Flame temperatures from Raman scattering

Pure rotational, as well as vibrational Raman scattering has been observed from stable diatomic molecules in high-temperature flames. Accurate (rotational) flame temperatures may be determined from the rotational line intensities. For a hydrogen diffusion flame in air T_rot(N₂) = 1880 ± 21K, T_rot(H₂) = 1890 ± 80 K, T_vib(N₂) = 1995 ± 130 K, and T_vib(H₂) =1900 ± 150 K.     

Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables

Summary Limit theorems with a non-Gaussian limiting distribution have been obtained, under appropriate conditions for partial sums of instantaneous nonlinear functions of stationary Gaussian sequences with long range dependence by a number of people. The normalization has typically been n , with 1/2<<1 where n is the sample size. Here examples of limit theorems are given for quadratic functions with long range memory (not instantaneous) with a normalization n , 0<<1/2.Research supported in part by the Office of Naval Research     

Splay elasticity in an oligomeric liquid crystal

A magnetically-induced Freedericksz transition was used in conjunction with capacitance techniques to determine the splay elastic constant of the 4,4'-dialkoxyphenylbenzoate monomer '5OO5rsquo; [C₅H₁₁OC₆H₄COOC₆H₄OC₅H₁₁] and its dimer. As a function of reduced temperature in the nematic phase, it was found that K₁₁ of the dimer is only about 20 per cent larger than that of the monomer. Moreover, the values of K₁₁/S² versus reduced temperature, where S is the scalar order parameter, are equal to within experimental noise. These results suggest that for short oligomers Meyer's entropic model for splay elasticity in polymer liquid crystals is not applicable. A lowest order correction to the entropic model is suggested, which partially accounts for excluded volume and dispersive effects.     

Twist elasticity and anchoring in a lamellar nematic phase

Electro-optic measurements were performed on a lamellar nematic phase in which the mesogenic moieties lie in lamellae that are separated by partially perfluorinated side groups. The twist elastic constant K22, viscosity gamma(1), and the quadratic and quartic anchoring strength coefficients are reported. K22 and gamma(1) are found to be considerably smaller than that of typical three-dimensional nematics. The small K22 is due to the greatly weakened interactions between the spatially separated lamellae.     

Oscillation inequalities for rectangles

In this paper we extend previously obtained results on norm inequalities for square functions, oscillation and variation operators, with actions, to the case of actions. The technique involves the use of a result about vector valued maximal functions, due to Fefferman and Stein, to reduce the problem to a situation where we can apply our previous results.     

Detection of monobasic phosphorus acid esters by conversion to cholinesterase inhibitors

Many monobasic acids of quinquevalent phosphorus form cholinesterase inhibitors when exposed to ketene. Based upon this finding, a sensitive test to detect the presence of these compounds on filter paper has been developed. Seventeen out of nineteen of these acids tested gave positive results. Negative results obtained with the remaining two are attributable to steric factors or to the high hydrolysis rate of the acetylated product. Only one of eighteen phosphorus compounds other than the monobasic acids examined, namely n-butylphosphonic acid, gave a positive test; an explanation is offered to account for this exception.