Probing the interior of neutron stars with gravitational waves

We show here how the internal structure of a neutron star can be inferred from its gravitational wave spectrum. Under the premise that the frequencies and damping rates of a few w-mode oscillations are found, we apply an inversion scheme to determine its mass, radius, and density distribution. In addition, an accurate equation of state of nuclear matter can also be determined.     

High-resolution angular measurement using surface-plasmon-resonance via phase interrogation at optimal incident wavelengths

It is demonstrated that ultrahigh-resolution angular measurement can be achieved via surface-plasmon-resonance excitation in which the phase difference between p- and s-polarized reflected waves is monitored as a function of the incidence angle. Resolutions down to 1.9 x 10(-6) deg are obtained by performing the measurements at optimal incident wavelengths. This represents an order of magnitude improvement compared with previously reported values.     

Nonexistence of abelian difference sets: Lander's conjecture for prime power orders

In 1963 Ryser conjectured that there are no circulant Hadamard matrices of order 4$"> and no cyclic difference sets whose order is not coprime to the group order. These conjectures are special cases of Lander's conjecture which asserts that there is no abelian group with a cyclic Sylow -subgroup containing a difference set of order divisible by . We verify Lander's conjecture for all difference sets whose order is a power of a prime greater than 3.

     

Nuclear hyperfine coupling interactions in the rotational spectra of the linear and bent isomers of HF-N2O

The rotational spectra of six isotopomers of the linear and bent isomers of HF-N₂O have been collected in the 7-18 GHz region with a Fourier transform microwave spectrometer. The nuclear hyperfine structure in the spectra produced by HF spin-spin coupling interaction and nuclear quadrupole coupling interactions due to the D nucleus of DF and the nuclei of N₂O have been resolved and analyzed. In the linear isomer, H in HF is bonded to the terminal N in N₂O. The NF bond lengths are 2.9808(2) Å for the HF-containing isotopomers and 2.9732(2) Å for the DF-containing isotopomers. The zero point angles are 23.1° for HF and 31-34° for N₂O. The hyperfine constants suggest that the HF bond is lengthened by 0.0105 Å upon complexation and that the electric field gradients of the two nitrogen nuclei in N₂O are perturbed differently in the complex. In the bent isomer, the hydrogen bond is formed between HF and O in N₂O. The intermolecular distances are 3.4942(2) Å for the HF-containing isotopomers and 3.4436(2) Å for the DF-containing isotopomers, with HF and N₂O forming angles of 34° and 46°, respectively, with the intermolecular axis. The nuclear quadrupole coupling constants of the two nitrogen nuclei do not indicate electric field gradient perturbation in this isomer.     

Low-energy spectra in t-J-type models at low doping levels

Based on a variational approach, we propose that there are two kinds of low-energy states in the t-J-type models at low doping. In a quasiparticle state an unpaired spin bound to a hole with a well-defined momentum can be excited with spin waves. The resulting state shows a suppression of antiferromagnetic order around the hole with the profile of a spin bag. These spin-bag states with spin and charge or hole separated form a continuum of low-energy excitations. Very different properties predicted by these two kinds of states explain a number of anomalous results observed in the exact diagonalization studies on small clusters up to 32 sites.     

Design and synthesis of a diverse morpholine template library

Efficient and general procedures have been developed for the solution-phase preparation of substituted morpholine derivatives, and a library has been produced around generic structure 1. This library was designed with proprietary modeling software for use as a general screening library. The 30 R1 reagents were phenols, and the 275 R2 reagents were taken from five different reagent classes, giving a variety of product classes in the final library of 8250 potential products. All of the library members were generated from a common intermediate, mesylate (5), which was synthesized efficiently, in bulk, in three steps from N-benzylethanolamine (2). High-throughput chemistry using robotics was carried out to produce the 7907 library members, which were individually characterized by reversed-phase LC/MS analysis.     

The enumerative geometry of surfaces and modular forms

Let be a surface, and let be a holomorphic curve in representing a primitive homology class. We count the number of curves of geometric genus with nodes passing through generic points in in the linear system for any and satisfying .

When , this coincides with the enumerative problem studied by Yau and Zaslow who obtained a conjectural generating function for the numbers. Recently, Göttsche has generalized their conjecture to arbitrary in terms of quasi-modular forms. We prove these formulas using Gromov-Witten invariants for families, a degeneration argument, and an obstruction bundle computation. Our methods also apply to blown up at 9 points where we show that the ordinary Gromov-Witten invariants of genus constrained to points are also given in terms of quasi-modular forms.     

Experimental study of optimum spacing problem in the cooling of simulated electronic package

  An experimental investigation has been performed to determine the effects of different arrangements of obstacles on the cooling of simulated electronic package. The considered simulated electronic package consisted of a channel formed by two parallel plates. The bottom plate is attached with five identical electrically heated square obstacles, which are perpendicular to the mean airflow and arranged with different side-to-side distances. The experimental results show that the conventional equi-spaced arrangement might not be the optimum option and should be avoided. A better thermal performance could be obtained when the side-to-side distances between the obstacles followed a geometric series. For example, at Re=800, the highest temperature of the optimum arrangement could be reduced by 12% compare to the equi-spaced arrangement and the maximum temperature difference among the five obstacles is lower than that of equi-spaced arrangement by 32.1%. Received on 17 December 1999