Adsorption spectroscopy by polariton-induced desorption (ASPID)

A new spectroscopic technique is proposed as a means of determining the energy and momentum of adsorbed atoms and molecules. The method, abbreviated to ASPID (adsorption spectroscopy by polariton-induced desorption), uses surface phonon polaritons (SPPs) to desorb atoms. Because one may create nearly-monoenergetic SPPs, the binding energy range is determined directly from the spectrum of final energies. A kinematical analysis may be used to analyze adatom momenta, and hence band structures. The angular distribution of the SPP-desorbed atoms may be used to monitor adsorbed-film temperature. We provide an estimate of the SPP desorption rate, and conclude that the proposed experiment is feasible.     

Copolyesteramides—I. Anionic copolymers of ω-laurolactam with ϵ-caprolactone

Anionic copolymerisation of ω-laurolactam with ε-caprolactone yields copolyesteramides with NH(CH₂)₁₁CO and O(CH₂)₅CO unit contents similar to those in the feeds. Over the major part of the composition range, only the amide component crystallises, showing the γ-nylon 12 form. A transition of crystalline type to that of poly(ε-caprolactone) occurs at low (ca. 20 mol%) amide-group content and with marked depression of the degree of crystallinity of the polyester component. I.R. spectroscopy indicates the co-existence of amide-ester with amide-amide hydrogen-bonding in the copolymers, and the monotonic form of the T_m vs composition curve is explained in terms of this dual bonding. It is suggested that such interactions between the sub-species may be a general feature underlying the properties of linear aliphatic copolyesteramides.     

Polynomial realization of pseudoline arrangements

An arrangement of pseudolines is called d-stretchable if it is isomorphic to an arrangement of graphs of polynomial functions, each of degree at most d; in particular, it is 1-stretchable (classically: “stretchable”) if and only if it is isomorphic to an arrangement of lines. We show that (i) if every arrangement of n pseudolines is d-stretchable, then d ≦ cn^1/2, and (ii) every arrangement of n pseudolines is d-stretchable with d = cn².     

Kinetics of the gas-phase reactions of the OH radical with (C2H5)3PO and (CH3O)2P(S)Cl at 296 ± 2 K

The kinetics of the gas-phase reactions of the OH radical with (C₂H₅O)₃PO and (CH₃O)₂P(S)Cl and of the reactions of NO₃ radicals and O₃ with (CH₃O)₂P(S)Cl have been studied at room temperature. Using a relative rate technique, the rate constants determined for the reactions of the OH radical with (C₂H₅O)₃PO and (CH₃O)₂P(S)Cl at 296 ± 2 K and 740 torr total pressure of air were (5.53 ± 0.35) × 10^?11 and (5.96 ± 0.38) × 10^?11 cm³ molecule^?1 s^?1, respectively. Upper limits to the rate constants for the NO₃ radical and O₃ reactions with (CH₃O)₂P(S)Cl of <3 × 10^?14 cm³ molecule^?1 s^?1 and <2 × 10^?19 cm³ molecule^?1 s^?1, respectively, were obtained. These data are compared and discussed with previous literature data for organophosphorus compounds.     

The photoelectron spectrum of phosphorus pentafluoride

The He(I) photoelectron spectrum of PF₅ has been determined. Assignments for the six observed bands are suggested and comparisons with several semi-empirical molecular orbital calculations are made. Particular interest is associated with the fifth band since it exhibits vibrational fine structure.     

Synthetic studies in the lsoxazoko[4,5-b] pyrazine system

The synthesis of 3-methylisoxazolo[4,5-b]pyrazine ( 5 ) and its 7-oxide ( 6 ) is reported. Nitration of 6 furnished the 6-nitro derivative ( 8 ) while reaction with phosphoryl chloride provided the chloro derivative ( 7 ). Efforts to functionalize the methyl group in 5 were not successful.     

Multivariate θ-generalized normal distributions

A new family of continuous multivariate distributions is introduced, generalizing the canonical form of the multivariate normal distribution. The well-known univariate version of this family, as developed by Box, Tiao and Lund, among others, has proven a valuable tool in Bayesian analysis and robustness studies, as well as serving as a unified model for least θ's and maximum likelihood estimates. The purpose of the family introduced here is to extend, to a degree of generality which will permit practical applications, the useful role played by the univariate family to a multidimensional setting.     

Limiting distributions of two random sequences

For fixed p (0 ≤ p ≤ 1), let {L₀, R₀} = {0, 1} and X₁ be a uniform random variable over {L₀, R₀}. With probability p let {L₁, R₁} = {L₀, X₁} or = {X₁, R₀} according as $\text{X}{}_1\text{≥}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}$; with probability 1 ? p let {L₁, R₁} = {X₁, R₀} or = {L₀, X₁} according as $\text{X}{}_1\text{≥}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}$, and let X₂ be a uniform random variable over {L₁, R₁}. For n ≥ 2, with probability p let {L_n, R_n} = {L_{n ? 1}, X_n} or = {X_n, R_{n ? 1}} according as $\text{X}{}_{\mathrm{n}}\text{≥}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}$, with probability 1 ? p let {L_n, R_n} = {X_n, R_{n ? 1}} or = {L_{n ? 1}, X_n} according as $\text{X}{}_{\mathrm{n}}\text{≥}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}$, and let X_{n + 1} be a uniform random variable over {L_n, R_n}. By this iterated procedure, a random sequence {X_n}_{n ≥ 1} is constructed, and it is easy to see that X_n converges to a random variable Y_p (say) almost surely as n → ∞. Then what is the distribution of Y_p? It is shown that the Beta, (2, 2) distribution is the distribution of Y₁; that is, the probability density function of Y₁ is g(y) = 6y(1 ? y) I_0,1(y). It is also shown that the distribution of Y₀ is not a known distribution but has some interesting properties (convexity and differentiability).