Topological representation of posets

There is a canonical imbedding of a poset into a complete Boolean lattice and hence into a Boolean lattice. This gives it a representation as a collection of clopen sets of a Boolean space. There are reflective functions from a category of distributive posets to the subcategories of distributive and Boolean lattices and consequently a topological dual equivalence that extends the Stone duality of Boolean lattices.Presented by B. Jonsson.     

A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states

Part IIb presents some of the most important theorems for stable equilibrium states that can be deduced from the four postulates of the unified theory presented in Part I. It is shown for the first time that the canonical and grand canonical distributions are the only distributions that are stable. Moreover, it is shown that reversible adiabatic processes exist which cannot be described by the dynamical equation of quantum mechanics. A number of conditions are discussed that must be satisfied by the general equation of motion which is yet to be discovered.Part I of this paper appeared inFound. Phys. 6(1), 15 (1976). Part IIa appeared inFound. Phys. 6(2), 127 (1976). The numbering of the sections, equations, and references in this part of the paper continues from those in Part IIa.     

Toeplitz operators on weighted Bergman spaces

In [2], Axler, Conway and McDonald, discuss the essential spectrum of Toeplitz operator, with continuous symbol, on the unweighted Bergman space. This paper extends their results to the weighted Bergman space, where the weight and its logarithm are assumed to be locally integrable.This paper represents part of the author's Ph.D. thesis, written at Indiana University under the direction of Professor John B. Conway.     

Polarit?t bin?rer L?sungsmittelgemische: Bestimmung von ET(30)-Werten und Korrelation mit kinetischen L?sungsmittel-Effekten

Zusammenfassung Zur empirischen Beschreibung der Polarität binärer Lösungsmittelgemische wurden mit einem solvatochromen Betain-Farbstoff E_T-Werte für folgende Systeme bestimmt: Methanol/Butanol-2, Methanol/2-Methylbutanol-2, Methanol/Pyridin, Methanol/Acetonitril, Methanol/Toluol und Ethanol/ 2,2,2-Trifluorethanol. In allen Systemen treten mehr oder weniger starke Abweichungen vom idealen Mischungsverhalten auf, was im einzelnen diskutiert wird. In den genannten Lösungsmittelgemischen wurde parallel die Kinetik der Ligandensubstitution an einem neutralen Kupfer(II)-bis-chelatkomplex vermessen. Die E_T-Werte korrelieren mit den lnkWerten (k = Geschwindigkeitskonstante für den durch das Solvens induzierten Ligandenaustausch). Dies weist darauf hin, daß die Bildung des Übergangszustandes durch H-Brücken erleichtert wird.

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Polarity of binary solvent mixtures: Determination of E_T(30)-values and correlation with kinetic solvent effects

Summary The polarity of binary solvent mixtures is empirically described by E_T-values as determined with a solvatochromic betaine dye. The following mixtures were studied: methanol/butanol-2, methanol/2-methylbutanol-2, methanol/pyridine, methanol/acetonitrile, methanol/toluene and ethanol/2,2,2-trifluoroethanol. All mixtures behave as more or less non-ideal systems which is discussed in detail. Parallel to the determination of E_T-values the kinetics of ligand substitution in a neutral copper(II)-bis-chelate complex were studied in the same set of solvent mixtures. The E_T-values correlate with the corresponding lnk-values (k = rate constant for solvent induced ligand substitution). This would mean that the formation of the transition state is facilitated by hydrogen bonding.

Für finanzielle Unterstützung bedanken wir uns bei der Deutschen Forschungsgemeinschaft und dem Verband der Chemischen Industrie e.V. Der verwendete Salicylaldehyd wurde uns von der Firma Bayer AG, Leverkusen, zur Verfügung gestellt.     

Displacement of fibrinogen from the air/aqueous interface by dilauroylphosphatidylcholine lipid

Fibrinogen (FB) and other serum proteins leak into the aqueous alveolar lining layer due to lung injuries. The adsorption of these serum proteins at the air/aqueous interface can produce higher surface tensions than the pulmonary lipids, and acute respiratory distress syndrome (ARDS) can ensue. By having a molecular adsorption mechanism, as compared to a particulate adsorption mechanism of other longer chain lipids, dilauroylphosphatidylcholine (DLPC) lipid can expel FB from the air/aqueous interface at 25 degrees C, in water or in phosphate-buffered saline, as proven by tensiometry (also at 37 degrees C), ellipsometry, and infrared reflection-absorption spectroscopy. Moreover, before FB is displaced by DLPC at the interface, there is a substantial initial enhancement in the FB adsorption, consistent with some interaction or binding of DLPC with FB to produce a more hydrophobic protein surface. After the FB molecules have been displaced by DLPC, or when DLPC has already adsorbed at the interface, FB molecules are less favored to adsorb near the DLPC monolayer with the lecithin headgroups facing toward them. The results have implications for possible uses of DLPC lipid in potential lung surfactant formulations in treating patients with ARDS.     

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the -algebra of a CKT family, and prove a universality theorem for -algebras generated by these families. In both cases, the -algebras generated by quiver algebras play the universal role.

     

Tests of scaling of the proton electromagnetic structure functions

Deep-inelastic structure functions W₁ and W₂ have been extracted from electron-proton scattering cross sections that were measured in recent experiments at SLAC. The structure functions display deviations from scaling in the variable ω in the kinetic range 1.5 ? ω ? 3.0 and 2 ? Q² ? 15 GeV².