Information theory for experiments with known conditional probabilities: Application to the prediction of branching ratios

Information theory is used, under conditions of incomplete data, to provide a maximally conservative prior expectation of a population distribution. This is done by systematically refining the estimates of the full distribution via the incorporation of fragmentary data in the form of conditional probabilities. The net effect is to reduce the available phase space volume of the distribution as more data are incorporated. The above refinements are then applied to calculate estimates of branching ratios for chemical reactions with more than one possible product. Two new branching ratio expressions are derived: one for the case where each product's internal state distribution is known for reactions originating from various specific reactant state?, and when the joint state-to-state reactive probability is known.     

Wavelet based in eigenvalue problems in quantum mechanics

The use of Daubechies' compact support wavelets in quantum mechanical eigenvalue problems is investigated. It is shown that these orthogonal multiresolution functions provide an efficient basis for systems in which the potentials vary strongly in different regions.     

The density of states for interacting systems with inelastic transitions and its relation to the collision lifetime

The quantum mechanical excess density of states ρ(E) is shown to be given in terms of the S matrix by (i/2π) Tr{SdS⁺/dE}, giving the relationship ρ(E) = h⁻¹ Tr{Q}, where Q is the collision lifetime matrix of Smith.     

Synthesis and Diels-Alder Reactions of a New Kind of Chiral Dienophiles: Cyclic Vinyl-p-tolylsulfilimines

A new kind of chiral dienophiles, cyclic vinyl-p-tolylsulfilimines (2a and 2b), were obtained from the corresponding (Z)-sulfinylacrylonitriles with HBF(4) and methanol. The asymmetric Diels-Alder reaction of optically pure 2a with cyclopentadiene under mild thermal or catalyzed conditions afforded only the endo-4a adduct with complete endo and pi-facial selectivities. The ability of the sulfilimine moiety to enhance the dienophilic reactivity of the double bond is similar to that of the sulfinyl group.     

Zeros of the Whittaker function associated to Coulomb waves

The zeros in the complex z plane of the Whittaker function W_c/z,µ(z),closely related to spherical waves in the quantum-mechanicalCoulomb problem, are investigated for varying real values ofthe parameters c and µ     

Studies of self-diffusion of poly(dimethylsiloxane) chains in PDMS model networks by pulsed field gradient NMR

We have measured the diffusion of poly(dimethylsiloxane) (PDMS) chains in PDMS model networks by using a pulsed field gradient NMR technique. The model networks have been prepared by tetrafunctional endliking of linear PDMS chains having molecular weights M_n of 3,700 and 7,400 g mol^?1. The diffusants have been incorporated in the networks by immersing pieces of them in PDMS linear chains with molecular weights M_n between 3,000 and 12,000 g mol^?1 and molecular weight distributions M_w/M_n between 1.1 and 1.7. Although spin-echo attenuation results were fitted to a model which takes into account polydispersity of the diffusant, these results did not exhibit any dependency upon the molecular weight distribution. The self-diffusion coefficients of PDMS chains in the PDMS model networks were found to be smaller than in the melt, and the exponents for the diffusion coefficient dependence on M_n in the networks were found to be about-1.3. Free diffusion will give an exponent equal to-1, whereas free volume contributions or behavior intermediate between free and entangled diffusion will increase the magnitude of the exponent.