A synthetic route to thionolactones

The treatment of O-alkyllactonium tetrafluoroborate salts with anh. NaSH in CH₃CN at 0°C led to five-, six-, and seven-membered thionolactones (44– 90% yield).     

A degenerate elliptic-parabolic system arising in competitive contaminant transport

The objective of this work is to study a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that this system admits a unique weak solution provided the nonlinear adsorption isotherm associated with the reaction process satisfies certain physically reasonable structural conditions, by addressing a more general problem. In addition, we conclude, that the solute concentrations stay non-negative if the source term is componentwise non-negative and investigate numerically the finite speed of propagation of compactly supported initial concentrations, in a two-component test case.     

Imaging spin-reorientation transitions in consecutive atomic Co layers on Ru(0001)

By means of spin-polarized low-energy electron microscopy, we show that the magnetic easy axis of one to three atomic-layer thick cobalt films on Ru(0001) changes its orientation twice during deposition: One-monolayer and three-monolayer thick films are magnetized in plane, while two-monolayer films are magnetized out of plane. The Curie temperatures of films thicker than one monolayer are well above room temperature. Fully relativistic calculations based on the screened Korringa-Kohn-Rostoker method demonstrate that only for two-monolayer cobalt films does the interplay between strain, surface, and interface effects lead to perpendicular magnetization.     

American option pricing under stochastic volatility: an efficient numerical approach

This paper develops a new numerical technique to price an American option written upon an underlying asset that follows a bivariate diffusion process. The technique presented here exploits the supermartingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte–Carlo algorithm (LSM) of Longstaff and Schwartz (Rev Financ Stud 14:113–147, 2001). Our approach also has the advantage of avoiding two main issues associated with LSM, namely its inherent bias and the basis functions selection problem. Extensive numerical results show that our approach yields very accurate prices in a computationally efficient manner. Finally, the flexibility of our method allows for its extension to a much larger class of optimal stopping problems than addressed in this paper.     

The Kabachnik–Fields and Pudovik Reactions on the Basis of E,Z‐Citral and Its Imines and (R,S)‐Citronellal

The Kabachnik–Fields reaction of E,Z‐citral with diethyl phosphite in the presence of isobutylamine has been found to form α‐aminophosphonates. The Pudovik reactions of diethyl phosphite with prenyl imines prepared on the basis of E,Z‐citral with isobutylamine also allowed us to obtain the same α‐aminophosphonates. We have managed to synthesize α‐aminophosphonates by the reaction of O,O‐dialkyl trimethylsilyl phosphites with prenyl imines in the presence of water or diethylamine. α‐Aminophosphonates were also synthesized by the reaction of diethyl phosphite with (R,S)‐citronellal in the presence of alkylamines. α‐Aminophosphonates obtained showed bacteriostatic activity against Staphylococcus aureus and Bacillus cereus. © 2012 Wiley Periodicals, Inc. Heteroatom Chem 24:36–42, 2013; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.21060     

Role of ion energy flux on the structural and morphological properties of silicon oxy-nitride composite films deposited by plasma focus device

ABSTRACT

Crystalline silicon oxy-nitride (SiON) composite films are deposited on Si substrate for multiple (5, 15, 25 and 50) focus shots (FS) by plasma focus device. The X-rays diffraction patterns reveal the development of various diffraction peaks related to Si, Si₃N₄, and SiO₂ phases which confirms the formation of SiON composite film. The intensity of Si₃N₄ (1 0 2) plane is linearly increased with the increase of FS. The Si₃N₄ (1 0 2) phase does not nucleate for 5 FS. Raman analysis confirms the formation of β–Si–N phase. Raman and Fourier transform infrared spectroscopy analysis reveals that the strength of chemical bonds like Si–N, Si–O formed during the deposition process of SiON composite films is associated with the bonds intensity which in turn depends on the number of FS. The field emission scanning electron microscopic analysis reveals that the surface morphology like size, shape and distribution of micro/nano-dimensional particles, film compactness and the formation of micro-rods, micro-teethes and micro-tubes of SiON composite films is entirely associated with the rise in substrate surface transient temperature which in turn depends on the increasing number of FS. The EDX spectrum confirms the presence of Si (22.5?±?4.7 at. %), N (13.4?±?4.5 at. %) and O (54.7?±?11.3 at. %) in the SiON composite film. The thickness of SiON composite film deposited for 50 FS is found to ～15.47?µm.     

Shape-Constrained Estimation Using Nonnegative Splines

We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.     

Zero-Divisor Graphs for Group Rings

Let R be a commutative ring with 1 ≠ 0, G be a nontrivial finite group, and let Z(R) be the set of zero divisors of R. The zero-divisor graph of R is defined as the graph Γ(R) whose vertex set is Z(R)* = Z(R)?{0} and two distinct vertices a and b are adjacent if and only if ab = 0. In this paper, we investigate the interplay between the ring-theoretic properties of group rings RG and the graph-theoretic properties of Γ(RG). We characterize finite commutative group rings RG for which either diam(Γ(RG)) ≤2 or gr(Γ(RG)) ≥4. Also, we investigate the isomorphism problem for zero-divisor graphs of group rings. First, we show that the rank and the cardinality of a finite abelian p-group are determined by the zero-divisor graph of its modular group ring. With the notion of zero-divisor graphs extended to noncommutative rings, it is also shown that two finite semisimple group rings are isomorphic if and only if their zero-divisor graphs are isomorphic. Finally, we show that finite noncommutative reversible group rings are determined by their zero-divisor graphs.