Diophantine inequalities with mixed powers

It is shown that λ₁, λ₂,…, λ₆, μ are not all of the same sign and at least one ratio $\text{λ}{}_{\mathrm{i}}\text{λ}{}_{\mathrm{j}}$ is irrational then the values taken by $\text{λ}{}_1\text{x}{}_1{}^3\text{+ ? + λ}{}_6\text{x}{}_6{}^3\text{+ μy}{}^3$ for integer values of x₁ ,…, x₆, y are everywhere dense on the real line. A similar result holds for expressions of the form $\text{λ}{}_1\text{x}{}_1{}^3\text{+ ? + λ}{}_4\text{x}{}_4{}^3\text{+ μ}{}_1\text{y}{}_1{}^2\text{+ μ}{}_2\text{y}{}_2{}^3$.     

Multi-species time-history measurements during n-hexadecane oxidation behind reflected shock waves

Species concentration time-histories were measured during oxidation for the large, normal-alkane, diesel-surrogate component n-hexadecane. Measurements were performed behind reflected shock waves in an aerosol shock tube, which allowed for high fuel loading without pre-test heating and possible decomposition and oxidation. Experiments were conducted using near-stoichiometric mixtures of n-hexadecane and 4% oxygen in argon at temperatures of 1165–1352 K and pressures near 2 atm. Concentration time-histories were recorded for five species: C₂H₄, CH₄, OH, CO₂, and H₂O. Methane was monitored using DFG laser absorption near 3.4 μm; OH was monitored using UV laser absorption at 306.5 nm; C₂H₄ was monitored using a CO₂ gas laser at 10.5 μm; and CO₂ and H₂O were monitored using tunable DFB diode laser absorption at 2.7 and 2.5 μm, respectively. These time-histories provide critically needed kinetic targets to test and refine large reaction mechanisms. Comparisons were made with the predictions of two diesel-surrogate reaction mechanisms (Westbrook et al. [1]; Ranzi et al. [9]) that include n-hexadecane, and areas of needed improvement in the mechanisms were identified. Comparisons of the intermediate product yields of ethylene for n-hexadecane with those found for other smaller n-alkanes, show that an n-hexadecane mechanism derived from a simple hierarchical extrapolation from a smaller n-alkane mechanism does not properly simulate the experimental measurements.     

Supported ionic liquid catalysis--a new concept for homogeneous hydroformylation catalysis

The new concept of supported ionic liquid catalysis involves the surface of a support material that is modified with a monolayer of covalently attached ionic liquid fragments. Treatment of this surface with additional ionic liquid results in the formation of a multiple layer of free ionic liquid on the support. These layers serve as the reaction phase in which a homogeneous hydroformylation catalyst was dissolved. Supported ionic liquid catalysis combines the advantages of ionic liquid media with solid support materials which enables the application of fixed-bed technology and the usage of significantly reduced amounts of the ionic liquid. The concept of supported ionic liquid catalysis has successfully been used for hydroformylation reactions and can be further expanded into other areas of catalysis.     

Sound insulation of domestic roofing systems—Part 3

In the two previous parts of this group of papers, the results of measurements of the sound transmission properties of each of the two components of a domestic roofing system were presented and discussed. In this third and final part, the effect on the transmission properties of combining the roof and ceiling components will be investigated and discussed. Comments will also be made on the contribution by the roofing system to the sound insulation provided by the whole building external envelope against the principal types of external noise.     

Quantitative laboratory spectra and spectral line parameters for the v2 and v4 bands of PH3 applicable to spectral radiative models of the atmosphere of Jupiter

Quantitative laboratory PH₃ absorption spectra were obtained in the 800–1350 cm^-1 region, at ～0.05 cm^-1 resolution, with gas amounts corresponding to observed PH₃ absorptions in the atmosphere of Jupiter. A compilation of spectral line positions, intensities and ground state energies has been generated for the v₂ and v₄ bands of PH₃. Line-by-line calculations have been compared with the experimental spectra.     

Study of optical output couplers for submillimeter wavelength backward-wave oscillators (BWO's)

The machining of slow wave structures for high frequency BWO's is extremely difficult beyond l THz. Recently a microfabrication technique using photolithography and ion-beam assisted etching has been used to construct a prototype BWO operating at 200 to 265 GHz.The output coupler for such tubes remains a problem. Waveguides do not exist or are very lossy at the frequencies of interest (300 to 2000 GHz).This paper discusses several scaled experiments of optical output couplers for submillimeter BWO's. Various designs of planar antennas (Vivaldi horns) and lens-feed systems (hyperhemispherical lens) were constructed and tested between 20 and 100 GHz using a spectrum analyzer. The lens system was also tested at 337 GHz using a CO₂ pumped FIR laser.     

Solid‐state amidization and imidization reactions in vapor‐deposited poly(amic acid)

The condensation polymerization of 4,4′‐oxydianiline with pyromellitic dianhydride for the formation of poly(amic acid) and the subsequent imidization for the formation of polyimides were investigated for films prepared with vapor‐deposition polymerization techniques. Fourier transform infrared spectroscopy, thermal analysis, and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry of films at different temperatures indicated that additional solid‐state polymerization occurred before imidization. The experiments revealed that, upon vapor deposition, poly(amic acid) oligomers formed that had a number‐average molecular weight of about 1500 Da. Between 100–130 °C, these chains underwent an additional condensation reaction and formed slightly higher molecular weight oligomers. Calorimetry measurements showed that this reaction was exothermic [enthalpy of reaction (ΔH) ～ ?30 J/g] and had an activation energy of about 120 kJ/mol. The experimental ΔH values were compared with results from ab initio molecular modeling calculations to estimate the number of amide groups formed. At higher temperatures (150–300 °C), the imidization of amide linkages occurred as an endothermic reaction (ΔH ～ +120 J/g) with an activation energy of about 130 kJ/mol. The solid‐state kinetics depended on the reaction conversion as well as the processing conditions used to deposit the films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5999–6010, 2004