Representation of cyclotomic fields and their subfields

Let $\mathbb{K}$ be a finite extension of a characteristic zero field $\mathbb{F}$ . We say that a pair of n × n matrices (A,B) over $\mathbb{F}$ represents $\mathbb{K}$ if $\mathbb{K} \cong {{\mathbb{F}\left[ A \right]} \mathord{\left/ {\vphantom {{\mathbb{F}\left[ A \right]} {\left\langle B \right\rangle }}} \right. \kern-0em} {\left\langle B \right\rangle }}$ , where $\mathbb{F}\left[ A \right]$ denotes the subalgebra of $\mathbb{M}_n \left( \mathbb{F} \right)$ containing A and 〈B〉 is an ideal in $\mathbb{F}\left[ A \right]$ , generated by B. In particular, A is said to represent the field $\mathbb{K}$ if there exists an irreducible polynomial $q\left( x \right) \in \mathbb{F}\left[ x \right]$ which divides the minimal polynomial of A and $\mathbb{K} \cong {{\mathbb{F}\left[ A \right]} \mathord{\left/ {\vphantom {{\mathbb{F}\left[ A \right]} {\left\langle {q\left( A \right)} \right\rangle }}} \right. \kern-0em} {\left\langle {q\left( A \right)} \right\rangle }}$ . In this paper, we identify the smallest order circulant matrix representation for any subfield of a cyclotomic field. Furthermore, if p is a prime and $\mathbb{K}$ is a subfield of the p-th cyclotomic field, then we obtain a zero-one circulant matrix A of size p × p such that (A, J) represents $\mathbb{K}$ , where J is the matrix with all entries 1. In case, the integer n has at most two distinct prime factors, we find the smallest order 0, 1-companion matrix that represents the n-th cyclotomic field. We also find bounds on the size of such companion matrices when n has more than two prime factors.     

Oxidative addition of phenyl bromide to Pd(BINAP) vs Pd(BINAP)(amine). Evidence for addition to Pd(BINAP)

[STRUCTURE: SEE TEXT] The rates of oxidative addition of phenyl bromide to [Pd(BINAP)2] have been measured in the presence and absence of added amine to assess a previous hypothesis that addition to [Pd(BINAP)(amine)] is faster than addition to [Pd(BINAP)]. These data show that addition to the amine complex is not faster than addition to [Pd(BINAP)]. Instead, they are consistent with oxidative addition, even in the presence of amine, to [Pd(BINAP)] as the major pathway. These data underscore the value of studying the stoichiometric reactions of isolated complexes when assessing the mechanism of a catalytic process.     

Structure of certain level 2 standard modules for $$A_5^{(2)}$$ and the Göllnitz–Gordon identities

We employ the technique of Lepowsky–Wilson Z-algebras to analyze the structure of certain level 2 standard modules for the affine Lie algebra \(A_5^{(2)}\) that are contained in the tensor product of two inequivalent level 1 standard modules for \(A_5^{(2)}\). As a corollary, we obtain a vertex-operator-theoretic interpretation of the Göllnitz–Gordon identities.     

DNA and RNA binding studies on a novel bromo-bridged dimeric copper(II) complex stabilized from a Schiff base ligand

Abstract

A novel red copper(II) compound, bis(μ-bromo)bis(2-(benzothiazol-2-yl-hydrazono)-1,2-diphenyl-ethanone)-dicopper(II) (1), has been fostered by equimolar reaction of a Schiff-base ligand, 2-(benzothiazol-2-yl-hydrazono)-1,2-diphenyl-ethanone (LH), with copper(II) bromide in satisfactory yield. 1 has thoroughly been characterized by C, H and N elemental analyses, FT-IR and UV-vis (both in solid state and in solution) spectroscopies, and room-temperature magnetic susceptibility and conductivity measurements. Dimeric 1 bears symmetric rare bromo-bridges in its crystal structure. 1 retains its solid-state identity even in a protic solvent like methanol. 1 in methanol displays two-step one-electron redox response. Theoretical calculations based on DFT were executed to probe the electronic structure of 1 and to augment its color. DNA- and RNA-binding aspects of both LH and 1 have been explored. Thermodynamic binding parameters have been determined. LH is a major-groove binder to DNA, while 1 manifests itself as a minor-groove binder. This binding has been corroborated through molecular docking. Nucleic acid binding aspect of such type of rare bromo-bridged red copper(II) dimer is unprecedented.     

Gold-Catalyzed 1,2-Dicarbofunctionalization of Alkynes with Organohalides**

Herein, we report the first gold-catalyzed 1,2-dicarbofunctionalization of alkynes using organohalides as non-prefunctionalized coupling partners. The mechanism of the reaction involves an oxidative addition/π-activation mechanism in contrast to the migratory insertion/cis-trans isomerization pathway that is predominantly observed with other transition metals yielding products with anti-selectivity. Mechanistic insights include several control experiments, NMR studies, HR-MSMS analyses, and DFT calculations that strongly support the proposed mechanism.     

