Local complete intersections in and Koszul syzygies

We study the syzygies of a codimension two ideal . Our main result is that the module of syzygies vanishing (scheme-theoretically) at the zero locus is generated by the Koszul syzygies iff is a local complete intersection. The proof uses a characterization of complete intersections due to Herzog. When is saturated, we relate our theorem to results of Weyman and Simis and Vasconcelos. We conclude with an example of how our theorem fails for four generated local complete intersections in and we discuss generalizations to higher dimensions.

     

Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width

The Multicut problem can be defined as: given a graph G and a collection of pairs of distinct vertices {s_i,t_i} of G, find a minimum set of edges of G whose removal disconnects each s_i from the corresponding t_i. Multicut is known to be NP-hard and Max SNP-hard even when the input graph is restricted to being a tree. The main result of the paper is a polynomial-time approximation scheme (PTAS) for Multicut in unweighted graphs with bounded degree and bounded tree-width. That is, for any ε>0, we present a polynomial-time (1+ε)-approximation algorithm. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provide some hardness results: we prove that Multicut is still NP-hard for binary trees and that it is Max SNP-hard if we drop any of the three conditions (unweighted, bounded-degree, bounded tree-width). Finally we show that some of these results extend to the vertex version of Multicut and to a directed version of Multicut.     

Distinctive field dependence of the longitudinal muon polarization for Mu* in polycrystalline silicon

A distinctive longitudinal magnetic field dependence of the muon polarization for anomalous muonium in polycrystalline semiconductor targets has been predicted. The polarization exhibits a cusp,i.e., a discontinuous jump in the slope from negative to positive. Measurements of the longitudinal polarization for polycrystalline silicon in fields up to 0.5 T, and temperatures 53 and 200 K have been made at LAMPF. A cusp in the field dependence indeed occurs at 0.345 T, in excellent agreement with the prediction. No cusp is observed at 200 K because Mu^* has been thermally ionized.     

An SIS waveguide heterodyne receiver for 600 HGz-635 GHz

A waveguide SIS heterodyne receiver using a Nb/AlO_X/Nb junction has been built for astronomical observations of molecular transitions in the frequency range 600 GHz - 635 GHz, and has been successfully used at the Caltech Submillimeter Observatory (CSO). We report double sideband (DSB) receiver noise temperatures as low as 245 K at 600 GHz -610 GHz, and near 300 K over the rest of the bandwidth. These results confirm that SIS quasiparticle mixers work well at submillimeter-wave frequencies corresponding to photon energies of at least 90% of the superconductor energy gap. In addition, we have systematically investigated the effect on the receiver performance of the overlap between first-order and second-order photon steps of opposite sign at these frequencies. The receiver noise increases by as much as 40% in the region of overlap. We infer potential limitations for operating submillimeter-wave Nb/AlO_x/Nb mixers.     

Probing microscopic chaotic dynamics by observing macroscopic transport processes

We derive the Kramers equation, namely, the Fokker-Planck equation for an oscillator, from a completely deterministic picture. The oscillator is coupled to a “booster”, i.e., a deterministic system in a fully chaotic state, wherein diffusion is derived from the sensitive dependence of chaos on initial conditions and friction is a consequence of the linear response of the booster to the action exerted on it by the oscillator. To deal with the Hamiltonian nature of the system of interest and of its coupling to the booster, we extend the earlier theoretical derivation of macroscopic transport coefficients from deterministic dynamics. We show that the frequency of the oscillator can be tuned to the microscopic frequencies of the booster without affecting the canonical nature of the “macroscopic” statistics. The theoretical predictions are supported by numerical simulations.     

The solid solutions Na3(1−x)Alx2xPO4: room temperature powder neutron diffraction studies of the two compositions x=0.025 and x=0.2

The crystal structures of the high-temperature modifications of sodium and silver orthophosphates have been determined using powder neutron diffraction (PND) data. II-Na₃PO₄ adopts the space group Fm3m with at 400°C. The PO³⁻₄ group is centered around the origin, but it shows high orientational disorder. The sodium ions occupy the and sites. II-Ag₃PO₄, at 650°C, is similar with . The structure of I-Ag₃PO₄ at room temperature

Full-size image (<1K)

has been re-examined by single-crystal X-ray diffraction. The derived model, with R=0.019 for 116 independent reflections, is in agreement with the latest work reported in the literature. The structure of I-Ag₃PO₄ at 375°C, as determined by PND, has , and displays no gross modifications from that observed at 25°C, although the anisotropic nature of the silver sites is markedly more pronounced at this higher temperature. The cation mobility is discussed in relation to the high-temperatures structures.     

Continuous-wave CO2 laser spectroscopy of SF6, WF6, and UF6

The linear absorption of CO₂ laser radiation in SF₆, WF₆, and UF₆ has been measured by using optoacoustic detection techniques. Absolute absorption coefficients per Torr as low as 1 × 10^?7 cm^?1 Torr^?1 in a 2-cm active path length could be measured by taking advantage of calibration measurements performed with SF₆.     

Fluorescence anisotropy decay study of self-association of bacterial luciferase intermediates

The fluorescence dynamics parameters of the fluorescent transient flavin-luciferase species from the typesVibrio fischeri andPhotobacterium leiognathi are presented. The fluorescence anisotropy decay is a single exponential function for both types. The correlation time is 70 ns for theP. leiognathi fluorescent transient intermediate (2°C, aqueous buffer, pH 7.0), consistent with the rotational correlation time of the luciferase macromolecule (77 kD) to which the flavin fluorophore is rigidly attached. In contrast, for theV. fischeri species the observed correlation time for the anisotropy decay function is 133 ns. This suggests that protein self-association occurs in theV. fischeri case and this is confirmed by filtration, where the fluorescent transient fromV. fischeri does not pass through a 100,000 molecular weight cutoff membrane, whereas theP. leiognathi species does. The filtration method also demonstrates self-association in the luciferase peroxyflavin and photoflavin fromV. fischeri. A monomer-dimer equilibrium also explains the previously reported high correlation times for theV. harveyi luciferase-flavin species. It is proposed that the self-association competes with the lumazine protein interaction in the bioluminescence reaction.     

A telescope illumination system for a wide-field endoscope

Endoscopic illumination systems conduct light down a built-in fibre-optic bundle to illuminate the object. Many modern endoscopes employ wide-field imaging optical systems and therefore require an illuminating beam of large divergence. This is commonly provided by placing a strong diverging lens at the far end of the fibre bundle, but it results in a poor uniformity of illumination in the object space. This paper describes the design of a telescopic illumination system to overcome this problem.