Second-order perturbational treatment of normal coordinates in the string model for the hydration reaction of formaldehyde

A perturbation theory for normal coordinates of nonadiabatic solvation is presented by means of the “string model” of chemical reactions. The dynamic normal coordinate is introduced for the perturbational treatment of the “intrinsic” normal coordinates that are orthogonal to the reaction path. The reaction is defined as the intrinsic reaction coordinate (IRC ) that is treated as a string. The string is thrown in the external force field that acts as a nonadiabatic source of perturbation. As an application of the present treatment, the effect of a water molecule for hydration reaction of formaldehyde is calculated. A second-order perturbation effect for the enhancement of the reaction rate is found.     

Catalytic Alkynylation of Polyfluoroarenes by Amide Base Generated In Situ

We herein demonstrate that the amide base generated in situ from CsF and N(TMS)₃ catalyzes the deprotonative coupling reactions of terminal alkynes with polyfluoroarenes, wherein mono- and dialkynylations occur efficiently for penta- and hexafluorobenzenes, respectively. Tetraalkynylated products could also be synthesized from dialkynylated compounds.     

Molecular orientation of azobenzene chromophores in ultrathin polymer nanosheets studied by attenuated total reflection spectroscopy

This paper describes characterization of molecular orientation for azobenzene moieties in a polymer nanosheet. Copolymers of N-[4-(phenylazo)phenyl] acrylamide (PAZoA) with tert-pentyl acrylamide (tPA) were synthesized and the monolayers deposited on tapered quartz waveguides by Langmuir–Blodgett (LB) technique. Spectroscopic properties of the copolymer (p(tPA/PAZoA)) monolayers were monitored by integrated optical waveguide technique on the molecular level. Molecular orientation of the azobenzene was precisely determined by polarized absorption spectra. It was found that the azobenzene groups took a horizontal orientation and distributed uniformly in the p(tPA/PAZoA) monolayer without significant PAZoA aggregation. Photoisomerization process from trans to cis form was also investigated. More than half of the trans form (60–70%) was photoisomerized under unpolarized light irradiation, and the photoisomerization rate was independent on the PAZoA contents. This implies that the microenvironment of PAZoA moieties was almost the same in three different p(tPA/PAZoA) monolayers.     

Phosphine‐Catalyzed anti‐Carboboration of Alkynoates with 9‐BBN‐Based 1,1‐Diborylalkanes: Synthesis and Use of Multisubstituted γ‐Borylallylboranes

Trialkylphosphine organocatalysis has enabled the regioselective anti‐carboboration of alkynoates with 9‐BBN‐based 1,1‐diborylalkanes to produce secondary allylboranes with β‐alkoxycarbonyl and γ‐boryl substituents. The utility of the densely functionalized allylboranes was demonstrated by the highly diastereoselective allylation of N‐(trimethylsilyl)aldimines to produce homoallylamines containing tertiary allylborane and acrylate moieties.     

Palladium-catalyzed allylic oxidation of olefins by t-butyl hydroperoxide and tellurium(IV) oxide

Treatment of several cyclic olefins, β-pinene, allylbenzene, and estragole with palladium(II) salt in acetic acid in the presence of t-butyl hydroperoxide and tellurium(IV) oxide afforded mainly the corresponding allylic acetates. The reaction proceeded catalytically with palladium(II) salt, t-BuOOH working as a reoxidizing agent.     

Long cycles passing through a specified edge in a 3-connected graph

We prove the following theorem: For a connected noncomplete graph G, let τ(G): = min{d_G(u) + d_G(v)|d_G(u, v) = 2}. Suppose G is a 3-connected noncomplete graph. Then through each edge of G there passes a cycle of length ≥ min{|V(G)|, τ (G) − 1}. © 1997 John Wiley & Sons, Inc.     

Connected subgraphs with small degree sums in 3‐connected planar graphs

It is well‐known that every planar graph has a vertex of degree at most five. Kotzig proved that every 3‐connected planar graph has an edge xy such that deg(x) + deg (y) ≤ 13. In this article, considering a similar problem for the case of three or more vertices that induce a connected subgraph, we show that, for a given positive integer t, every 3‐connected planar graph G with |V(G)| ≥ t has a connected subgraph H of order t such that Σ_x∈V(H) deg_G(x) ≤ 8t − 1. As a tool for proving this result, we consider decompositions of 3‐connected planar graphs into connected subgraphs of order at least t and at most 2t − 1. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 191–203, 1999     

Statistics of reaction progress variable and mixture fraction gradients of a pulverised coal jet flame using Direct Numerical Simulation data

The statistical behaviour of the variances, covariance and gradients of the reaction progress variable (c), and the mixture fraction (ξ) have been analysed in a pulverised coal jet flame using a three-dimensional carrier phase direct numerical simulation (DNS) dataset. It has been observed that the Favre-probability density functions (PDFs) of c and ξ can be parametrised by the standard β function. Furthermore, the log-normal distribution has been found to accurately represent |?c| and |?ξ|. It is also found that ?c and ?ξ remain aligned throughout the flame brush. Finally the joint PDF of |?c| and |?ξ| has been compared with the product of the PDF of |?c| and PDF of |?ξ| extracted from carrier phase DNS, and it has been found that |?c| and |?ξ| are not statistically independent in the case investigated.The bivariate log-normal distributions with and without correlation have also been considered, and the former is found to be in better agreement with the carrier phase DNS data.     

On maximal weights of Hadamard matrices

Let $\text{Ω}{}_{\mathrm{n}}$ denote the set of all Hadamard matrices of order n. For $\text{H ? Ω}{}_{\mathrm{n}}$, define the weight of H to be the number of 1's in H and is denoted by w(H). For a subset $\text{Γ ? Ω}{}_{\mathrm{n}}$, define the maximal weight of Γ as w(Γ) = max{w(H) | H?Γ}. Two Hadamard matrices are equivalent if one of them can be transformed to the other by permutation and negation of rows and columns, and the equivalence class containing H is denoted by [H]. In this paper, we shall derive lower bounds for w([H]), which are best possible for n ? 20. We shall also determine the exact value of $\text{w(Ω}{}_{32}\text{)}$.