Vapor Phase Synthesis of SnS Facilitated by Ligand-Driven “Launch Vehicle” Effect in Tin Precursors

Extraordinary low-temperature vapor-phase synthesis of SnS thin films from single molecular precursors is attractive over conventional high-temperature solid-state methods. Molecular-level processing of functional materials is accompanied by several intrinsic advantages such as precise control over stoichiometry, phase selective synthesis, and uniform substrate coverage. We report here on the synthesis of a new heteroleptic molecular precursor containing (i) a thiolate ligand forming a direct Sn-S bond, and (ii) a chelating O^N^N-donor ligand introducing a “launch vehicle”-effect into the synthesized compound, thus remarkably increasing its volatility. The newly synthesized tin compound [Sn(SBu^t)(tfb-dmeda)] 1 was characterized by single-crystal X-ray diffraction analysis that verified the desired Sn:S ratio in the molecule, which was demonstrated in the direct conversion of the molecular complex into SnS thin films. The multi-nuclei (¹H, ¹³C, ¹⁹F, and ¹¹⁹Sn) and variable-temperature 1D and 2D NMR studies indicate retention of the overall solid-state structure of 1 in the solution and suggest the presence of a dynamic conformational equilibrium. The fragmentation behavior of 1 was analyzed by mass spectrometry and compared with those of homoleptic tin tertiary butyl thiolates [Sn(SBu^t)₂] and [Sn(SBu^t)₄]. The precursor 1 was then used to deposit SnS thin films on different substrates (FTO, Mo-coated soda-lime glass) by CVD and film growth rates at different temperatures (300–450 °C) and times (15–60 min), film thickness, crystalline quality, and surface morphology were investigated.     

An anhydrous precursor approach to BaYF5-based upconverting nanocrystals

With an objective to have easy access to high quality BaYF₅ matrix, we report here new anhydrous precursors of barium and yttrium which show a good compatibility in terms of co-thermal decomposition. These complexes not only fill the void of precursors for Ba-based upconverting (UC) nanomaterials but also provide a way to minimize the –OH concentration around these nanocrystals (NCs) to enhance their UC efficiency without requiring the usual core-shell structure. The precursors and the BaYF₅ NCs co-doped with Yb³⁺/Tm³⁺ ions were thoroughly characterized. The NCs were studied for upconversion properties and preliminary results are presented here. On the basis of these results, a mechanism for the energy transfer in Yb–Tm system is proposed.     

Synthesis of 14-deoxy-benzylidene-8,17-epoxy-diene-andrographolide derivatives and evaluation of their anticancer activities

Synthesis of 14-deoxy-benzylidene-8,17-epoxy-diene-andrographolide derivatives from andrographolide and evaluation of their anticancer activities were described herein. 3,19 hydroxy groups of andrographolide were protected by benzylidene which undergo m-chloroperbenzoic acid mediated epoxydation in moderate yield to form corresponding epoxy derivatives. Thereafter mild basic condition was applied to perform de-hydroxylation at C-14 which resulted in conjugated diene derivatives of benzylidene epoxy andrographolide. These compounds were examined against different human cancer cell lines and were found to inhibit their proliferation at IC₅₀ in the range of 3–20 μM in order to elucidated the role of allylic hydroxyl group at C-14.     

Organo-sulfonic acid catalyzed degradation kinetics and thermodynamic studies of nylon-6 by hydrothermal method

Nylon-6 as an engineering polymer and its starting monomer are both costly. Chemical reutilization offers some economic and environmental benefits. Depolymerization of nylon-6 was carried out by the conventional technique of hydrothermal method using various organo-sulfonic acids such as Methane sulfonic acid (MSA), para-toluene sulfonic acid (p-TSA), benzene sulfonic acid (BSA), and tetra-butyl ammonium bromide (TBAB) as a phase transfer catalyst. Various parameters such as temperature, time, normality of acids, and phase transfer catalyst concentration were varied to optimize its parameters, and characterization techniques such as amine value titrations and Fourier transform infrared spectroscopy were used for quantitative measurements. Solid-state ¹³C NMR was done for structure confirmation. A chemical kinetics interpretation shows degradation mechanism follows first-order kinetics under various catalysts. MSA has the highest reaction rate of 8.49 × 10^?2 h^?1 at 90°C; it decreases to 7.72 × 10^?2 h^?1 at 100°C. At the same time, aromatic Sulfonic acids such as p-TSA and BSA have a higher reaction rate of 8.995 × 10^?2 h^?1 and 5.582 × 10^?2 h^?1, respectively. The activation energy was lowered as the acidity of organo-sulfonic acids increased as benzene sulfonic acid has the lowest E_a. Followed by p-TSA, and MSA has the highest E_a. Free energy shows a similar kind of value. A simple theoretical model was used to calculate the activation energy. Thermodynamic parameters such as heat of enthalpy and entropy of reaction were evaluated using the Eryig–Polanyi equation. The combined catalytic effect of organo-sulfonic acids and phase-transfer catalyst provides a better environment-friendly method for depolymerizing nylon-6.