Novel and Highly Effective Method for the Trimethylsilylation of Alcohols and Phenols with Hexamethyldisilazane (HMDS), Catalyzed by I2 Generated in situ Using Fe(NO3)3⋅9 H2O/NaI under Heterogeneous and Neutral Conditions

Structurally diverse alcohols and phenols were trimethylsilylated in a clean and efficient reaction with hexamethyldisilazane (HMDS) based on the use of I₂ generated in situ from Fe(NO₃)₃?9 H₂O/NaI. The reaction occurs very rapid in good‐to‐high yield in CH₂Cl₂ at room temperature, and the use of toxic and corrosive molecular I₂ is avoided.     

Production decisions under joint price and production uncertainty

While production decisions in the presence of price uncertainty have been extensively studied, this is not so for the case in which the level of production is itself uncertain. In this paper,we provide a decision analysis under multiplicative production uncertainty, both with and without price uncertainty. We depict equilibrium and obtain comparative statics results with the aid of a diagram based on the difference between expected price and marginal cost. Comparative statics results are obtained for the model with production uncertainty alone and also for simultaneous price and production uncertainty (including two special cases). We first derive results based on the Arrow–Pratt coefficients of risk aversion, and then supplement these with the Ross measure of relative risk aversion, since this proves useful in the presence of multiple sources of uncertainty. We find that increases in risk (both price and production) or input prices reduce expected output. However, expected output supply is an increasing function of (expected) price only for “low” levels of risk aversion, and in general the relationship is ambiguous.     

Decidability and Specker sequences in intuitionistic mathematics

A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema (which we call ED ) about intuitionistic decidability that asserts “there exists an intuitionistic enumerable set that is not intuitionistic decidable” and show that the existence of a Specker sequence is equivalent to ED . We show that ED is consistent with some certain well known axioms of intuitionistic analysis as Weak Continuity Principle, bar induction, and Kripke Schema. Thus, the assumption of the existence of a Specker sequence is conceivable in intuitionistic analysis. We will also introduce the notion of double Specker sequence and study the existence of them (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Observation of a half step magnetization in the {Cu3}-type triangular spin ring

We report pulsed field magnetization and ESR experiments on a {Cu3} nanomagnet, where antiferromagnetically coupled Cu(2+) (S = 1/2) ions form a slightly distorted triangle. The remarkable feature is the observation of a half step magnetization, hysteresis loops, and an asymmetric magnetization between a positive and a negative field in a fast sweeping external field. This is attributed to an adiabatic change of magnetization. The energy levels determined by ESR unveil that the different mixing nature of a spin chirality of a total S = 1/2 Kramers doublet by virtue of Dzyaloshinskii-Moriya interactions is decisive for inducing half step magnetization.     

Load-Deformation Behavior of Nitinol Stents

The rate of fracture of Nitinol stents in the superficial femoral artery (SFA) is higher than desirable. Development of more fracture-resistant stents requires a better understanding of in-vivo loads, how stents deform under these loads, and the influence of the artery on stent deformation. In the work reported here, testing devices were designed and constructed to measure loads in stents undergoing tensile, bending, and torsional deformations. Tests to measure mechanical stiffnesses were performed on stents, mock arteries, and stents emplaced in mock arteries. Significant stent/artery interaction was observed under tension and bending; little interaction occurred under torsion loads. The results are explained by changes in stent geometry under load. The deformation, load, and stent/artery interaction information will be useful in validating finite element codes for designing and analyzing stents.     

Synthesis and Structure Elucidation of Pyrimidobenzimidazoles and Fused Derivatives II [1]. Dodecahydrobenzimidazo-[2,1-b]quinazolines and Decahydrobenzimidazo-[2,1-b]benzo[h]quinazolines [2]

Summary.  The cyclization reactions of trans-3a-hexahydro-2-benzimidazolamine with 2-alkylidene- and 2-benzylidenecyclohexanones and α-tetralones, respectively, yield mixtures of two isomeric condensates each. Thorough high resolution NMR analyses (¹H and ¹³C NMR, HH-COSY, gs-HSQC, gs-HMBC, 1D TOCSY, and 1D NOE difference spectra) revealed that the corresponding isomers are in all cases linearly fused diastereomeric 12α- and 12β-substituted trans-6aα-dodecahydrobenzimidazo[2,1-b]quinazolines and 7α-substituted trans-8aβ- and trans-8aα-decahydrobenzimidazo[2,1-b]benzo[h]quinazolines, respectively. The formation of corresponding angularly fused regioisomers was not observed so far. The stereochemistry and the tautomerism of some bases and their hydrochlorides as well as the regiospecific course of the cyclization reactions are discussed. Biological tests showed that the novel compounds don’t exert remarkable antibacterial and antimycotic effects. Received November 3, 1999. Accepted November 30, 1999     

A Bounded Translation of Intuitionistic Propositional Logic into Basic Propositional Logic

In this paper we prove a bounded translation of intuitionistic propositional logic into basic propositional logic. Our new theorem, compared with the translation theorem in [1], has the advantage that it gives an effective bound on the translation, depending on the complexity of formulas.