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     

Metal-catalyzed cyclopropanation on the 8-oxabicyclo[3.2.1]oct-6-ene template

Cyclopropanations of an 8-oxabicyclo[3.2.1]octene substrate using diazocarbonyl compounds provided exo, exo-cyclopropanated products as the sole or major diastereomeric oxatricyclic products. Reductive cleavage of a meso-oxatricyclic ketone by samarium iodide resulted in desymmetrization without concomitant oxygen bridge cleavage.     

Characterization of Kovar-to-Kovar laser welded joints and its mechanical strength

For the packaging of a pump laser in butterfly package, the most crucial assembly step is the fiber-to-laser diode coupling and attachment. The use of laser welding as the joining method offers several advantages if compared with the adhesive joints: strong joining strength, short process time and less contamination. This paper reports on laser welding process characteristics; weld strength and its fracture mode. The penetration depth and melt area of laser spot welds were found to be complicated functions of laser pulse energy, intensity, and beam diameter. Effects of pulse width, input power and size of the focal spot on the rate of energy input to the workpieces and consequently, the weld strength were reported. The weld strength was found to be dependent on the overlapping area between the two joining materials. Surface roughness, R_a, has influence on the fraction of energy absorbed, A, and therefore, affecting the penetration depth. Thermal analysis was carried out on the laser-welded joints and its heat-affected zone (HAZ) induced by various power densities was examined. These data are important in order to optimize and utilize the laser welding process as an effective manufacturing tool for fabrication of reliable pump laser.     

Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

Determination of vitamin U and its degradation products by high- performance liquid chromatography with fluorescence detection

A high-performance liquid chromatographic method has been developed for the determination of vitamin U in tablets and capsules. Threonine was employed as the internal standard through the assay. The o-phthalaldehyde derivatives were prepared and then chromatographed isocratically on a reversed-phase C18 column. The optimum reaction time for both vitamin U and threonine at pH 10.5 is 5 min. Vitamin U and its major degradation product in the dosage forms, viz., methionine sulphoxide, were separated and quantified with a relative standard deviation of about 1%, using a fluorescence detector with excitation and emission wavelengths at 340 and 450 nm respectively. A linear relationship has been established between the peak area ratio of vitamin U/threonine and the concentration of vitamin U over the range of 2.5-50 micrograms/ml.