Preparation and structure elucidation of 1,6,9,13‐tetraoxadispiro(4.2.4.2)tetradecane

The tricyclic title compound, a symmetrical dispiro oxygen heterocycle, was isolated as a byproduct in the hydrogenation of furfuryl alcohol in the presence of hydrochloric acid. NMR studies and single crystal X‐ray analysis have established the relative stereochemistry of the two ketal carbons. Formation of the observed trans stereoisomer under equilibrating conditions is attributed to the anomeric effect.     

A C2-symmetric analogue of dppf: synthesis and structures of the indenyl-diphosphine complex 1,3-(Ph2PSe)2(C9H6) and the racemic and meso isomers of the heterobimetallic complex Mo(CO)4(1-PPh2-η-C9H6)2Fe

The preparation, isolation and characterisation of 1,3-bis(diphenylphosphino)indene (1) from indene and chlorodiphenylphosphine is described. The reaction of 1 with selenium gives the diselenide adduct 1,3-bis(diphenylselenophosphino)indene (2) which was characterised crystallographically. Deprotonation of 1 and treatment with ferrous chloride gives the unstable tetraphosphine complex bis(1,3-bis(diphenylphosphino)indenyl)iron(II) (3). Complex 3 decomposes to the diphosphine complex bis(1-diphenylphosphinoindenyl)iron(II) (4) via replacement of one diphenylphosphine substituent per indenyl ligand by a hydrogen atom. Complex 4 was also prepared by treatment of two equivalents of 1-diphenylphosphinoindenide with ferrous chloride. The heterobimetallic complex tetracarbonyl(bis(1-diphenylphosphinoindenyl)iron(II))molybdenum(0) (5) was also prepared and crystal structures of both the meso (5a) and C₂-symmetric racemic (5b) isomers are reported.     

Derivatization of peptides and small proteins for improved identification and detection in capillary zone electrophoresis (CZE)

Peptides and small proteins, of limited molecular weight (MW) can be derivatized with a 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (6-AQC) reagent, leading to a single capillary zone electrophoresis (CZE) peak, suggestive of a completely tagged product. The number of tags per molecule was demonstrated by matrix assisted, laser desorption, time-of-flight mass spectrometry (MALDI-TOFMS) studies. In CZE, these species have greatly improved plate count and peak shape, improved (lowered) detectabilities, and in general, improved identification properties in the CZE mode in high performance capillary electrophoresis (HPCE). The formation of what appears to be a single, homogeneously tagged product is a function of how the derivatizations are performed. Once these conditions are optimized, virtually all peptides and small proteins tested (limited MW) can form single, fully tagged products, with the desirable CZE properties. These derivatization approaches thus lead to products that perform and are detected much better in CZE than their precursors (native, untagged peptides). The determined plate counts for these tagged peptides were as high as 6 million plates/m, which was very reproducible, and 59–12,000 times higher than the untagged (native) molecules. The peak symmetry was also improved greatly. The limit of detection (LOD) of some tested 6-AQC tagged peptides were nine to 209 times improved (lower) with ultraviolet (UV) absorption detection, again as compared with that for the native species. The LOD could be further lowered via laser induced fluorescence (LIF) detection in CZE, especially when acetonitrile (ACN) containing buffers were used.     

The rate at which energy decays in a damped String

The energy in a string subject to positive viscous damping is known to decay exponentially in time. Under the assumption that the damping is of bounded variation, we identify the best rate of decay with the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup. We analyze the spectrum of this nonselfadjoint operator in some detail. Our bounds on its real eigenvalues and asymptotic form of its large eigenvalues translate into criteria for over/underdamping and a proof that the decay rate achieves its (negative) minimum over those dampings whose total variation does not exceed a prescribed value.     

Reducible and finite Dehn fillings

We show that the distance between a finite filling slope anda reducible filling slope on the boundary of a hyperbolic knotmanifold is one.     

Eigenvalue computation for unitary rank structured matrices

In this paper we describe how to compute the eigenvalues of a unitary rank structured matrix in two steps. First we perform a reduction of the given matrix into Hessenberg form, next we compute the eigenvalues of this resulting Hessenberg matrix via an implicit QR-algorithm. Along the way, we explain how the knowledge of a certain ‘shift’ correction term to the structure can be used to speed up the QR-algorithm for unitary Hessenberg matrices, and how this observation was implicitly used in a paper due to William B. Gragg. We also treat an analogue of this observation in the Hermitian tridiagonal case.