Bonding of multiple noble-gas atoms to CUO in solid neon: CUO(Ng)n (Ng=Ar, Kr, Xe; n=1, 2, 3, 4) complexes and the singlet-triplet crossover point

Laser-ablated U atoms co-deposited with CO in excess neon produce the novel CUO molecule, which forms distinct Ng complexes (Ng=Ar, Kr, Xe) with the heavier noble gases. The CUO(Ng) complexes are identified through CO isotopic and Ng reagent substitution and comparison to results of DFT frequency calculations. The U[bond]C and U[bond]O stretching frequencies of CUO(Ng) complexes are slightly red-shifted from neon matrix (1)Sigma(+) CUO values, which indicates a (1)A' ground state for the CUO(Ng) complexes. The CUO(Ng)(2) complexes in excess neon are likewise singlet molecules. However, the CUO(Ng)(3) and CUO(Ng)(4) complexes exhibit very different stretching frequencies and isotopic behaviors that are similar to those of CUO(Ar)(n) in a pure argon matrix, which has a (3)A" ground state based on DFT vibrational frequency calculations. This work suggests a coordination sphere model in which CUO in solid neon is initially solvated by four or more Ne atoms. Up to four heavier Ng atoms successively displace the Ne atoms leading ultimately to CUO(Ng)(4) complexes. The major changes in the CUO stretching frequencies from CUO(Ng)(2) to CUO(Ng)(3) provides evidence for the crossover from a singlet ground state to a triplet ground state.     

A parallel synthesis demonstration library of tri-substituted indazoles containing new antimutagenic/antioxidant hits related to benzydamine

A solution phase strategy for the multiple parallel synthesis of a demonstration library of indazoles is described by which regio-selectivity problems inherent to previous syntheses of this nucleus are largely overcome. Synthesis of selected components proceeded satisfactorily indicating that a fully realized library of indazole analogs could readily be produced using this methodology. Simple modifications of the basic nucleophilic aromatic substitution route unambiguously produce a range of N-1 substitutions (alkyl, aryl and aralkyl) in 50-75% yields. Next a range of substituents was introduced at the C-3 position in 50-80% yields by O-alkylation. Careful choice of reagents and reaction conditions were required to prevent by-product formation due to competing alkylation at N-2 (trace to 15% yields). When present, these contaminants were readily removed by chromofiltration. A third diversity site was sketched in at C-5 in 75-90% yield by reductive alkylation or acylation. Screening of some of the demonstration library members in vitro revealed highly active antioxidants suggesting that producing a full library would be worthwhile.     

Monte Carlo study of electron correlation functions for small molecules

A study is made of electron-electron correlation functions for use in trial wave functions for small molecules. New forms are proposed that have only a few variational parameters, and these parameters have physical meanings that are easily discerned. Total energies for H₂, LiH and Li₂ computed using these correlation functions are presented, and comparison is made with previous forms, including the Jastrow-Pade form often used in Monte Carlo studies. We further treat the possibility that correlation depends not only on the separation of a pair of electrons but also on the location of the electron pair relative to the nuclei — indicative of a density-dependent or many body correlation effect. Our results indicate that such a many-body correlation effect is weakly present.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

On the theoretical, conceptual, and philosophical foundations for research in mathematics education

The current infatuation in the U.S. with “what works” studies seems to leave education researchers with less latitude to conduct studies to advance theoretical and model-building goals and they are expected to adopt philosophical perspectives that often run counter to their own. Three basic questions are addressed in this article:What is the role of theory in education research? How does one's philosophical stance influence the sort of research one does? And,What should be the goals of mathematics education research? Special attention is paid to the importance of having a conceptual framework to guide one's research and to the value of acknowledging one's philosophical stance in considering what counts as evidence.     

ChemInform Abstract: A Matrix Isolation and Computational Study of Molecular Palladium Fluorides: Does PdF6 Exist?

Binary palladium fluorides from PdF to PdF₆ are investigated by matrix‐isolation methods using thermal evaporation and laser ablation to generate Pd atoms for reaction with F₂‐doped Ar and Ne matrices as well as neat F₂ matrices.     

On Balazard,Saias, and Yor’s equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)$S\left(t\right)$ in the theory of the Riemann zeta-function.     

On local regularization for an inverse problem of option pricing

We explore the theoretical and numerical application of local regularization methods to an ill-posed inverse problem arising from financial option pricing. In addition, we provide an algorithm and show results through numerical examples.