A Collocation Code for Singular Boundary Value Problems in Ordinary Differential Equations

We present a MATLAB package for boundary value problems in ordinary differential equations. Our aim is the efficient numerical solution of systems of ODEs with a singularity of the first kind, but the solver can also be used for regular problems. The basic solution is computed using collocation methods and a new, efficient estimate of the global error is used for adaptive mesh selection. Here, we analyze some of the numerical aspects relevant for the implementation, describe measures to increase the efficiency of the code and compare its performance with the performance of established standard codes for boundary value problems.     

A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook

Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s ₁ψ₁ summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares. Dedicated to Richard Askey on the occasion of his 70th birthday. 2000 Mathematics Subject Classification Primary—33D15 B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency. A. J. Yee: Research partially supported by a grant from The Number Theory Foundation.     

Restructuring risk in credit default swaps: An empirical analysis

This paper estimates the price for restructuring risk in the US corporate bond market during 1999–2005. Comparing quotes from default swap (CDS) contracts with a restructuring event and without, we find that the average premium for restructuring risk represents 6%–8% of the swap rate without restructuring. We show that the restructuring premium depends on firm-specific balance-sheet and macroeconomic variables. And, when default swap rates without a restructuring event increase, the increase in restructuring premia is higher for low-credit-quality firms than for high-credit-quality firms. We propose a reduced-form arbitrage-free model for pricing default swaps that explicitly incorporates the distinction between restructuring and default events. A case study illustrating the model’s implementation is provided.     

Investigation of copolymers of styrene and ethyl methacrylate by size exclusion chromatography and gradient HPLC

Summary Copolymers of styrene and ethyl methacrylate have been separated according to composition by gradient HPLC on silica columns or CN bonded phase columns. This mode of separation according to composition was applied to fractions obtained by size exclusion chromatography (SEC). From viscosity and molecular mass data of copolymers with a styrene content ranging from 7.5 to 95.3 mass-% it can be concluded that SEC separates mainly by molecular mass even in this copolymer system. Thus, chromatographic cross-fractionation is possible by prefractionation by SEC and subsequent separation according to composition by gradient HPLC.

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Untersuchung von Copolymeren von Styrol und Ethylmethacrylat durch Ausschluß-Chromatographie und Gradienten-HPLC

     

Small shear viscosity of a quark-gluon plasma implies strong jet quenching

We derive an expression relating the transport parameter q and the shear viscosity eta of a weakly coupled quark-gluon plasma. A deviation from this relation can be regarded as a quantitative measure of "strong coupling" of the medium. The ratio T{3}/q, where T is the temperature, is a more broadly valid measure of the coupling strength of the medium than eta/s, where s denotes the entropy density. Different estimates of q derived from existing Relativistic Heavy Ion Collider data are shown to imply radically different structures of the produced matter.     

Surface Trapping and STM Observation of Conformational Isomers of a Bis(Terpyridine) Ligand from Metallosupramolecular Grids

Tetranuclear Co‐grid complexes incorporating bis‐tridentate ligands, namely 4,6‐bis(2,2′‐bipyrid‐6‐yl)‐2‐phenylpyrimidine, were electrosprayed onto a Au(111) substrate under an ultrahigh vacuum. Fragmentation occurs leaving the ligands in four different conformations. Most ligands are found to form H‐bonded dimers. The most abundant conformer of the ligand on the Au surface is an asymmetric form, which has not been observed before. The present results indicate that the fragmentation of coordination compounds during the deposition process, in principle, allows for surface trapping, identification, and investigation of high energy, out‐of‐equilibrium conformations of the ligand molecules at low temperatures, which otherwise would not be observable.