Diffeomorphism finiteness for manifolds with ricci curvature andL n/2-norm of curvature bounded

Partially supported by NSF Grants.     

Volume comparison and the σk-Yamabe problem

In this paper we study the problem of finding a conformal metric with the property that the kth elementary symmetric polynomial of the eigenvalues of its Weyl-Schouten tensor is constant. A new conformal invariant involving maximal volumes is defined, and this invariant is then used in several cases to prove existence of a solution, and compactness of the space of solutions (provided the conformal class admits an admissible metric). In particular, the problem is completely solved in dimension four, and in dimension three if the manifold is not simply connected.     

A first-principles study of surface and subsurface H on and in Ni(1 1 1): diffusional properties and coverage-dependent behavior

Periodic, self-consistent, density functional theory (GGA-PW91) calculations are performed for both surface and subsurface atomic hydrogen on and in Ni(1 1 1). At a low coverage (θ=0.25 ML), the binding energies (BEs) of a hydrogen atom in surface fcc, subsurface octahedral (first layer), and subsurface octahedral (second layer) sites are −2.89, −2.18, and −2.11 eV, respectively. The activation energy barriers for hydrogen diffusion from the surface to the first subsurface layer and from the first to the second subsurface layer are estimated to be 0.88 and 0.52 eV, respectively. In the entire coverage range studied, hydrogen occupies surface fcc and hcp sites and subsurface octahedral sites. In addition, the magnitude of the BE per hydrogen atom and the magnetization of the nickel slabs both decrease as hydrogen coverage increases. Vibrational frequencies of hydrogen at various surface and subsurface sites are calculated and are in reasonable agreement with experimental data. A phase stability calculation with a 2 × 2 surface unit cell shows that a p(2 × 2)-2H overlayer structure (θ=0.5 ML) and a p(1 × 1)-1H structure (θ=1.0 ML) are stable at low hydrogen pressures, in agreement with numerous experimental results. A very large increase in pressure is required to populate subsurface sites. After such an increase occurs, the first subsurface layer is filled completely.     

Nonparametric estimation of distributions with categorical and continuous data

In this paper we consider the problem of estimating an unknown joint distribution which is defined over mixed discrete and continuous variables. A nonparametric kernel approach is proposed with smoothing parameters obtained from the cross-validated minimization of the estimator's integrated squared error. We derive the rate of convergence of the cross-validated smoothing parameters to their ‘benchmark’ optimal values, and we also establish the asymptotic normality of the resulting nonparametric kernel density estimator. Monte Carlo simulations illustrate that the proposed estimator performs substantially better than the conventional nonparametric frequency estimator in a range of settings. The simulations also demonstrate that the proposed approach does not suffer from known limitations of the likelihood cross-validation method which breaks down with commonly used kernels when the continuous variables are drawn from fat-tailed distributions. An empirical application demonstrates that the proposed method can yield superior predictions relative to commonly used parametric models.     

Properties of compounds of type NaxSi46 and NaxSi136

A qualitative account is given of the electrical and magnetic properties of compounds of the type Na_xSi₁₃₆. It is suggested that a metal-insulator transition takes place with decreasing x. It is conjectured that in sintered powders the resistance is due to amorphous contacts between grains, leading to a resistivity proportional to $\text{A}\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$.     

Spherical coordinate representations of solvent composition for liquid chromatography method development using experimental design

One of the major techniques used for the method development of ternary and quaternary high performance liquid chromatography (HPLC) systems has been to use mixture designs, often referred to as "Glajch's Triangle". This technique does not allow for the systematic and simultaneous optimization of other factors such as gradient time, pH and temperature that affect the quality of separations. An alternative approach is to use experimental designs. The condition, however, that the composition of all components of the mobile phase must total 100% presents a problem when trying to mathematically represent ranges of each mobile phase constituent of a ternary or quaternary system. A method is described here, based on spherical coordinate representations, that adheres to the constraints of the mobile phase composition and allows experimental designs, such as central composite and factorial designs, to be applied to the simultaneous optimization of the mobile phase composition. Other factors, in particular temperature and gradient time, can then be included in the design. As a result of applying these designs to the HPLC separation of phenols and corticosteroids, it was found necessary to include three-way interactions between experimental factors in the model. The significance of these interactions shows that they need to be considered in HPLC method development.     

The nonaqueous,potentiometric titration of free hydrochloric acid in chloride-containing polymers

The thermal and/or catalytic degradation of chloride-containing polymers causes dehydrohalogenation which produces hydrochloric acid. A nonaqueous method has been developed for the termination of hydrochloric acid. The sample is dissolved in tetrahydrofuran and titrated potentiometrically with a standard tetrabutylammonium hydroxide solution in a 7.5% (V/V) aqueous tetrahydrofuran solution with a combination glass-calomel electrode. The method has a relative precision of ±3.7% at the 95% confidence limit and a sensitivity of 25 ppm HCI.     

Effect of subsurface oxygen on the reactivity of the Ag(111) surface

Periodic, self-consistent, density functional theory calculations have been performed to demonstrate that subsurface oxygen (O(sb)) dramatically increases the reactivity of the Ag(111) surface. O(sb) greatly facilitates the dissociation of H2, O2, and NO and enhances the binding of H, C, N, O, O2, CO, NO, C2H2, and C2H4 on the Ag(111) surface. This effect originates from an O(sb)-induced upshift of the d-band center of the Ag surface and becomes more pronounced at higher O(sb) coverage. Our findings point to the important role that near-surface impurities, such as O(sb), can play in determining the thermochemistry and kinetics of elementary steps catalyzed by transition metal surfaces.     

<Emphasis Type="Italic">L</Emphasis>-Carnitine Supplementation: A New Paradigm for its Role in Exercise

Summary. Early research investigating the effects of L-carnitine supplementation has examined its role in substrate metabolism and in acute exercise performance. These studies have yielded equivocal findings, partially due to difficulties in increasing muscle carnitine concentrations. However, recent studies have proposed that L-carnitine may play a different role in exercise physiology, and preliminary results have been encouraging. Current investigations have theorized that L-carnitine supplementation facilitates exercise recovery. Proposed mechanism is as follows: 1) increased serum carnitine concentration enhances capillary endothelial function; 2) increased blood flow and reduced hypoxia mitigate the cascade of ensuing, destructive chemical events following exercise; 3) thus allowing reduced structural damage of skeletal muscle mediated by more intact receptors in muscle needed for improved protein signaling. This paradigm explains decreased markers of purine catabolism, free radical formation, and muscle tissue disruption after resistance exercise and the increased repair of muscle proteins following long-term L-carnitine supplementation.