On molecular topological properties of hex‐derived networks

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure–activity relationship/quantitative structure–property relationship study, physico‐chemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study hex‐derived networks HDN1(n) and HDN2(n), which are generated by hexagonal network of dimension n and derive analytical closed results of general Randić index R_α(G) for different values of α, for these networks of dimension n. We also compute the general first Zagreb, ABC, GA, ABC₄, and GA₅ indices for these hex‐derived networks for the first time and give closed formulae of these degree‐based indices for hex‐derived networks. Copyright © 2016 John Wiley & Sons, Ltd.     

Quaternary Stereogenic Centers through Enantioselective Heck Arylation of Acyclic Olefins with Aryldiazonium Salts: Application in a Concise Synthesis of (R)‐Verapamil

We describe herein a highly regio‐ and enantioselective Pd‐catalyzed Heck arylation of unactivated trisubstituted acyclic olefins to provide all‐carbon quaternary stereogenic centers. Chiral N,N ligands of the pyrimidine‐ and pyrazino‐oxazoline class were developed for that purpose, providing the desired products in good to high yields with enantiomeric ratios up to >99:1. Both linear and branched substituents on the olefins were well‐tolerated. The potential of this new method is demonstrated by the straightforward synthesis of several O‐methyl lactols and lactones containing quaternary stereocenters, together with a concise enantioselective total synthesis of the calcium channel blocker verapamil.     

Catalytic Asymmetric Transfer Hydrogenation of Imines: Recent Advances

In this review article recent developments in the asymmetric transfer hydrogenation of imines from 2008 up to today are presented. The main methodology involves either metal‐catalyzed procedures in the presence of a chiral ligand or organocatalyzed technologies using a Hantzsch ester and a chiral BINOL‐derived phosphoric acid. The most important procedures are collected, paying special attention to the application of this methodology in synthetic organic chemistry.

     

Nano titania-supported sulfonic acid catalyzed synthesis of α,α′-bis(substituted-benzylidene)cycloalkanones and of their xanthene derivatives under solvent-free conditions

An efficient, rapid and green synthesis of α,α′-bis(substituted-benzylidene)cycloalkanones and their xanthene derivatives is reported under solvent-free conditions using nano titania-supported sulfonic acid (n-TSA) as a reusable catalyst. This method offers many advantages, such as environmental friendliness reaction conditions, simplicity, short reaction times, easy work-up, reusability of catalyst, and high yields of products. Eight new compounds are reported too.     

火试金-原子吸收光谱法测定锡阳极泥中金、银含量

锡阳极泥是锡冶炼过程中的一种中间产物,其中含有大量的金、银等贵金属。准确测定锡阳极泥中金、银含量有很重要的现实意义。采用火试金法能实现锡阳极泥中金、银含量的连续测定,方法准确度高,精密度好,金、银回收率在97.46%~101.66%,能很好地满足锡阳极泥中高品位金、银的测定。     

Surfactant-Free and Controlled Synthesis of Hexagonal CeVO4 Nanoplates: Photocatalytic Activity and Superhydrophobic Property

Nanomaterials with both superhydrophobic surface properties as well as photocatalytic activities could have important industrial applications. Herein, we synthesized CeVO₄ nanocrystals with hexagonal nanoplate structures from the reaction of decavanadate (K₆V₁₀O₂₈⋅9 H₂O) and CeCl₃⋅H₂O precursors via a hydrothermal method. This synthetic route has four advantages: 1) the reaction condition is relatively mild, 2) it doesn′t need surfactants or templates, 3) it requires no expensive equipment, and 4) products are of higher purity. During synthesis, solution pH, and reaction temperature were found to play important roles in determining the growth process and final morphologies of the CeVO₄ products. These products were characterized spectrophotometrically and via scanning and transmission electron microscopy. Furthermore, the wettability of the as-synthesized film CeVO₄ nanoplates was studied by measuring water contact angle (CA). The largest CA measured was at 169.5 ° for a glass substrate treated with 0.06 g mL⁻¹ CeVO₄ followed by 2 % 1 H, 1 H, 2 H, 2 H-perfluorodecyltriethoxysilane. Finally, the CeVO₄ nanoplates exhibited excellent photocatalytic activity in degradation of rhodamine B (RhB) under UV irradiation and was stable even after repeated cycles of use.     

Influence of Ag+ on the Magnetic Response of [2.2.2]Paracyclophane: NMR Properties of a Prototypical Organic Host for Cation Binding Based on DFT Calculations

The complexation of metal cations into a host–guest situation is particularly well exemplified by [2.2.2]paracyclophane and Ag^I, which leads to a strong cation–π interaction with a specific face of the host molecule. Through this study we sought a deeper understanding of the effects the metal center has on the NMR spectroscopic properties of the prototypical organic host, generating theoretical reasons for the observed experimental results with an aim to determine the role of the cation–π interaction in a host–guest scenario. From an analysis of certain components of the induced magnetic field and the ¹³C NMR shielding tensor under its own principal axis system (PAS), the local and overall magnetic behavior can be clearly described. Interestingly, the magnetic response of such a complex exhibits a large axis-dependent behavior, which leads to an overall shielding effect for the coordinating carbon atoms and a deshielding effect for the respective uncoordinated counterparts, evidence that complements previous experimental results. This proposed approach can be useful to gain further insight into the local and overall variation of NMR shifts for host–guest pairs involving both inorganic and organic hosts.     

How do the positive embeddings of Banach lattices depend on the αth derivatives of K?

Let K and S be locally compact Hausdorff spaces and X be an abstract space. Suppose that T is a positive Banach lattice isomorphism from into . Then for each ordinal α the cardinalities of the αth derivatives and satisfy the following inequality Moreover, if then is a continuous image of a subset of which can be taken closed when K is compact. The first statement of this result for is a vector‐valued extension of a Cengiz's theorem and the second one is vector‐valued version of a Holsztyński's theorem. A simple example shows that the number is sharp in these vector‐valued theorems.     

Applications of ‐invariant distributions

In this sequel to the article 17 , a criterion for the regularity of fundamental solutions of differential operators with positive symbol is proved in analogy to Hörmander's criteria, see 9 , 12 . It implies that the temperate fundamental solution of the operator is not regular. Furthermore, a formula for the convolution of two ‐invariant distributions is presented, and, finally, L. Schwartz' question on the surjectivity of linear partial differential operators with constant coefficients on the space is completely answered in the case of ‐invariant differential operators.     

On σ-commutativity in Menger algebras of n-place functions

We present an abstract characterization of various types of Menger algebras of n-place functions allowing certain permutations of variables.