Operationally unsaturated pincer/rhenium complexes form metal carbenes from cycloalkenes and metal carbynes from alkanes

Operationally unsaturated (i.e., 16/18-electron) (PNPR)Re(H)4, where PNPR is N(SiMe2CH2PR2)2, is reactive at 22 degrees C with cyclic olefins. The first observed products are generally (PNPR)Re(H)2(cycloalkylidene), with hydrogenated olefin as the product of hydrogen abstraction from the tetrahydride. The tetrahydride complex with R = tBu generally fails to react (too bulky), that with R = cyclohexyl suffers a (controllable) tendency to abstraction of 3H from one ring, forming an eta3-cyclohexenyl compound, and that with R = iPr generally gives the richest bimolecular reactivity. The cyclic monoolefins studied show distinct reactivity, C6 giving first the carbene and then coordinated cyclohexadiene, C5 giving carbene, then diene, and then eta5-C5H5, C8 giving carbene and then eta2-cyclooctyne, and C12 giving an eta3-allyl. Norbornene gives a pi-complex of the norbornene in thermal equilibrium with its carbene isomer; at 90 degrees C, hydrocarbon ligand Calpha-Cbeta bond cleavage occurs to give, for the first time, a carbyne complex from an internal olefin. Two compounds synthesized here have the formal composition "(PNPR)Re + olefin", and each of these is capable of dehydrogenating the methyl group of a variety of alkanes at 110 degrees C to form (PNP)ReH triple bond (CR).     

Characterization of etched electrochemical detection for electrophoresis in micron inner diameter capillaries

An enhanced etched electrochemical (EC) detection technique has been developed for CE in micron inner diameter capillaries. The design improvements allow for better alignment between the capillary bore and the electrode. This new method involves utilizing a carbon fiber microelectrode and etching both the carbon fiber and the detection end of a micrometer-sized inner diameter capillary to limit dead volume and analyte diffusion at the amperometric EC detector. To understand the factors affecting enhanced detector efficiency, a detailed examination of the relationship between detector design and performance has been completed by exploring the effects of varying electrode diameter, tip shape, and size, in addition to the etch length of the capillary outlet. The enhanced detection provides peak efficiencies as high as 75000 theoretical plates and estimated detection limits as low as 40 nM for dopamine. This etched detection method should further facilitate volume-limited sample analysis by CE.     

Nitro- and fluoropolyformals. III. Copolyformals from mixtures of fluoro- and nitro-α,ω-diols

Polyformals of fluoro-, nitramine-, and C-nitrodiols show widely differing properties with respect to glass transition temperature, melting transition, and solubility. Polymers with desirable combinations of these properties, e.g., low T_g, high nitro content, and good solubility in polar solvents, were expected to result from acid-promoted copolycondensation of appropriate mixtures of diols with formaldehyde. A series of such condensations were carried out and the polymers obtained from binary mixtures of fluoro- and nitrodiols, different nitrodiols, and fluoro- or nitrodiols and carboranediols, were characterized by GPC, ¹H-NMR, and DSC analysis.     

Trace element analysis of some shaving powders commonly marketed in Nigeria using instrumental neutron activation analysis

Instrumental neutron activation analysis (INAA) technique has been employed viak ₀ approximation method to determine elemental composition of five shaving powders commonly marketed in Nigeria. Fe displayed the highest concentrations in the range 1000–2000 g·g^–1. Na and Zn concentrations were established in the range 200–400 g·g^–1. Heavy elements like Ga, La, Cr, Co, Ag, Ce and Nd concentrations were noted in the lower range of 1–10 g·g^–1 Br, As, Sb, Sm, Eu, W, Cs, Tb, Yb, Hf, Ta, Th and U concentrations were established in even lower traces in the <1 g·g^–1 range. Results obtained for a certified reference material, CANMET BL-1 and CERT (in house) Kaolin standard compared favourably with the literature values thus establishing the results presented for the shaving powders.     

A Bernstein Type Theorem for Entire Willmore Graphs

We show that every two-dimensional entire graphical solution of the Willmore equation with square integrable second fundamental form is a plane.     

Would weighted-student funding enhance intra-district equity in Texas? A simulation using DEA

We use data envelopment analysis to model the educational production function, and then explore how a shift to weighted student funding using the student weights embedded in the Texas School Finance Formula would alter the allocation of inputs and potential outputs. School outputs are measured as value-added reading and math scores on standard achievement tests. We find that if school districts allocated their resources efficiently, then they would not allocate their resources to campuses according to the funding model weights. Policies that promote greater efficiency would also enhance equity in educational outcomes.     

A Domain Embedding Method Using the Optimal Distributed Control and a Fast Algorithm

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. The method is based on formulating the problem as an optimal distributed control problem inside a disc in which the arbitrary domain is embedded. The optimal distributed control problem inside the disc is solved rapidly using a fast algorithm developed by Daripa et al. [3,7,10–12]. The arbitrary domains can be simply or multiply connected and the proposed method can be applied, in principle, to a large number of elliptic problems. Numerical results obtained for Dirichlet problems associated with the Poisson equation in simply and multiply connected domains are presented. The computed solutions are found to be in good agreement with the exact solutions with moderate number of grid points in the domain.     

ABC and the Hasse principle for quadratic twists of hyperelliptic curves

Conditionally on the ABC conjecture, we apply work of Granville to show that a hyperelliptic curve $C_{/\mathbb{Q}}$ of genus at least three has infinitely many quadratic twists that violate the Hasse Principle iff it has no $\mathbb{Q}$-rational hyperelliptic branch points.     

Surface reactions of monoethylgermane on Si(100)-(2×1)

The adsorption and decomposition of monoethylgermane (GeH₃Et) on the Si(100)-(2×1) surface was investigated with the intent of elucidating the surface processes leading to the deposition of germanium. The low-temperature adsorption of the molecule was explored, as well as its thermal decomposition. H₂ and C₂H₄ are observed as the desorption products in temperature-programmed desorption experiments. The ethylene is produced by a hydride elimination reaction within the adsorbed ethyl groups. The amount of Ge which can be deposited in a reaction cycle is correlated with the number of sites occupied by the ethyl groups upon the dissociation of GeH₃Et.