Three-valued derived logics for classical phase spaces

Reichenbach proposed a three-valued logic to describe quantum mechanics. In his development, Reichenbach presented three different negation operators without providing any criteria for choosing among them. In this paper we develop two three-valuedderived logics for classical systems. These logics are derived in that they are based on a theory of physical measurement. In this regard they have some of the characteristics of the quantum logic developed by Birkhoff and von Neumann. The theory of measurement used in the present development is the one used previously in developingbivalent derived logics for classical systems. As these systems are derived logics, many of the ambiguities possessed by systems such as Reichenbach's are avoided.     

On an alternative supermatrix reduction

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even reduction) which arises in connection with the possible extension of manifold structure group reductions. The study was initiated by consideration of generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated together. They can be unified into some kind of sandwich semigroups. We also define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.Alexander von Humboldt Fellow. On leave of absence from Theory Division, Nuclear Physics Laboratory, Kharkov State University, Kharkov 310077, Ukraine     

Unique continuation theorems for the\bar \partial - Operator and applications

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz ₀ of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away fromz ₀ cannot vanish to infinite order atz ₀ unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection and kernel in planar domains. Research supported by NSF Grant DMS-8922810.     

Structures formed by the chiral assembly of racemic mixtures of enantiomers: iodination products of elaidic and oleic acids

The self-assembled monolayer structure of the products of elaidic acid iodination (the racemic mixture of 9,10-(9S,10R)-diiodooctadecanoic acid and 9,10-(9R,10S)-diiodooctadecanoic acid) and the products of oleic acid iodination (the racemic mixture of 9,10-(9R,10R)-diiodooctadecanoic acid and 9,10-(9S,10S)-diiodooctadecanoic acid) are studied by high-resolution scanning tunneling microscopy. For the iodination products of elaidic acid, the separation of enantiomers into distinct chiral domains during the formation of the 2-D crystal on the highly ordered pyrolytic graphite (HOPG) surface is not observed. Instead, within the diiodooctadecanoic acid SAM, each row of molecules is composed of opposite racemates. The two opposite racemates pack alternately inside a row, using different faces to adsorb on the surface. The unit cell is composed of a pair of opposite racemates, forming a heterochiral structure. For the iodination products of oleic acid, the racemic mixture is observed to exhibit quasi-phase separation during the formation of the 2-D crystal on the HOPG surface. Each row is composed of homochiral acid molecules, either the 9,10-(9R,10R)-diiodooctadecanoic acid (R) or the 9,10-(9S,10S)-diiodooctadecanoic acid (S). The R row and the S row pack alternately, with a unit cell composed of four molecules. Two of the molecules in the unit cell are the 9,10-(9R,10R)-diiodooctadecanoic acid (R) molecules; two are the 9,10-(9S,10S)-diiodooctadecanoic acid (S) molecules. In the unit cell, the two molecules that have the same chirality pack antiparallel inside the homochiral row, using different faces to adsorb on the surface. These results suggest that several different types of chiral assembly are possible. Enantiomers with opposite chirality exhibit many chiral assembly patterns, forming heterochiral structures on the surface in addition to separation to form macroscopic chiral domains. By using different conformations, similar enantiomers with opposite chirality will display many chiral assembly patterns to form heterochiral structures on the surface.     

Tandem (quadrupole-time-of-flight) electrospray mass spectrometry of oligo(vinyl acetates) with isopropylol or (1-hydroxyethyl)-2-oxyisopropanyl end groups

Poly(vinyl acetates) with either isopropylol or (1-hydroxyethyl)-2-oxyisopropanyl end groups were analysed by tandem mass spectrometry using a quadrupole-time-of-flight (Q-TOF) instrument. Random scission along the polymer backbone was not observed. Instead the initial scissions were derived from the cleavage of end-group species. The resultant macrocations were subject to further elimination reactions that eventually produced polyene macrocations. A smaller fraction of the initial macrocations also reacted by loss of ketene and this reaction produced macrocations containing vinyl alcohol units.     

Oxygen isotope corrections for online delta(34)S analysis

Elemental analyzers have been successfully coupled to stable-isotope-ratio mass spectrometers for online measurements of the delta(34)S isotopic composition of plants, animals and soils. We found that the online technology for automated delta(34)S isotopic determinations did not yield reproducible oxygen isotopic compositions in the SO(2) produced, and as a result calculated delta(34)S values were often 1-3 per thousand too high versus their correct values, particularly for plant and animal samples with high C/S ratio. Here we provide empirical and analytical methods for correcting the S isotope values for oxygen isotope variations, and further detail a new SO(2)-SiO(2) buffering method that minimizes detrimental oxygen isotope variations in SO(2).     

Heterogeneous reactions : VI. Reactions of trimethylchlorosilane,dimethyldichlorosilane and chloromethyldimethylchlorosilane with potassium t-butoxide and sodium methoxide

The heterogeneous gas-solid reaction of trimethylchlorosilane and an equal molar mixture of potassium t-butoxide and sodium methoxide gave exclusively trimethyl-t-butoxysilane. A similar reaction utilizing dimethyldichlorosilane as the vapor phase substrate gave predominant incorporation of butoxide. The heterogeneous reaction of chloromethyldimethylchlorosilane with these two bases was extensively studied. The parameters investigated for the latter system include the dependence of the product distribution on temperature, nitrogen flow rate and the relative hydroxide content of the solid alkoxide base. These studies allow the assessment of the relative reactivities of these bases under the conditions of heterogeneous gas/solid reaction. Under these conditions and with partially hydrolyzed bases a substantial amount of displacement of the chloromethyl group from chloromethyldimethylchlorosilane is observed. The role of hydroxide ion in this reaction is discussed. Convenient syntheses of t-butyl methyl ether and dimethylchloromethoxysilane are reported.     

Polymers for catalytic cation radical chemistry

Cation radical polymers which have cation radical functions at up to 5% of the poly(styrene) monomer sites have been prepared, and their effectiveness in catalyzing the cation radical Diels-Alder reaction is demonstrated.     

Sequential versus direct multiphoton absorption

We present results of exact calculations on a three-level Morse oscillator modeling HF which suggest that multiphoton absorption proceeds by sequential single-level transitions, transitions arising from coupling between non-adjacent states being dynamically negligible. The time-dependent Schrödinger equation is integrated in the Floquet formalism.