Raman spectral study of the constitution and equilibria of nitric acid and d-nitric acid

From relative integrated intensity measurements of the symmetric stretching vibration of nitrate ion in nitric acid solutions (both HNO ₃ /H ₂ O and DNO ₃ /D ₂ O), the mass law concentration quotients, Q were obtained as functions of concentration. By extrapolation the limiting dissociation constants were estimated to be 24.4 and 15 respectively at 25°C. It is shown that this constant refers to a process in which the ion pair H ₃ O⁺ NO ₃ ^– is in equilibrium with the dispersed, solvated H ₃ O⁺ and NO ₃ ^– ions.     

Laser induced time-dependent thermal lensing studies of vibrational relaxation: translational cooling in CH3F

Time-resolved measurements of the thermal lens effect have been made for CH₃F, CH₃CI and C₂H₄. This technique is compared to others used in the study of vibrational relaxation phenomena and is found to be applicable to the study of a wide variety of gaseous systems at relatively low pressures. Translational cooling has been observed in CH₃F and an approximate lower limit of 200 msec^-1 has been established for the rate of this cooling process, which corresponds to equilibration of the ν₃ and ν₆ states, in a mixture of 0.2 torr CH₃F and 10 torr Ar.     

On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the configuration space of Yang-Mills theories is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that is contained in a zero measure subset of with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on . Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space .     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).