Synthesis of oligo(spiroketal)s by polycondensation of silyl ethers derived from naturally occurring myo‐inositol with 1,4‐cyclohexanedione

Oligo(spiroketal)s (OSKs) were synthesized from myo‐inositol, a naturally occurring cyclic compound bearing six hydroxyl groups. The successful synthesis of OSKs was achieved using silyl ethers 2 derived from 1,4‐di‐O‐alkylated myo‐inositol 1 as monomers, which underwent polycondensation with 1,4‐cyclohexanedione (CHD) at 0 °C in the presence of trimethylsilyl triflate as a catalyst. Because of the irreversible nature of the condensation reaction of silyl ethers with ketones, the resulting OSKs 7 had higher molecular weights than previously reported OSKs that were obtained by polycondensation of tetraols 1 with CHD, where backward hydrolysis of the ketal functions occurred. In addition, another series of OSKs, 8, were synthesized using silyl ethers 3 derived from 2,5‐di‐O‐alkylated myo‐inositol 6 , which are more symmetric monomers than silyl ethers 2 . Silyl ethers 3 underwent efficient polycondensation with CHD, whereas tetraol 6 did not, demonstrating that the derivation of such tetraols into the corresponding silyl ethers is a powerful strategy to access OSKs. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2407–2414     

A fast iterative method to find the matrix geometric mean of two HPD matrices

The purpose of this research is to present a novel scheme based on a quick iterative scheme for calculating the matrix geometric mean of two Hermitian positive definite (HPD) matrices. To do this, an iterative scheme with global convergence is constructed for the sign function using a novel three‐step root‐solver. It is proved that the new scheme is convergent and shown to have global convergence behavior for this target, when square matrices having no pure imaginary eigenvalues. Next, the constructed scheme is used and extended through a well‐known identity for the calculation of the matrix geometric mean of two HPD matrices. Ultimately, several experiments are collected to show its usefulness.     

第二类端点奇异Fredholm积分方程的分数阶退化核方法

本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法，设计了两种计算格式，一是在全区间上使用分数阶Taylor展开式近似核函数，二是在包含奇点的小区间上采用分数阶插值，在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件，并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果，且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围.     

Maximizing the mean subtree order

This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our main goal is to describe the structure of optimal trees in and , the families of all trees and caterpillars, respectively, of order . We begin by establishing a powerful tool called the Gluing Lemma, which is used to prove several of our main results. In particular, we show that if is an optimal tree in or for , then every leaf of is adjacent to a vertex of degree at least . We also use the Gluing Lemma to answer an open question of Jamison and to provide a conceptually simple proof of Jamison's result that the path has minimum mean subtree order among all trees of order . We prove that if is optimal in , then the number of leaves in is and that if is optimal in , then the number of leaves in is . Along the way, we describe the asymptotic structure of optimal trees in several narrower families of trees.     

Study of degradation behavior of besifloxacin,characterization of its degradation products by LC–ESI–QTOF–MS and their in silico toxicity prediction

Knowledge and understanding of the stability profile of a drug is important as it affects its safety and efficacy. In the present work, besifloxacin, a new, fourth‐generation fluoroquinolone antibiotic, was subjected to different forced‐degradation conditions as per International Conference on Harmonization (ICH) guidelines such as hydrolysis (acid, base and neutral), oxidation, thermal and photolysis. The drug degraded under acidic, basic, oxidative and photolytic conditions while it was found to be stable under dry heat and neutral hydrolytic conditions. In total, five degradation products (DPs) were formed under different conditions—DP1 and DP2 (photolysis), DP3 (oxidation), DP4 (acidic), DP3 and DP5 (basic). The chromatographic separation of besifloxacin and its degradation products was achieved on a Sunfire C₁₈ (250 mm × 4.6 mm, 5 μm) column with 0.1% aqueous formic acid–acetonitrile as a mobile phase. The gradient RP‐HPLC method was developed and validated as per ICH guidelines. The degradation products were characterized with the help of LC–ESI–QTOF mass spectrometric studies and the most likely degradation pathway of the drug was proposed. In silico toxicity assessment of the drug and its degradation products was carried out, which indicated that DP3 and DP4 carry a mutagenicity alert.