Microwave assisted oxidation of some aromatics by hydrogen peroxide at supported tungsten catalyst

Summary The oxidation of some arenes with the alkyl side groups by means of hydrogen peroxide is been presented. As the activator of hydrogen peroxide tungstoboric acid was chosen. The catalyst was examined under both homogeneous and heterogeneous conditions. The reactions under conventional conditions were compared with the microwave assisted reactions.     

Polypropylene/Poly (Trimethylene Terephthalate)–Blend Fibers

Polypropylene (PP)/polyester (PES)–blend fibers were prepared by extruder melt spinning. The polymer blend consisted of PP and a “master batch” (MB) based on polytrimethylene terephthalate (PTT) or polyethylene terephthalate (PET), binary PTT/PET or PP/PTT blends, and also on a ternary PP/(PTT/PET) blend. The phase structure of PP/PES–blend fibers was examined. PES microfibers showed separation from the PP matrix in blend fibers. The impact of MB composition and rheological characteristics on phase structure parameters indicate a significant contribution of the PTT in the binary MB on the length of dispersed PES microfibers in the PP matrix. However, the blends of PP and ternary MB (PP/PTT/PET) have a lower diameter and length of the PES microfibers. The presence of PTT/PET (PES) enhances the structural and mechanical properties of the blend PP/PES fibers. In addition, PTT increases the tensile strength of the PP/PES–blend fibers if a binary MB is used, while the fiber nonuniformity is reduced in the presence of a ternary MB.     

Multivariate Hörmander-Type Multiplier Theorem for the Hankel transform

Let $\mathcal{H}(f)(x)=\int_{(0,\infty)^{d}} f(\lambda) E_{x}(\lambda) d\nu(\lambda )$ , be the multivariate Hankel transform, where $E_{x}(\lambda)=\prod_{k=1}^{d} (x_{k} \lambda_{k})^{-\alpha _{k}+1/2}J_{\alpha_{k}-1/2}(x_{k} \lambda_{k})$ , with dν(λ)=λ ^2α dλ, α=(α ₁,…,α _d ). We give sufficient conditions on a bounded function m(λ) which guarantee that the operator $\mathcal{H}(m\mathcal{H} f)$ is bounded on L ^p (dν) and of weak-type (1,1), or bounded on the Hardy space H ¹((0,∞) ^d ,dν) in the sense of Coifman-Weiss.     

Structure and stability of online chat networks built on emotion-carrying links

High-resolution data of online chats are studied as a physical system in the laboratory in order to quantify collective behavior of users. Our analysis reveals strong regularities characteristic of natural systems with additional features. In particular, we find self-organized dynamics with long-range correlations in user actions and persistent associations among users that have the properties of a social network. Furthermore, the evolution of the graph and its architecture with specific k$k$-core structure are shown to be related with the type and the emotion arousal of exchanged messages. Partitioning of the graph by deletion of the links which carry high arousal messages exhibits critical fluctuations at the percolation threshold.     

On the Ratio Between 2-Domination and Total Outer-Independent Domination Numbers of Trees

A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D.A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D,and the set V(G)\D is independent.The 2-domination(total outer-independent domination,respectively)number of a graph G is the minimum cardinality of a 2-dominating(total outer-independent dominating,respectively)set of G.We investigate the ratio between2-domination and total outer-independent domination numbers of trees.     

NMR frequency and magnetic dipole moment of (3)He nucleus

We present new gas-phase NMR spectra which relate the resonance frequency of (3)He nucleus to the resonance frequency of the proton in tetramethylsilane (TMS). We discuss the dependence of (3)He resonance frequency on the density of the solvent gas, and we consider in detail the absolute shielding scales of both nuclei. Finally, we analyse the accuracy of the results, using the relationship between the resonance frequencies, absolute shielding constants and magnetic dipole moments of (1)H and (3)He nuclei.     

Stereocontrolled Synthesis of Chiral Heteroaromatic Propellers with Small Optical Bandgaps

Chiral heteroaromatic propellers based on radially π‐extended hexapyrrolohexaazacoronenes were obtained in a concise synthesis from suitably functionalized donor–acceptor monopyrroles. To overcome steric hindrance, a new cyclodehydrogenation method was developed, and it uses bromine electrophiles as oxidative coupling agents instead of the commonly employed high‐potential oxidants. The new reaction offers high yields of propeller‐shaped targets, even for electron‐deficient precursors, and shows electrophile‐dependent stereoselectivity, with N‐bromosuccinimide and dibromine yielding, respectively D₆‐ and C₂‐symmetric products. The propeller azacoronenes are chiral and can be separated into configurationally stable enantiomers. In addition to providing steric bulk, peripheral functionalization considerably affects the electronic properties of the propellers, which exhibit reduced optical and electrochemical band gaps, and a more clearly defined electroreduction behavior.