Infinitely many solutions for a resonant sublinear Schrödinger equation

In this paper, we consider a nonlinear sublinear Schrödinger equation at resonance in . By using bounded domain approximation technique, we prove that the problem has infinitely many solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

ALTERNATELY LINEARIZED IMPLICIT ITERATION METHODS FOR SOLVING QUADRATIC MATRIX EQUATIONS

A numerical solution of the quadratic matrix equations associated with a nonsingular M-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingular M-matrix solution of the quadratic matrix equations is developed, and its corresponding theory is given. Some numerical examples are provided to show the efficiency of the new method.     

An Efficient Synthesis of 14‐Aryl or Alkyl‐14H‐Dibenzo[a. j]Xanthenes Using Reusable HBF4‐SiO2 Catalyst Under Thermal and Solvent‐Free Conditions

A simple and convenient procedure for the synthesis of 14‐aryl or alkyl‐14H‐dibenzo[a. j]xanthene derivatives is described through a one‐pot condensation of β‐naphthol with various aryl or alkyl aldehydes in the presence of HBF₄‐SiO₂ as the catalyst under thermal and solvent‐free conditions.     

Self-repairing and superhydrophobic film of gold nanoparticles and fullerene pyridyl derivative based on the self-assembly approach

In this paper, we report that thin gold films can be prepared on the water/toluene interface by self-assembly of gold nanoparticles (NPs) and fullerene pyridyl derivatives. The assembled films were characterized using UV–vis spectroscopy and transmission electron microscope (TEM). The films show self-repairing and superhydrophobic properties.     

Novel Composite of Multiwalled Carbon Nanotubes and Gold Nanoparticles Stabilized by Chitosan and Hydrophilic Ionic Liquid for Direct Electron Transfer of Glucose Oxidase

A novel composite was fabricated through dispersing multiwalled carbon nanotubes (MWNTs) in gold nanoparticle (GPs) colloid stabilized by chitosan and ionic liquid (i.e., 1‐butyl‐3‐methylimidazolium tetrafluoroborate, BMIMBF₄). Transmission electron microscopy (TEM) experiment showed that the GPs highly dispersed on the MWNTs probably due to the electrostatic interaction among GPs, MWNTs and the imidazolium cation of BMIMBF₄. X‐ray photoelectron spectroscopy (XPS) indicated that thus‐formed gold nanostructure was mediated by BMIMBF₄. When glucose oxidase (GOD) was immobilized on the composite (MWNTs‐GPs) its ultraviolet‐visible absorption spectrum kept almost unchanged. The immobilized GOD coated glassy carbon electrode (GOD/MWNTs‐GPs/GC) exhibited a pair of well‐defined peaks in 0.10 M pH 7.0 phosphate buffer solution (PBS), with a formal potential of ?0.463 V (vs. SCE). The electrochemical process involved two‐electron transfer. The electron transfer coefficient was ca.0.56 and the electron transfer rate constant was 9.36 s^?1. Furthermore, the immobilized GOD presented good catalytic activity to the oxidation of glucose in air‐saturated PBS. The K_m and I_m values were estimated to be 13.7 μM and 0.619 μA. The GOD/MWNTs‐GPs/GC electrode displayed good stability and reproducibility.     

Theoretical study and rate constants calculation for the reactions of SiH3 radical with SiH3CH3 and SiH2(CH3)2

The multiple‐channel reactions SiH₃ + SiH₃CH₃ → products and SiH₃ + SiH₂(CH₃)₂ → products are investigated by direct dynamics method. The minimum energy path (MEP) is calculated at the MP2/6‐31+G(d,p) level, and energetic information is further refined by the MC‐QCISD method. The rate constants for individual reaction channels are calculated by the improved canonical variational transition state theory (ICVT) with small‐curvature tunneling (SCT) correction over the temperature range of 200–2400 K. The theoretical three‐parameter expression k₁(T) = 2.39 × 10⁻²³T^4.01exp(−2768.72/T) and k₂(T) = 9.67 × 10⁻²⁷T^4.92exp(−2165.15/T) (in unit of cm³ molecule⁻¹ s⁻¹) are given. Our calculations indicate that hydrogen abstraction channel from SiH group is the major channel because of the smaller barrier height among eight channels considered. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

A new prenylated arylbenzofuran derivative from Morus alba L.

<正>2-[3,5-Di-O-β-D-glucosyl-4-(3-methylbut-2-enyl)phenyl]benzofuran-6-ol,a new prenylated arylbenzofuran derivative was isolated from Morus alba L.Its structure was elucidated by various spectroscopic methods including MS,~1H NMR,~(13)C NMR,DEPT,~1H-~1HCOSY,HMQC and HMBC.     

A Comparative Study of the Modification of Gold and Glassy Carbon Surfaces with Mixed Layers of In Situ Generated Aryl Diazonium Compounds

In situ generated aryl diazonium cations were synthesized in the electrochemical cell by reaction of the corresponding amines with NaNO₂ in aqueous HCl. This paper reports a study of the formation of mixed layers from in situ generated aryl diazonium cations. Firstly, glassy carbon (GC) and gold electrode surfaces were modified with five single in situ generated aryl diazonium salts to obtain their corresponding reductive potential followed by the modification of GC and gold surfaces with eight binary mixed layers of in situ generated aryl diazonium salts. The difference between GC and gold surfaces in terms of in situ formation of two‐component aryl diazonium salt films was compared. The behavior of the mixed layers formed from in situ generated aryl diazonium salts relative to diazonium salts that were pre‐synthesized prior to surface modification was also investigated. Cyclic voltammetry and X‐ray photoelectron spectroscopy were used to characterize the resulting modified GC and gold surfaces. It is found that for some aryl diazonium salts the potential at which reductive adsorption is achieved on gold and GC surfaces is significantly different. For the eight sets of binary mixed layers, the species with more anodic potential are more difficult to attach to the both GC and gold surfaces. The behavior of the mixed layers formed from in situ generated aryl diazonium salts and the pre‐synthesized diazonium salts is similar; which emphasizes the advantage of the in situ approach without any apparent difference in behavior to the presynthesized diazonium salts.     

A Comparative Study of Modifying Gold and Carbon Electrode with 4‐Sulfophenyl Diazonium Salt

A comparison of the reductive adsorption behavior of 4‐sulfophenyl diazonium salt and subsequent electrochemical reactivity on gold relative to carbon was studied with some significant differences observed. The ability of the 4‐sulfophenyl layer adsorbed onto gold to block access of the redox probe ferricyanide to the underlying electrodes, as determined via cyclic voltammetry was inferior to the same layers formed on glassy carbon electrodes thus indicating a more open, porous layer formed on gold. More significantly, the 4‐sulfophenyl layers are shown to be far less electrochemically stable on gold than on glassy carbon. Electrochemical and X‐ray photoelectron spectroscopy (XPS) evidence suggests the instability is due to cleavage of the bond between sulfonate functional group and phenyl ring. These results provide further evidence that although aryl diazonium salt layers are relatively stable on gold surfaces compared with alkanethiol based self‐assembled monolayer (SAMs), the stability is not as high as is observed on carbon.