Multicomponent Molecular Orbital–Climbing Image–Nudged Elastic Band Method to Analyze Chemical Reactions Including Nuclear Quantum Effect

To analyze the H/D isotope effects on hydrogen transfer reactions in XHCHCHCHY?XCHCHCHYH (X, Y=O, NH, or CH₂) including the nuclear quantum effect of proton and deuteron, we propose a multicomponent molecular orbital‐climbing image‐nudged elastic band (MC_MO–CI–NEB) method. We obtain not only transition state structures but also minimum‐energy paths (MEPs) on the MC_MO effective potential energy surface by using MC_MO–CI–NEB method. We find that nuclear quantum effect affects not only stationary‐point geometries but also MEPs and electronic structures in the reactions. We clearly demonstrate the importance of including nuclear quantum effects for H/D isotope effect on rate constants (k_H/k_D).     

Duality Theorems for Separable Convex Programming Without Qualifications

In the research of mathematical programming, duality theorems are essential and important elements. Recently, Lagrange duality theorems for separable convex programming have been studied. Tseng proves that there is no duality gap in Lagrange duality for separable convex programming without any qualifications. In other words, although the infimum value of the primal problem equals to the supremum value of the Lagrange dual problem, Lagrange multiplier does not always exist. Jeyakumar and Li prove that Lagrange multiplier always exists without any qualifications for separable sublinear programming. Furthermore, Jeyakumar and Li introduce a necessary and sufficient constraint qualification for Lagrange duality theorem for separable convex programming. However, separable convex constraints do not always satisfy the constraint qualification, that is, Lagrange duality does not always hold for separable convex programming. In this paper, we study duality theorems for separable convex programming without any qualifications. We show that a separable convex inequality system always satisfies the closed cone constraint qualification for quasiconvex programming and investigate a Lagrange-type duality theorem for separable convex programming. In addition, we introduce a duality theorem and a necessary and sufficient optimality condition for a separable convex programming problem, whose constraints do not satisfy the Slater condition.     

Power and reversal power links for binary regressions: An application for motor insurance policyholders

In binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented. A Bayesian inference approach using MCMC is developed for the presented models. The methodology is illustrated considering a sample of motor insurance policyholders selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

The weakest contractive conditions for Edelstein’s mappings to have a fixed point in complete metric spaces

In this paper, we give the answer to the following problem: Let (X, d) be a complete metric space and let T be a mapping on X satisfying \(d(Tx, Ty) < d(x, y)\) for any \(x, y \in X\) with \(x \ne y\). Then what are the weakest additional assumptions to imply the same conclusion as in the Banach contraction principle?     

One-Step Synthesis of Cyclobutene-Annulated Fullerenes through a Cascade Reaction

The physicochemical properties of fullerene-based materials typically vary depending on the type and mode of addition of functional groups; therefore, developing fullerene derivatives with novel structures is imperative for further progress in materials science. In this study, we develop an efficient one-step strategy for synthesizing cyclobutene-annulated fullerene derivatives (cyclobutenofullerenes) and characterize their electronic properties. Despite the steric strain, cyclobutenofullerenes can be easily prepared via a one-step reaction of C₆₀ with a secondary propargylic phosphate. Structural analysis of the reaction intermediates suggests that the cascade reaction proceeds through a formal [2+2] cycloaddition of C₆₀ with an allene, caused by the 1,3-migration of the propargylic phosphate, followed by an additional 1,3-migration and the subsequent 1,2-elimination of the phosphodiester moiety.     

Study on transport of molecules in gel by surface-enhanced Raman spectroscopy

Cellulose - Surface-enhanced Raman spectroscopy (SERS)-based biosensors have recently been extensively developed because of their high sensitivity and nondestructive nature. Conventional SERS...