Policy Sciences.

Journal of the Operational Research Society -     

Dinuclear Zn(II) catalysts as biomimics of RNA and DNA phosphoryl transfer enzymes: changing the medium from water to alcohol provides enzyme‐like rate enhancements

Phosphodiesters are notoriously hydrolytically inert compounds that are demonstrated to have large accelerations of P‐OR cleavage promoted by transition and lanthanide metal ions in methanol and ethanol media. This review commentary describes recent findings of how a simple mononuclear and a dinuclear Zn(II) complex promote the cleavage of a series of RNA models and DNA models in alcohol media. The discussion centers on the analysis of the mechanisms of cleavage, energetics of the catalytic process, on recent findings of electrophilic assistance of leaving group departure, and the observation of a rapid hydrolytic reaction of a DNA model promoted by the dinuclear Zn(II) complex in ethanol containing less than 2% water. Copyright © 2009 John Wiley & Sons, Ltd.     

Periodic orbits and unstable manifolds for ordinary differential equations

Consider the unstable manifold of a hyperbolic periodic orbit of an ordinary differential equation under C¹ perturbations of the vector field and under approximation by a one-step numerical method, which is at least first order. Trajectories bounded backwards in time near the periodic orbit perturb Hausdorff continuously. This result as applied to numerical perturbations improves on Alouges-Debussche [1], who give only continuity of the unstable maniford, and on Beyn [3], who gives continuity of trajectories only when the periodic orbit is unstable. As a corollary, we find that attractors perturb Hausdorff continuously when the attractor equals a union of locally continuous unstable manifolds of invariant sets     

Genus Two Curves with Many Elliptic Subcovers

We determine all genus 2 curves, defined over ?, which have simultaneously degree 2 and 3 elliptic subcovers. The locus of such curves has three irreducible 1-dimensional genus zero components in ?₂. For each component, we find a rational parametrization and construct the equation of the corresponding genus 2 curve and its elliptic subcovers in terms of the parameterization. Such families of genus 2 curves are determined for the first time. Furthermore, we prove that there are only finitely many genus 2 curves (up to ?-isomorphism) defined over ?, which have degree 2 and 3 elliptic subcovers also defined over ?.     

The Milstein Scheme for Stochastic Delay Differential Equations Without Using Anticipative Calculus

The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delay differential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This article employs an elementary method to derive the Milstein scheme and its first order strong rate of convergence for stochastic delay differential equations.     

Facile growth of monolayer MoS<Subscript>2</Subscript> film areas on SiO<Subscript>2</Subscript>

Areas of single-layer MoS₂ film can be prepared in a tube furnace without the need for temperature control. The films were characterized by means of Raman spectroscopy, photoluminescence, low-energy electron diffraction and microscopy, and X-ray photoelectron spectroscopy and mapping. Transport measurements show n-doped material with a mobility of 0.26 cm² V^-1 s^-1.     

Optimal rates of convergence for estimating Toeplitz covariance matrices

Toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging, target detection, speech recognition, and communications systems. In this paper, we consider optimal estimation of large Toeplitz covariance matrices and establish the minimax rate of convergence for two commonly used parameter spaces under the spectral norm. The properties of the tapering and banding estimators are studied in detail and are used to obtain the minimax upper bound. The results also reveal a fundamental difference between the tapering and banding estimators over certain parameter spaces. The minimax lower bound is derived through a novel construction of a more informative experiment for which the minimax lower bound is obtained through an equivalent Gaussian scale model and through a careful selection of a finite collection of least favorable parameters. In addition, optimal rate of convergence for estimating the inverse of a Toeplitz covariance matrix is also established.