Relative morsification theory

In this paper we develop a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known morsification results for non-isolated singularities and generalise them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalisations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalised jet-space we show how to interpret the newly defined invariants as certain intersection multiplicities; finally, we characterise which invariants can be interpreted as intersection multiplicities in the above mentioned generalised jet space.     

Apparatus for High-Resolution Solid Hydrogen Matrix Isolation Spectroscopy and Its Application

Apparatus integrating a Fourier transform-infrared (FT-IR) spectrometer and a mid-infrared difference frequency generation (DFG) laser spectrometer was built for the study of the matrix isolation spectrum in solid molecular hydrogen. A 3-cm-long molecular hydrogen crystal was grown in a liquid-helium Dewar, and its infrared absorption spectrum in the 1-5 μm region was recorded to test the system. The W₀(0) (ν=0←0, J=6←0) line around 2410 cm⁻¹ of solid hydrogen was investigated with the DFG laser spectroscopy. High-resolution matrix isolation spectrum of CO² co-deposited with hydrogen on a BaF₂ cold plate at liquid-helium temperature was studied.     

Studies on the blends of cardanol-based epoxidized novolac resin and CTPB

Cardanol-based novolac-type phenolic resins were synthesized with different mole ratios of cardanol-to-formaldehyde, viz., 1:0.6, 1:0.7, and 1:0.8. These novolac resins were epoxidized with molar excess of epichlorohydrin at 120 °C in basic medium. The epoxidized novolac resins were, separately, blended with different weight ratios of carboxyl-terminated polybutadiene liquid rubber ranging between 0-25 wt% with an interval of 5 wt%. All the blends were cured at 150 °C with 40 wt% polyamide. The formation of various products during the curing of blend samples has been studied by Fourier-transform infra-red spectroscopic analysis. The tensile strength and elongation-at-break of the cured samples increased up to 15 wt% in the blend and decreased thereafter. This blend sample was also found to be most thermally stable system. The blend morphology, studied by scanning electron microscopy analysis, was finally correlated with the structural and property changes in the blends.     

The convergence rate of continued fractions representing solutions of a Riccati equation

The aim of this note is to generalize and apply results on matrix continued fractions representing the solution of discrete matrix Riccati equations. Assuming uniform bounds for the norm of the matrix coefficients of the continued fraction, the minimal and maximal solutions of the corresponding algebraic Riccati equation can be accurately enclosed.     

Synthesis of O-unprotected glycosyl selenoureas. A new access to bicyclic sugar isoureas

β-d-Gluco and mannopyranosyl selenoureas have been prepared by coupling of the corresponding glycosylamines with phenyl isoselenocyanate in aqueous pyridine. Alkyl and aryl isoselenocyanates, and 1,4-phenylene diisoselenocyanate have been obtained from the corresponding formamides with an excess of triphosgene, black selenium and triethylamine. Treatment of the O-unprotected β-d-glucopyranosyl selenourea with aqueous oxygen peroxide afforded a 1,2-trans-fused bicyclic isourea.     

Sn/Ge(1 1 1) α-phase: characterization of image resonances by specular electron reflection and selective electron scattering

Image potential resonances on the Sn/Ge(1 1 1) α-phase are investigated by two closely related methods: specular electron reflection and so-called selective electron scattering. Electrons from image resonances are detected on this surface at 120 and 300 K, i.e. below and above the phase transition at about 200 K. The dispersion of the image resonances reveals at these two temperatures equivalent effective electron masses, which are characteristic for this type of electronic surface states. The results of the two methods are consistent according to the similarity of the scattering processes. Changes in the loss peak intensity with the annealing temperature are assigned to the surface quality and are reflected by characteristic photoemission intensities.     

A first-principles study of surface and subsurface H on and in Ni(1 1 1): diffusional properties and coverage-dependent behavior

Periodic, self-consistent, density functional theory (GGA-PW91) calculations are performed for both surface and subsurface atomic hydrogen on and in Ni(1 1 1). At a low coverage (θ=0.25 ML), the binding energies (BEs) of a hydrogen atom in surface fcc, subsurface octahedral (first layer), and subsurface octahedral (second layer) sites are −2.89, −2.18, and −2.11 eV, respectively. The activation energy barriers for hydrogen diffusion from the surface to the first subsurface layer and from the first to the second subsurface layer are estimated to be 0.88 and 0.52 eV, respectively. In the entire coverage range studied, hydrogen occupies surface fcc and hcp sites and subsurface octahedral sites. In addition, the magnitude of the BE per hydrogen atom and the magnetization of the nickel slabs both decrease as hydrogen coverage increases. Vibrational frequencies of hydrogen at various surface and subsurface sites are calculated and are in reasonable agreement with experimental data. A phase stability calculation with a 2 × 2 surface unit cell shows that a p(2 × 2)-2H overlayer structure (θ=0.5 ML) and a p(1 × 1)-1H structure (θ=1.0 ML) are stable at low hydrogen pressures, in agreement with numerous experimental results. A very large increase in pressure is required to populate subsurface sites. After such an increase occurs, the first subsurface layer is filled completely.     

Single Production of Charged Top-Pions at High Energy Linear e+e- Colliders

The dominant decay modes of charged top-pions (π±t ) are tb or ~b. We consider the single production ofcharged top-pions in association with a top quark via e+ e- annihilation and calculate the production cross section of theprocesses e+ e- → t-bπ+ (tb-π-) at the leading order. We find that it can reach 1.2 fb with reasonable parameter values.The charged top-pions may be detected via the channel tbπ± in the future high energy e+ e- colliders.     

Effect of aeration on lignin peroxidase production by Streptomyces viridosporus T7A

The effect of aeration on lignin peroxidase production by Streptomyces viridosporus T7A was studied in a bench-scale bioreactor using a previously optimized growth medium (0.65% yeast extract and 0.1% corn oil, pH7.0) at 37°C and natural pH. Airflow rates of 0.3, 1.0, and 1.5 vvm and a fixed agitation of 200 rpm were initially studied followed by 1.0 vvm and 200, 300, 400, and 500 rpm. The use of 1.0 vvm and 400 rpm increased enzyme concentration 1.8-fold (100–180 U/L) and process productivity 4.8-fold (1.4–6.7 U/[L·h]) in comparison with the use of 200 rpm and 0.3 vvm. The inexpensive corn oil, used as carbon source, besides its antifoam properties, proved to be nonrepressive for enzyme production.     

Hg1-xCdxTe/Cd1-zZnzTe的X射线反射率及半峰全宽的动力学研究

X射线衍射摇摆曲线的计算机模拟是一种获得材料晶体质量参量的有效方法，其中材料本征摇摆曲线的计算是计算机模拟的基础。用X射线动力学理论计算了Hg1-xCdxTe和Cd1-zZnzTe本征反射率曲线，并研究了组分、膜厚分别对本征反射率和半峰全宽的影响。结果表明Hg1-xCdxTe和Cd1-zZnzTe的本征反射率和半峰全宽与材料组分和厚度有明显的依赖关系，且该依赖关系取决于X射线在材料中的散射和吸收的相对强弱。薄膜的厚度也是直接影响本征摇摆曲线峰形、半峰全宽和反射率的重要因素，当薄膜厚度小于穿透深度时，表征本征反射率曲线的各个参量均与薄膜厚度有直接的关系。对于(333)衍射面，碲镉汞材料厚度大于7μm后，本征反射率和半峰全宽将不再发生明显变化。