Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Infrared spectra and rotational isomerism of epifluorohydrin and other propene oxide derivatives

The infrared spectrum for the vapour, liquid and solid states of epifluorohydrin has been studied, and evidence has been obtained for the presence of rotational isomers. The dominant conformer in all phases corresponds to a gauche structure, which was the only form identified in the vapour by microwave spectroscopy [1]. Similar evidence for conformational equilibria has been found for the chloro, bromo and iodo derivatives, and the enthalpy differences between the rotational isomers of these compounds were measured respectively as 4580 ± 970, 3950 ± 400, and 2350 ± 170 J mol^?1 respectively. At low temperatures, epiiodohydrin was found to crystallize in one of two possible crystalline phases. These two phases correspond to the two rotational isomeric conformations of the molecule.     

Photosensitized dehydrochlorination of poly(vinyl chloride). III. Reaction of thermally degraded poly(vinyl chloride) with hydrogen chloride

Films prepared from thermally degraded poly(vinyl chloride) were photolyzed in the presence of hydrogen chloride. When the light was filtered through a Pyrex disk, the absorbance in the region between 270 nm and about 415 nm decreased and reached a minimum value but the absorbance increased at wavelengths shorter than 270 nm and longer than 415 nm. Maximum bleaching occurred at a wavelength which depended on that of the irradiating light. When the Pyrex filter was omitted, an additional slower photodehydrochlorination reaction was superimposed on the photobleaching reaction. Photolysis of hexane or ethanol solutions of 1,8-diphenyloctatetra-1,3,5,7-ene and hydrogen chloride showed a similar reaction involving bleaching of the absorption of the polyene structure. The problems of using absorbance as an indication of the extent of the photodegradation of poly(vinyl chloride) are discussed.     

First observation ofΩ * resonances

In a experiment at the CERN SPS charged hyperon beam using incident Ξ^?, we have obtained evidence for the production of two Ω^* resonances decaying into Ξ^?π⁺ K ^?, with the following parameters:M ₁=2251±12,Γ ₁=48±20 MeV/c², 78 ±23 events, andM ₂=2284±12,Γ ₂=26±23 MeV/c² 45±10 events. The first state is also observed as a 4.2σ effect in a subsample which contains an additionalK ⁺ orK ⁰ in the final state. Production cross sections and branching ratios to Ξ^* K ^? and Ξ^? K ^* are presented.     

Electrochemical properties and structures of the mixed-valence lithium cuprates Li3Cu2O4 and Li2NaCu2O4

The electrochemical performances of Li₃Cu₂O₄ and Li₂NaCu₂O₄ as cathode materials in lithium coin type batteries have been studied. In Li₃Cu₂O₄, the copper was oxidised to the III level when cycling. The replacement of the lithium by the sodium ions in the octahedral sites in Li₂NaCu₂O₄ might have an effect on the pathway of the lithium ions during the (de)intercalations. Paper presented at the 7th Euroconference on Ionics, Calcatoggio, Corsica, France, Oct. 1–7, 2000.     

Dual-mode transducers for ultrasound imaging and thermal therapy

Medical imaging is a vital component of high intensity focused ultrasound (HIFU) therapy, which is gaining clinical acceptance for tissue ablation and cancer therapy. Imaging is necessary to plan and guide the application of therapeutic ultrasound, and to monitor the effects it induces in tissue. Because they can transmit high intensity continuous wave ultrasound for treatment and pulsed ultrasound for imaging, dual-mode transducers aim to improve the guidance and monitoring stages. Their primary advantage is implicit registration between the imaging and treatment axes, and so they can help ensure before treatment that the therapeutic beam is correctly aligned with the planned treatment volume. During treatment, imaging signals can be processed in real-time to assess acoustic properties of the tissue that are related to thermal ablation. Piezocomposite materials are favorable for dual-mode transducers because of their improved bandwidth, which in turn improves imaging performance while maintaining high efficiency for treatment. Here we present our experiences with three dual-mode transducers for interstitial applications. The first was an 11-MHz monoelement designed for use in the bile duct. It had a aperture that was cylindrically focused to 10 mm. The applicator motion was step-wise rotational for imaging and therapy over a 360°, or smaller, sector. The second transducer had 5-elements, each measuring for a total aperture of . It operated at 5.6 MHz, was cylindrically focused to 14 mm, and was integrated with a servo-controlled oscillating probe designed for sector imaging and directive therapy in the liver. The last transducer was a 5-MHz, 64-element linear array designed for beam-formed imaging and therapy. The aperture was with a pitch of 0.280 mm. Characterization results included conversion efficiencies above 50%, pulse-echo bandwidths above 50%, surface intensities up to , and axial imaging resolutions to 0.2 mm. The second transducer was evaluated in vivo using porcine liver, where coagulation necrosis was induced up to a depth of 20 mm in 120 s. B-mode and M-mode images displayed a hypoechoic region that agreed well with lesion depth observed by gross histology. These feasibility studies demonstrate that the dual-mode transducers had imaging performance that was sufficient to aid the guidance and monitoring of treatment, and could sustain high intensities to induce coagulation necrosis in vivo.     

Infrared and microwave spectra, molecular conformation and electric dipole moment of methyl thiolformate

The microwave spectrum (41-10 GHz) and the infrared spectrum (4000-50 cm⁻¹) of methyl thiolformate have been obtained and analyzed. The spectra are consistent with a single molecular conformation having a planar array of heavy atoms and with the alkyl group cis to the carbonyl group. The measured rotational constants are: A, 11042.22 MHz; B, 5118.27 MHz; C, 3562.03 MHz (κ = −0.5839). No internal rotation doublets were observed in the microwave spectrum for the ground vibrational state, which implies that the barrier hindering internal rotation of the methyl group is either much larger or much smaller than the corresponding value for methyl formate. If the former is true then a lower limit of 10.5 kJ mol⁻¹ may be placed on the barrier height.The dipole moment of methyl thiolformate was measured using the Stark effect to be 1.58 ± 0.05 Debyes (μ_A = 1.52 D; μ_B = 0.43 D) for the vapor, and for dilute solutions in benzene at 295 K the value of 1.6 ± 0.1 D was found from capacitance measurements.SCF computations using minimal basis sets of STO/3G atomic orbitals and extended basis sets of STO/4.31G atomic orbitals have been carried out for methyl thiolformate and methyl formate. Energy differences between rotational isomers and estimates of barrier heights are given together with the calculated dipole moments.