Measurable,nonleavable gambling problems

The optimal return function for a Borel measurable gambling problem with a bounded utility function was shown by Strauch (1967) to be universally measurable when the problem is leavable in the sense that the gambler may terminate play at any time. The same is shown here for the more general class of nonleavable problems. Research supported by National Science Foundation Grant DMS-8801085.     

Studies towards the total synthesis of (−)-borrelidin: a strategy for the construction of the C11-C15 cyanodiene fragment and the utility of RCM for macrocyclization using model systems

We report here a methodology for the construction of a conjugated cyanodiene synthon and the propensity of such synthons to participate in the olefin metathesis reaction. To this end, we have developed a strategy for the construction of the C11-C15 fragment of borrelidin and demonstrated the utility of the RCM reaction in the preparation of the final macrolide. To our knowledge, this is the first example of a RCM with a nitrile functionality on a diene.     

Surface modified ormosil nanoparticles

Organically modified silanes (ORMOSIL) such as vinyl triethoxysilane readily aggregate in the aqueous cores of reverse micelles where the triethoxysilane moieties are hydrolyzed to form a hydrated silica network and the vinyl groups protruded out from the surface of the nanoparticles toward the hydrophobic side of the micellar interface. These particles are spherical and the size distribution of the particles is relatively narrow, with an average diameter of 87 nm. Surface vinyl silica nanoparticles so formed have been oxidized to surface carboxylic silica nanoparticles, followed by chemical conjugation with polyethyleneglycol amine (PEG amine) through the ethyl-3-(3-dimethylaminopropyl) (EDCI) carbodiimide reaction. The characteristic surface groups have been identified by Fourier transform infrared spectroscopy, while the size and the morphology of the particles have been studied by dynamic light scattering and transmission electron microscopy. It has been found that about 80-85% of the carboxylic groups are PEGylated during the EDCI reaction.     

A tridentate CNO‐donor palladium(II) complex as efficient catalyst for direct C―H arylation: Application in preparation of imidazole‐based push–pull chromophores

A series of imidazolium chlorides for the formation of tridentate CNO‐donor palladium(II) complexes featuring N‐heterocyclic carbene moieties have been developed from cheap and readily available starting materials with high yields. Their palladium complexes were prepared by reactions between the ligand precursors and PdCl₂ using K₂CO₃ as base in pyridine with reasonable yields. These air‐stable metal complexes were characterized using ¹H NMR and ¹³C{¹H} NMR spectroscopy and elemental analyses. Heteronuclear multiple bond correlation experiments were performed to identify key NMR signals of these compounds. The structures of two of the complexes were also established by single‐crystal X‐ray diffraction analysis. One of these complexes was successfully applied in the direct C―H functionalization reactions between heterocyclic compounds and aryl bromides, producing excellent yields of coupled products. The coupling reactions were scalable, allowing grams of coupled products to be obtained with a mere 2 mol% of Pd loading. The catalyst system developed allowed the large‐scale preparation of several push–pull chromophores straightforwardly. Photophysical properties based on UV–visible and fluorescence spectroscopy for these chromophores were investigated. Deep blue photoluminescence with moderate quantum efficiency and twisted intramolecular charge transfer excited state were observed for these chromophores. Density functional theory (DFT) and time‐dependent DFT calculations were performed to support the experimental results.     

Estimating Precision in Functional Images

Abstract

Functional imaging of biologic parameters like in vivo tissue metabolism is made possible by Positron Emission Tomography (PET). Many techniques have been suggested for extracting such images from dynamic time-course sequences of reconstructed PET scans. Quantitating the precision of these estimates is important for drawing inferences on the biologic parameters. Analytic variance formulas are not immediate owing to the nonlinear methods used in extraction. The usual resampling approach is infeasible because each image reconstruction in PET is a computationally demanding solution to a high-dimensional linear inverse problem. We suggest an alternative simulation approach that approximates the distribution of reconstructed PET scans and performs a parametric bootstrap in the imaging domain. Results on a simplified model chosen to match the characteristics of PET reconstruction are very encouraging. Mixture analysis is used to estimate functional images; however, the suggested approach is general enough to extend to other techniques or imaging methods.     

Orbital order in NaTiO2: A first principles study

The debate over the orbital order in the layered triangular lattice system NaTiO₂ has been rekindled by the recent experiments of McQueen et al. [Phys. Rev. Lett. 101 (2008) 166402] on NaVO₂. In view of this, the nature of orbital ordering, in both high and low temperature phases, is studied using an ab-initio electronic structure calculation. The orbital order observed in our calculations in the low temperature structure of NaTiO₂ is consistent with the predictions of McQueen et al. An LDA plus dynamical mean-field calculation shows considerable transfer of spectral weight from the Fermi level but no metal–insulator transition, confirming the poor metallic behavior observed in transport measurements.     

A Convenient Route To 1,2-Dibenzoyl-1-Arylethylenes

Short and convenient syntheses of 1,2-cis-dibenzoyl-1-ary 1-ethylenes 5a-e, 6 and 8a-d from the corresponding aryl ethers and dibenzoyl acetylene have been developed using boron trifluoride-etherate or aluminium chloride as catalyst.     

Visible‐Light‐Induced Generation of H2 by Nanocomposites of Few‐Layer TiS2 and TaS2 with CdS Nanoparticles

Graphene analogues of TaS₂ and TiS₂ (3–4 layers), prepared by Li intercalation followed by exfoliation in water, were characterized. Nanocomposites of CdS with few‐layer TiS₂ and TaS₂ were employed for the visible‐light‐induced H₂ evolution reaction (HER). Benzyl alcohol was used as the sacrificial electron donor, which was oxidized to benzaldehyde during the reaction. Few‐layer TiS₂ is a semiconductor with a band gap of 0.7 eV, and its nanocomposite with CdS showed an activity of 1000 μmol h^?1 g^?1_. The nanocomposite of few‐layer TaS₂, in contrast, gave rise to higher activity of 2320 μmol h^?1 g^?1, which was attributed to the metallic nature of few‐layer TaS₂. The amount of hydrogen evolved after 20 and 16 h for the CdS/TiS₂ and CdS/TaS₂ nanocomposites was 14833 and 28132 μmol, respectively, with turnover frequencies of 0.24 and 0.57 h^?1, respectively.     

Memory in time-dependent density functional theory

Exact time-dependent density functionals remember both the entire history of the density and the initial wave function. We show that the two effects are intimately related, and all history dependence can be written as initial-state dependence, including that of the exchange-correlation kernel. For states that can be evolved from a ground state, all initial-state dependence is a dependence on a pseudo-prehistory, providing a route to excited-state densities from time-dependent density functional theory.