The stoichiometric hydrogenation of 1,1-diphenylethylene with hydridocobalt tetracarbonyl; differences from the hydroformylation reaction

The kinetics of the stoichiometric hydrogenation of 1,1-diphenylethylene with HCo(CO)₄ is cleanly second order, permitting a determination of the activation parameters. The rate is unaffected by the atmosphere over the reaction and is enhanced by substituting DCo(CO)₄ for HCo(CO)₄. These results contrast sharply with those secured in the hydroformylation of 1-alkenes and thus dual mechanistic pathways are available for the reaction of HCo(CO)₄ with unsaturated systems. It is very possible that the stoichiometric hydrogenation of 1,1-diphenylethylene involves a geminate free radical pair but definitive proof is still lacking.     

Physics of selective systems: Computation and biology

The statistical thermodynamics of systems displaying selective behavior is used to discuss some important ultimate physical limitations of computers and biological systems. These cluster around communication of information, measurement, and irreversible processes. The most fundamental limitation is irreducible increase of entropy accompanying selective acts like measurement of preparation. Relevant theory of machines (automata. Turing machines) and issues involved in physical realizations of those machines are discussed. Quantum measurement, the Einstein-Podolsky-Rosen paradox, the fundamental importance of irreversibility, information and entropy, and their relation to Goedel's theorems on completeness and consistency of formal systems are analyzed. Irreversibility of measurement appears necessary to provide quantum mechanics with the incompleteness needed to avoid inconsistency. Motivation and justification of computer paradigms for fundamental modeling of biological systems is given.     

Loschmidt's and Zermelo's paradoxes do not exist

A strict operational (i.e., informational) analysis of the meaning of preparing a system to realize the paradoxes of Loschmidt or Zermelo is made. Where reversal or recurrence are operationally realizable, no contradiction with the irreversible nature of macroscopic operations occurs. Paradox results either from neglecting irreversible phenomena in the means for preparing a reversed state, or from confusing elements or ensembles, which are meaningful in microstate language but meaningless operationally, with preparable macrostates, whoserepresentation in microstate language is an ensemble whose very definition is incompatible with that of any paradox-generating element or ensemble,Supported in part by NSF Grant No. GN 534.1.     

Anomalous resistivity of iodine-free 2H-NbSe2

Resistance ratios of crystals of 2H-NbSe₂ grown with and without iodine were measured over the temperature range 6K–40K. Iodine-free crystals had higher ratios than any NbSe₂ previously reported and exhibited an abrupt anomaly at the onset of the charge density wave phase. All crystals displayed a cubic temperature dependence of their resistivities below 18K.     

On bounded solutions of abstract differential equations

Summary We construct nontrivial bounded solutions of an abstract evolution equationu'(t)=Au(t) (—∞<t<∞) whereA generates a (C ₀) semigroup of operators {T _t;t≥0} such thatT _t converges strongly to zero ast→∞.

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Riassunto Si costruiscono soluzioni limitate non triviali di una equazioneu'(t)=Au(t) (—∞<t<∞) doveA è il generatore di un semigruppo di operatori {T _t;t≥0} tale cheT _t converge fortemente verso 0 pert→∞.

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Supported by National Science Foundation grant GP-12722.     

Elementary extensions of models of set theory

Model Theoretic methods are used to extend models of set theory while leaving specified sets fixed. In particular, every countable modelU of ZF has: (i) an extension leaving every set inU fixed, and (ii) for each (inU) regular cardinala an extension enlarginga but leaving each cardinal less thana fixed. Some of out results were announced in the abstract [8]. Our research was supported in part by NSF contracts 4297 and 5913. The first named author is an Alfred E. Sloan Foundation Fellow.