Some Boolean Algebras with Finitely Many Distinguished Ideals I

We consider the theory Th_prin of Boolean algebras with a principal ideal, the theory Th_max of Boolean algebras with a maximal ideal, the theory Th_ac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Th_sa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Th_prin and Th_sa. If T is a theory in a first order language and α is a linear order with least element, then we let Sentalg(T) be the Lindenbaum-Tarski algebra with respect to T, and we let intalg(α) be the interval algebra of α. Using rank diagrams, we show that Sentalg(Th_prin) ? intalg(ω⁴), Sentalg(Th_max) ? intalg(ω³) ? Sentalg(Th_ac), and Sentalg(Th_sa) ? intalg(ω² + ω²). For Th_max and Th_ac we use Ershov's elementary invariants of these theories. We also show that the algebra of formulas of the theory Tx of Boolean algebras with finitely many ideals is atomic.     

Synthesis,characterization, crystal structure and catalytic property of [Cu(SalAHE)2] (SalAHE = salicylaldehydeimine-1-hydroxyethane) complex for the oxidation of 3,5-di-tert-butylcatechol

The crystal structure, spectroscopic properties and catalytic property of the copper(II) complex, prepared by the reaction between copper(II) diacetate with the bidentate Schiff base, SalAHE (SalAHE = salicylaldehydeimine-1-hydroxyethane), are reported. This complex is able to oxidize 3,5-di-tert-butylcatechol to the respective o-quinone. The oxidation reaction was studied in CH₃CN with molecular oxygen at 0, 5, 15 and 25 °C. The progress of the catalytic reaction was followed by gas chromatographic analyses (GC).     

Solving the Combined Zoning and Location Problem for Several Emergency Units

This paper discusses methods for the solution of the combined zoning and location problem for several emergency units. This is a stochastic optimization problem. The stochastic aspects include ordered preference of servers. A constraint of equal workload for the servers is also dealt with. Non-linear programming techniques are adapted for its solution.     

The Chemistry of Stable Carbenes. Part 2. Benzoin-type condensations of formaldehyde catalyzed by stable carbenes

Stable carbenes derived from thiazole, 1H-imidazole, and 4H-1,2,4-triazole are efficient catalysts for benzointype condensations of formaldehyde. Catalysts derived from N-substituted thiazolium salts trimerize formaldehyde to dihydroxyacetone ( II ). Catalysts based on 1,4-disubstituted 4H-1,2,4-triazol-1-ium salts give glycolaldehyde ( I ) as the main product and no II , whereas N,N′-disubstituted 1H-imidazol-3-ium salts yield mixtures of both products. The isolation of several intermediates in the catalytic cycle provide a better insight into the reaction mechanism.     

Some properties of bivariate Gumbel Type A distributions with proportional hazard rates

We call a set of univariate distributions with the same mathematical form but different parameter values a family $\text{J}$. Consider a bivariate Gumbel Type A survival distribution, S₁₂(x₁, x₂), defined in (2.1), for which both marginal distributions, S₁(x₁), S₂(x₂), belong to the same family, $\text{J}$ of distributions. It is proved in this paper that subject to weak conditions, the crude hazard rates, h₁(t) and h₂(t), are proportional if and only if the marginal hazard rates, λ₁(t) and λ₂(t), are proportional (Theorem 1). It is also shown that the survival functions of W = min(X₁, X₂), and of the identified minimum, W_i = X_i, for X_i < X_j, j ≠ i, belong to the same family $\text{J}$ as do S₁(x₁), S₂(x₂) (Corollary 1). Counter-examples of distributions other than Gumbel Type A, for which these properties do not hold, are given. Some applications to the analysis of competing risks, using a family of Gompertz distributions, are discussed.     

Capillar-gas-chromatographische Bestimmung von Nitroglycerin in Plasma

Ohne Zusammenfassung

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Capillary gas-chromatographic determination of glycerol trinitrate in plasma

     

Measuring site-specific cluster-surface bond formation

Recent advances in dynamic force microscopy show that it is possible to measure the forces between atomically sharp tips and particular atomic positions on surfaces as a function of distance. However, on most ionic surfaces, the positive and negative ions can so far not be distinguished. In this paper, we use the CaF2(111) surface, where atomic resolution force microscopy has allowed identification of the positions of the Ca2+ and F- ions in the obtained images, to demonstrate that short-range interaction forces can be measured selectively above chemically identified surface sites. Combining experimental and theoretical results allows a quantification of the strength and distance dependence of the interaction of a tip-terminating cluster with particular surface ions and reveals details of cluster and surface relaxation. Further development of this approach will provide new insight into mechanisms of chemical bond formation between clusters, cluster deposition at surfaces, processes in adhesion and tribology, and single atom manipulation with the force microscope.