THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

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.     

Raman scattering from Pt(CN)42− adsorbed on Pt colloids

Raman scattering from Pt(CN)₄^2? adsorbed on Pt colloids (average diameter of 16 A) is compared with the Raman signal from the same amount of Pt(CN)₄^2? in solution. The wavelength dependence of the adsorbate Raman intensity is measured from 308 to 647 nm and compared with a Lorenz/Mie calculation of the enhancement factor for the electromagnetic field intensity on the surface of a Pt sphere as a function of sphere radius and incident wavelength.     

Acrylamide analysis: assessment of results from six rounds of Food Analysis Performance Assessment Scheme (FAPAS) proficiency testing

Six proficiency tests have now been completed in an ongoing program of the UK Food Analysis Performance Assessment Scheme (FAPAS) for the analysis of acrylamide in a range of food matrixes. Homogeneous test material samples were requested by laboratories throughout the world, with 29 to 45 submitting results for each test. Results were analyzed by appropriate statistical procedures, and z-scores were awarded for reported values. In the absence of both legislation and collaborative trial data, the target standard deviation was derived from the Horwitz equation, although it is acknowledged that there is a need to establish a "fit for purpose" target standard deviation specifically for acrylamide analysis. Participants were encouraged to use the analytical method routinely used in their own laboratory and to provide details of their procedure. Close examination of the data submitted indicates that performance is generally acceptable in terms of accuracy. There is no significant difference between results submitted by gas chromatography and liquid chromatography (GC and LC) methods, and no method dependency on the use of internal standards or sample size. However, choice of extraction solvent may be important, with indications that plain water is an acceptable extraction method. There is evidence from the most recent test that direct (underivatized) GC methodology may present problems, but more data are required and this aspect will be monitored in the continuing proficiency testing program.     

Synthesis, structures and spectroelectrochemistry of methyl-substituted bis(η-indenyl)iron(II) complexes

Several new methyl-substituted indenyl ferrocenes were prepared by metathesis reactions of the indenide (generated from the appropriate indene with BuLi) with ferrous chloride. The indenides used to prepare new ferrocenes were: 2-methyl-, 1,2-dimethyl-, 4,7-dimethyl-, 1,4,7-trimethyl-, and 1,3,4,7-tetramethyl-indenide. These indenyl ferrocenes, along with those prepared from indenide, 1-methylindenide, and 1,3-dimethylindenide, were then characterized by ¹H and ¹³C NMR, UV/visible spectroscopy, cyclic voltammetry and mass spectrometry. The cyclic voltammetry showed an additive relationship between oxidation potential and the number of methyl groups which is also position-dependent, whereas the UV/visible spectra showed two absorptions essentially unaffected by methyl substitution. Additionally, bis(2-methylindenyl)iron(II) and bis(4,7-dimethylindenyl)iron(II) were characterized by X-ray crystallography.     

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed.     

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.     

Synthesis and characterisation of phosphane-substituted Co3C clusters having a pendant allyl side-chain

Substituted μ₃-carbido-capped tricobalt carbonyl clusters have been synthesised by reaction of [Co₃(μ₃-C(O)OCH₂CHCH₂)(CO)₉] with a range of monodentate and chelating phosphane ligands. The products have been characterised by microanalysis, IR and NMR spectroscopy, mass spectrometry and, in the case of [Co₃(μ₃-CR)(CO)₇(dppe)], [Co₃(μ₃-CR)(CO)₇(dppm)], [Co₃(μ₃-CR)(CO)₇(PPh₃)₂], [Co₃(μ₃-CR)(CO)₇(PMe₃)₂] and [Co₃(μ₃-CR)(CO)₆(PEt₃)₃] (R=C(O)OCH₂CHCH₂), single crystal X-ray diffraction.     

The impact of intermediaries on a negotiation: an approach from game theory

Central European Journal of Operations Research - Standard approaches to model interaction networks are limited in their capacity to describe the nuances of real communication. We present a game...