Temperature dependence of structure and dynamics of the hydrated Ca2+ ion according to ab initio quantum mechanical charge field and classical molecular dynamics

Simulations using ab initio quantum mechanical charge field molecular dynamics (QMCF MD) and classical molecular dynamics using two‐body and three‐body potentials were performed to investigate the hydration of the Ca²⁺ ion at different temperatures. Results from the simulations demonstrate significant effects of temperature on solution dynamics and the corresponding composition and structure of hydrated Ca²⁺. Substantial increase in ligand exchange events was observed in going from 273.15 K to 368.15 K, resulting in a redistribution of coordination numbers to lower values. The effect of temperature is also visible in a red‐shift of the ion‐oxygen stretching frequencies, reflecting weakened ligand binding. Even the moderate increase from ambient to body temperature leads to significant changes in the properties of Ca²⁺ in aqueous environment. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Characterization of algebraic curves by Chebyshev quadrature

Complex potential theory is used to show that Chebyshev-type quadrature works particularly well on algebraic Jordan curves Γ in ℝ ^d , supplied with normalized arc length or a similar probability measure μ. Evaluating the integral ∫_Γ fdμ by the arithmetic mean of the value off on any cycle ofN equally spaced nodes on Γ (relative to μ), the quadrature error will, be bounded byAe ^−bN sup_Γ|f| for allN and all polynomialsf(x) of degree ≤cN. It is plausible that small shifts of the nodes would give quadrature error zero for such polynomials. There are related results for algebraic Jordan arcs and certain algebraic surfaces. The situation is completely different for nonalgebraic curves and surfaces, where corresponding quadrature remainders are at least of order 1/N.     

Dispersive estimates for the wave equation inside cylindrical convex domains: A model case

In this work, we will establish local in time dispersive estimates for solutions to the model-case Dirichlet wave equation inside a cylindrical convex domain $\mathrm{\Omega }?{\mathbb{R}}^3$ with a smooth boundary $?\mathrm{\Omega }\ne ?$. Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Nonoptimal Strichartz estimates for waves inside an arbitrary domain Ω have been proved by Blair–Smith–Sogge [1], [2]. Better estimates in strictly convex domains have been obtained in [4]. Our case of cylindrical domains is an extension of the result of [4] in the case where the curvature radius ≥0 depends on the incident angle and vanishes in some directions.     

XPS study of the oxidation of nanosize Ni/Si(100) films

The XPS (X-ray photoelectron spectroscopy) study of nickel oxide nanolayers obtained by magnetron sputtering of the metal and its subsequent oxidation in air at different temperatures (400°C and 1000°C) was performed. Silicon(100) was used as a substrate. Surface of the initial Ni/Si structure was shown to contain not only Ni metal, but also the NiO oxide. Annealing at 400°C results in a complete oxidation of the metal film. At a high-temperature annealing (1000°C), nickel interacts both with oxygen and silicon substrate to form NiSi silicide and a composite Ni-Si-O phase in transition layer. Electronconductivity of NiO films is determined by intercrystallite barriers. Activation energies of film electroconductivity in model gases (O₂, Ar, H₂) were found.     

On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes.     

App-based scaffolds for writing two-column proofs

This paper presents apps designed to assist students in understanding and developing proofs in geometric theorems. These technologies focus on triangle congruence, triangle similarity and properties of parallelograms. Focus group discussions and initial testing of the apps revealed that the apps offered a more engaging medium for learning proving and were capable of facilitating proof-writing skills in geometry.