Hypergeometrics and the cost structure of quadtrees

Several characteristic parameters of randomly grown quadtrees of any dimension are analyzed. Additive parameters have expectations whose generating functions are expressible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit values for various structure constants related to path length, retrieval costs, and storage occupation.     

Delayed fluorescence ODMR as a probe of triplet-triplet fusion probability

A kinetic scheme is presented to rationalize recent observations of delayed fluorescence ODMR in isotopically mixed naphthalene crystals, in which the sign of the signal changes from negative to positive as the critical concentration for triplet-triplet transport among the perprotonated traps is approached. The effects of chopped optical excitation, prolonged microwave pumping, temperature and light intensity are considered. The observation of positive DF-ODMR in the high concentration case is used to obtain a lower limit for the ratio of the annihilation constantk ₂ to the pair dissociation constantk _?1.     

Über eine Zerlegung des Haarschen Maßes auf kompakten Gruppen

Ohne Zusammenfassung     

A new simple synthesis of soluble high molecular weight polyphenylenes by the cotrimerization of mono- and bifunctional terminal acetylenes

The monofunctional acetylenes, phenylacetylene and m-ethynyltoluene, were each copolymerized with diethynylbenzene in a 1:1 mole ratio by using TiCl₄/3AlEt₂Cl as cyclotrimerization catalyst. The aromatic polymers which were produced were polydisperse with a molecular weight of ～10,000. Variation of catalyst concentration had no effect on the molecular weight profile. An excess of bifunctional acetylene produced some insoluble gel but when some of the monofunctional acetylene was withheld and added only after an initial molecular weight build-up by the excess bifunctional acetylene, soluble polymers with molecular weights of approximately 50,000 were obtained in high yield, provided the overall ratio of mono- to bifunctional acetylene was maintained at 1:1. The resulting polyphenylenes were highly soluble in benzene and chlorinated solvents but gave brittle films. This was attributed to a highly branched structure resulting from a lack of specificity by the catalyst. Thermogravimetric analysis showed the polymers to have high thermal stability.     

Ionization and appearance potential measurements in arene chromium tricarbonyls

The ionisation potentials and the appearance potentials for ions arising from the loss of carbonyl groups as well as certain other low-energy fragmentation ions have been measured for a series of substituted arene chromium tricarbonyls. The values obtained are found to correlate very well, for the loss of one and two carbonyl groups, with both the CO force constant k and the Hammett σ_p function and substituent on the benzene ring. The appearance potentials of the ions arising by the loss of three carbonyl groups do not exhibit a high correlation. Arene⁺ ions are found to occur at energies intermediate between those for the loss of two and three carbonyl groups.The various effects observed are discussed in terms of a model which involves definite contributions from both σ- and π- bonding of carbonyl groups in the gaseous cations.     

Phosphates D'énols: XI—Étude en Spectrométrie de Masse des Dérivés Diméthyliques

The mass spectrometric study of a series of enolic phosphates of type A leades to fragmentation patterns influenced by the nature of the substituents (R, R′ and R″). It is generally observed that a simple or double hydrogen rearrangement occurs with the loss of the enolic groups. When R and R′ are alkyl groups, the migrating groups are the hydrogen atoms on the alkyl group at position 1. When there is no alkyl group at position 1, the hydrogen atoms of the alkyl group at position 2 induce the rearrangement process. Finally, if R, R′ and R″ are hydrogen atoms, the loss of the enolic chain occurs without any rearrangement.