The finitary coding of two Bernoulli schemes with unequal entropies has finite expectation

It is well known that for any two Bernoulli schemes with a finite number of states and unequal entropies, there exists a finitary homomorphism from the scheme with the larger entropy to the one with smaller entropy. We prove that the average number of coordinates in the larger entropy scheme needed to determine one coordinate in the image point is finite.     

Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions

Diamagnetic susceptibilities _dhave been calculated for all positive ions, neutral atoms, and negative ions up to Krypton. It is pointed out that the electrons in the outermost orbitals give the maximum contribution to _d.

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Zusammenfassung Die diamagnetische Suszeptibilität _dsind für alle positiven Ionen, neutrale Atome und negativen Ionen bis zum Krypton (Z=36) berechnet worden. Dabei zeigt es sich, daß die äußersten Schalen den größten Beitrag liefern.

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Résumé Les susceptibilités diamagnetiques _dont été calculées pour tous les ions positives, les atomes neutres et les ions négatives jusqu'au Krypton (Z=36). On montre que les couches électroniques exterieures donnent la contribution la plus importante.

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This work has been supported in part by the National Research Council of Canada.     

Monoprotection of diols as a key step for the selective synthesis of unequally disubstituted diamondoids (nanodiamonds)

The monoprotection (desymmetrization) of diamondoid, benzylic, and ethynyl diols has been achieved using fluorinated alcohols such as 2,2,2-trifluoroethanol (TFE) under acidic conditions. This practical acid-catalyzed S(N)1 reaction opens the door for the synthesis of novel bifunctional diamondoids. With diamantane as an example, we show that the resulting monoethers can be used to prepare selectively, for instance, amino or nitro alcohols and unnatural amino acids. These are important compounds in terms of the exploration of electronic, pharmacological, and material properties of functionalized nanodiamonds.     

η-Alkynyl and vinylidene transition metal complexes: 10. Reaction of the metal-acetylide [(η-C5H5)(CO)(NO)W---CC---C(CH3)3]Li with 1,2-diiodoethane as electrophile and with various nucleophiles

Treatment of the η¹-acetylide complex [(η⁵-C₅H₅)(CO)(NO)W---CC---C(CH₃)₃]Li (4) with 1,2-diiodoethane in THF at −78 °C, followed by the addition of Li---CC---R [R=C(CH₃)₃, C₆H₅, Si(CH₃)₃, 6a–6c] or n-C₄H₉Li and protonation with H₂O, afforded the corresponding oxametallacyclopentadienyl complexes (η⁵-C₅H₅)W(I)(NO)[η²-O=C(CC---R)CH=CC(CH₃)₃] (7a–7c), 8c and (η⁵-C₅H₅)W(I)(NO)[η²-O=C(n-C₄H₉)CH=CC(CH₃)₃] (9). The formation of these metallafuran derivatives is rationalized by the electrophilic attack of 1,2-diiodoethane onto the metal center of 4 to form first the neutral complex [(η⁵-C₅H₅)(I)(CO)(NO)W---CC---C(CH₃)₃] (5). Subsequent nucleophilic addition of Li---CC---R 6a–6c or n-C₄H₉Li and a reductive elimination step followed by protonation leads to the products 7a–7c and 9. One reaction intermediate could be trapped with CF₃SO₃CH₃ and characterized by a crystal structure analysis. The identity of another intermediate was established by infrared spectroscopic data. The oxametallacyclopentadienyl complex 10 forms in the presence of excess 1,2-diiodoethane through an alternative pathway and crystallizes as a clathrate containing iodine.     

Quantitatively probing the means of controlling nanoparticle assembly on surfaces

As a means of developing a simple, cost-effective, and reliable method for probing nanoparticle behavior, we have used atomic force microscopy to gain a quantitative 3D visual representation of the deposition patterns of citrate-capped Au nanoparticles on a substrate as a function of (a) sample preparation, (b) the choice of substrate, (c) the dispersion solvent, and (d) the number of loading steps. Specifically, we have found that all four parameters can be independently controlled and manipulated in order to alter the resulting pattern and quantity of as-deposited nanoparticles. From these data, the sample preparation technique appears to influence deposition patterns most broadly, and the dispersion solvent is the most convenient parameter to use in tuning the quantity of nanoparticles deposited onto the surface under spin-coating conditions. Indeed, we have quantitatively measured the effect of surface coverage for both mica and silicon substrates under preparation techniques associated with (i) evaporation under ambient air, (ii) heat treatment, and (iii) spin-coating preparation conditions. In addition, we have observed a decrease in nanoparticle adhesion to a substrate when the ethylene glycol content of the colloidal dispersion solvent is increased, which had the effect of decreasing interparticle-substrate interactions. Finally, we have shown that substrates prepared by these diverse techniques have potential applicability in surface-enhanced Raman spectroscopy.     

An Improved Computational Strategy to Estimate Residual Stresses from Crack Compliance Data

The successive cracking (crack compliance) method is a destructive technique aimed at determination of residual stresses in various structural members. The laboratory measurements performed during extension of a crack are followed by a computational analysis. We propose a modification of the numerical approach in order to simplify the method and improve its accuracy. The basic idea of the proposed modification is to approximate plastic strains rather than the residual stresses directly. Furthermore, we use the goal oriented adaptive finite element method that generates optimal meshes for evaluation of strains at specific points.