Measuring neutron-star radii with gravitational-wave detectors

Coalescing binary neutron stars (NS) are expected to be an important source of gravitational waves (GW) detectable by laser interferometers. We present here a simple method for determining the compactness ratio M/R of NS based on the observed deviation of the GW energy spectrum from point-mass behavior at the end of inspiral. Our method is based on the properties of quasiequilibrium binary NS sequences and does not require the computation of the full GW signal h(t). Combined with the measurement of the NS masses during inspiral, the determination of M/R will allow very strong constraints to be placed on the equation of state of dense nuclear matter.     

Forthcoming articles

Transition Metal Chemistry -     

A Bessel-Schwarz inequality for Gramians and related bounds for determinants

Summary Using the Gram matrix as a ? generalized inner product ?, several inequalities are derived which generalize the Schwarz and Bessel inequalities. The same approach is then used to obtain several well-known inequalities for determinants which have appeared in the literature. The research of the author was supported by the Air Force Office of Scientific Research under Grant AFOSR 400-63, and by the U.S. Naval Ordnance Laboratory, White Oak, Silver Spring, Maryland. Several of the results contained in this paper were presented to the American Mathematical Society at the Annual Meeting, 1963 (see the Notices Amer. Math. Soc., Vol. 10, No. 1, Part 1, p. 83).     

A comparison of mathematical programming modeling systems

We compare three mathematical programming modeling languages, GAMS, OMNI and MathPro. To understand the properties of these languages, we formulate four linear programs in each language. The formulations are representative of the kinds of model structures one encounters in practice. Each of the languages focuses on a different view of linear programs. GAMS approximates algebra, OMNI uses the activity view and MathPro uses a block schematic. We summarize our experiences with the languages and suggest areas for further enhancement.     

Hybrid fluorocarbon-hydrocarbon CO2-philic surfactants. 1. synthesis and properties of aqueous solutions

Six different hybrid fluorocarbon-hydrocarbon (F-H) sulfate and sulfonate surfactants, with variations in the relative F/H carbon chain length, have been synthesized and characterized in aqueous solution. These compounds have been targeted for potential activity in densified CO2. Tensiometric data and chemical analyses were consistent with surfactants of high chemical purity. Fluorination in terms of the F/H ratio exerts a strong control over all the surfactant physicochemical properties, including critical micelle concentrations (cmc's) and adsorption isotherms. One of these partially fluorinated surfactants (the sulfonate phi-F6H4) achieves very low surface tensions in water (gamma(cmc) approximately 19 mN m(-1)) more reminiscent of fully fluorinated double-chain compounds. Detailed 19F NMR studies revealed that omega'-CF3 groups can exhibit separate signals for monomeric and micellized forms, hence facilitating cmc determinations. Small-angle neutron scattering investigations confirmed the presence of ellipsoidal or extended disklike micelles, depending on the F-H chain asymmetry. For example, a symmetric hybrid F8H8 generates disklike micelles, whereas chain asymmetry in F8H4 or phi-F6H4 tends to drive cylindrical aggregation structures. These changes are consistent with variations in the surfactant packing parameter caused by the different chain F/H ratios. Hence, adsorption and aggregation are shown to respond in a predictable way to the molecular structure of these unusual surfactants.     

Self-affine surface morphology of plastically deformed metals

We analyze the surface morphology of metals after plastic deformation over a range of scales from 10 nm to 2 mm using atomic force microscopy and scanning white-light interferometry. We demonstrate that an initially smooth surface during deformation develops self-affine roughness over almost 4 orders of magnitude in scale. The Hurst exponent H of one-dimensional surface profiles initially decreases with increasing strain and then stabilizes at H approximately 0.75. We show that the profiles can be mathematically modeled as graphs of a fractional Brownian motion. Our findings can be understood in terms of a fractal distribution of plastic strain within the deformed samples.     

Universal Taylor Series on General Doubly Connected Domains

In this paper, a proof is given that there exists a universalTaylor series – in the sense of Nestoridis – inthe complement of a disk with respect to every center. Thisanswers a question asked by G. Costakis. 2000 Mathematics SubjectClassification 30B30.     

Synthesis of the carbocyclic core of the cornexistins by ring-closing metathesis

An advanced intermediate in the synthesis of the phytotoxins cornexistin and hydroxycornexistin has been synthesized. Sequential palladium-mediated sp(2)-sp(3) fragment coupling and ring-closing diene metathesis have been used to construct the nine-membered carbocyclic core found in the natural products. [reaction--see text]