Busemann–Petty Problems for General L_p-Intersection Bodies

For 0 p 1, Haberl and Ludwig defined the notions of symmetric L p-intersection body and nonsymmetric L p-intersection body. In this paper, we introduce the general L p-intersection bodies.Furthermore, the Busemann–Petty problems for the general L p-intersection bodies are shown.     

Cu3V2O8 Nanoparticles as Intercalation‐Type Anode Material for Lithium‐Ion Batteries

Cu₃V₂O₈ nanoparticles with particle sizes of 40–50 nm have been prepared by the co‐precipitation method. The Cu₃V₂O₈ electrode delivers a discharge capacity of 462 mA h g^?1 for the first 10 cycles and then the specific capacity, surprisingly, increases to 773 mA h g^?1 after 50 cycles, possibly as a result of extra lithium interfacial storage through the reversible formation/decomposition of a solid electrolyte interface (SEI) film. In addition, the electrode shows good rate capability with discharge capacities of 218 mA h g^?1 under current densities of 1000 mA g^?1. Moreover, the lithium storage mechanism for Cu₃V₂O₈ nanoparticles is explained on the basis of ex situ X‐ray diffraction data and high‐resolution transmission electron microscopy analyses at different charge/discharge depths. It was evidenced that Cu₃V₂O₈ decomposes into copper metal and Li₃VO₄ on being initially discharged to 0.01 V, and the Li₃VO₄ is then likely to act as the host for lithium ions in subsequent cycles by means of the intercalation mechanism. Such an “in situ” compositing phenomenon during the electrochemical processes is novel and provides a very useful insight into the design of new anode materials for application in lithium‐ion batteries.     

Identification of antibacterial and antioxidant constituents of the essential oils of Cynanchum chinense and Ligustrum compactum

The aim of this research was to determine the chemical composition, antioxidant and antibacterial properties of the essential oils from Cynanchum chinense and Ligustrum compactum and isolation of antioxidant and antibacterial constituents from the essential oils. Thirty-eight components were identified in essential oils. Based on bioactivity-guided fractionation, guaiacol, linalool and 2-phenylethanol were isolated and identified as active constituents. Both L. compactum flower oil and 2-phenylethanol showed high antibacterial performance, with inhibition zone from 22.8 ± 0.8 to 11.9 ± 2.0 mm at highest concentration, and minimum inhibitory concentration values ranging from 0.25% to 1%. In both DPPH and ABTS assay, the active constituent guaiacol (IC₅₀ = 4.15 ± 0.72 and 9.12 ± 0.98 μg mL^? 1, respectively) exhibited high antioxidant activity, and the oils showed moderate antioxidant activity. These results indicate potential efficacy of active constituents and essential oils of L. compactum and C. chinense to control food-borne pathogenic and spoilage bacteria.     

Preparation and Electrochemical Properties of Tin–Iron–Carbon Nanocomposite as the Anode of Lithium‐Ion Batteries

Tin–iron–carbon nanocomposite is successfully prepared by a sol–gel method followed by a chemical vapor deposition (CVD) process with acetylene gas as the carbon source. The structural properties, morphology, and electrochemical performances of the nanocomposite are comprehensively studied in comparison with those properties of tin–carbon and iron–carbon nanocomposites. Sheet‐like carbon architecture and different carbon contents are induced thanks to the catalytic effect of iron during CVD. Among three nanocomposites, tin–iron–carbon demonstrates the highest reversible capacity of 800 mA h g^?1 with 96.9 % capacity retention after 50 cycles. It also exhibits the best rate capability with a discharge capacity of 420 mA h g^?1 at a current density of 1000 mA g^?1. This enhanced performance is strongly related to the carbon morphology and content, which can not only accommodate the large volume change, but also improve the electronic conductivity of the nanocomposite. Hence, the tin–iron–carbon nanocomposite is expected to be a promising anode for lithium‐ion batteries.     

Cytotoxicity of guanine-based degradation products contributes to the antiproliferative activity of guanine-rich oligonucleotides

Guanine-rich oligonucleotides (GROs) have attracted considerable attention as anticancer agents, because they exhibit cancer-selective antiproliferative activity and can form G-quadruplex structures with higher nuclease resistance and cellular uptake. Recently, a GRO, AS1411 has reached phase II clinical trials for acute myeloid leukemia and renal cell carcinoma. The antiproliferative activity of GROs has been associated with various protein targets; however the real mechanisms of action remain unclear. In this study, we showed evidence that antiproliferative activity of GROs (including AS1411) is mainly contributed by the cytotoxicity of their guanine-based degradation products, such as monophosphate deoxyguanosine (dGMP), deoxyguanosine (dG) and guanine. The GROs with lower nuclease resistance exhibited higher antiproliferative activity. Among nucleotides, nucleosides and nucleobases, only guanine-based compounds showed highly concentration-dependent cytotoxicity. Our results suggest that it is necessary to reconsider the cancer-selective antiproliferative activity of GROs. Since guanine-based compounds are endogenous substances in living organisms, systematic studies of the cytotoxicity of these compounds will provide new information for the understanding of certain diseases and offer useful information for drug design.     

Invariants of finite groups generated by generalized transvections in the modular case

We investigate the invariant rings of two classes of finite groups G ≤ GL(n, F _q) which are generated by a number of generalized transvections with an invariant subspace H over a finite field F _q in the modular case. We name these groups generalized transvection groups. One class is concerned with a given invariant subspace which involves roots of unity. Constructing quotient groups and tensors, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other is concerned with different invariant subspaces which have the same dimension. We provide a explicit classification of these groups and calculate their invariant rings.     

Existence of the positive composite optical vortices

Optical vortices as topological objects exist ubiquitously in nature. In this paper, we use the principle of variational method and mountain pass lemma to develop some existence theorems for the stationary vortex wave solution of a coupled nonlinear Schrödinger equations, which describe the possibility of effective waveguiding of a weak probe beam via the cross‐phase modulation‐type interaction. The main goal is to obtain a positive solution, of minimal action if possible, with all vector components not identically zero. Additionally, as demanded by beam confinement, we prove the exponential decay of the soliton amplitude at infinity. Copyright © 2017 John Wiley & Sons, Ltd.