ring system

The reaction of 1,1-dimethyl-trans-2,3,-bis(2′,2′-dimethylcyclopropylidene)-1-silirane with S₈ gives a mixture of four isomeric products derived from incorporation of one sulfur atom and a cyclopropylcarbinyl-to-butenyl type rearrangement. This silirane reacts with t-butyl mercaptan to give a product of mercaptan addition in which a cyclopropylcarbinyl-to-butenyl rearrangement also has occurred. Hexamethylsilirane reacts with S₈ to give 1,1,4,4,5,5-hexamethyl-2,3-dithia-1-silacyclopentane in high yield. These reactions are discussed in terms of free radical mechanisms.