Self-Assembly of Alkylammonium Chains on Montmorillonite: Effect of Interlayer Cations,CEC, and Chain Length

Recently, polymeric materials have been filled with synthetic or natural inorganic compounds in order to improve their properties. Especially, polymer clay nanocomposites have attracted both academic and industrial attention. Currently, the structure and physical phenomena of organoclays at molecular level are difficultly explained by existing experimental techniques. In this work, molecular dynamics (MD) simulation was executed using the CLAYFF and CHARMM force fields to evaluate the structural properties of organoclay such as basal spacing, interlayer density, energy and the arrangement of alkyl chains in the interlayer spacing. Our results are in good agreement with available experimental or other simulation data. The effects of interlayer cations (Na⁺, K⁺, Ca²⁺), the cation exchange capacity, and the alkyl chain length on the basal spacing and the structural properties are estimated. These simulations are expected to presage the microstructure of organo-montmorillonite and lead relevant engineering applications.     

Ring-contraction from benzo[b][1,4]thiazines to benzo[d]thiazolines induced by oxygen

An unexpected ring-contraction from benzo[b]pyrazino[1,2-d][1,4]thiazine-1,4-diones (6) to benzo[4,5]thiazolo[3,2-a]pyrazine-1,4-diones (7) has been developed. The preliminary mechanistic studies showed the transformation contained two independent steps: the first step is the formation of a Michael adduct upon the addition of the protic solvent, in the presence of base, to the C-2-C-3 double bond of compound 6, and the second step is a ring-contraction induced by oxygen via the migration of sulfur atom from C-2 to C-3 position. And its scope is also studied.     

Refractive properties of imidazolium ionic liquids with alanine anion [C n mim][Ala] (n = 2, 3, 4, 5, 6)

Russian Journal of Physical Chemistry A - Imidazolium ionic liquids with alanine anion, [C n mim][Ala] (n = 2, 3, 4, 5, 6), were prepared and characterized. The standard addition method was used to...     

Synthesis of 2,3,6-trisubstituted pyridines by transition-metal free cyclization of 1,3-diynes with amino acids

Amino acids are firstly employed in transition-metal free heterocyclization reaction of 1,3-diynes in the presence of K₃PO₄ and DMSO at 120 °C. This method produces 2,3,6-trisubstituted pyridines with up to 86% yield. The –CO₂H group on the amino acids is crucial for this heterocyclization reaction. The mechanism of such a heterocyclization reaction is discussed, as well.     

Multiplicative Jordan Decomposition in Integral Group Ring of Group K_8×C_5

In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper "The multiplicative Jordan decomposition in group rings II.     

Estimated conditional score function for missing mechanism model with nonignorable nonresponse

Missing data mechanism often depends on the values of the responses, which leads to nonignorable nonresponses. In such a situation, inference based on approaches that ignore the missing data mechanism could not be valid. A crucial step is to model the nature of missingness. We specify a parametric model for missingness mechanism, and then propose a conditional score function approach for estimation. This approach imputes the score function by taking the conditional expectation of the score function for the missing data given the available information. Inference procedure is then followed by replacing unknown terms with the related nonparametric estimators based on the observed data. The proposed score function does not suffer from the non-identifiability problem, and the proposed estimator is shown to be consistent and asymptotically normal. We also construct a confidence region for the parameter of interest using empirical likelihood method. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. We apply the proposed method to a data set from research in a growth hormone and exercise intervention study.     

On the proof of Erdős’ inequality

Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality \({\left\| {p'} \right\|_{\left[ { - 1,1} \right]}} \leqslant \frac{1}{2}{\left\| p \right\|_{\left[ { - 1,1} \right]}}\) for a constrained polynomial p of degree at most n, initially claimed by P. Erd?s, which is different from the one in the paper of T.Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval (?1, 1) and establish a new asymptotically sharp inequality.     

Kontsevich–Zagier integrals for automorphic Green’s functions. II

We introduce interaction entropies, which can be represented as logarithmic couplings of certain cycles on a class of algebraic curves of arithmetic interest. In particular, via interaction entropies for Legendre–Ramanujan curves \( Y^n=(1-X)^{n-1}X(1-\alpha X)\) (\( n\in \{6,4,3,2\}\)), we reformulate the Kontsevich–Zagier integral representations of weight-4 automorphic Green’s functions \( G_2^{\mathfrak H/\overline{\varGamma }_0(N)}(z_1,z_2)\) (\(N=4\sin ^2(\pi /n )\in \{1,2,3,4\}\)), in a geometric context. These geometric entropies allow us to establish algebraic relations between certain weight-4 automorphic self-energies and special values of weight-6 automorphic Green’s functions.