Influence of methyl‐modified silyl groups on the properties of polymers and Si/B/N/C ceramics derived from N‐silylated borazine derivatives

Thermal silazane cleavage of dichloroboryldisilylamines (SiCl_mMe_3?m)N(SiMe₃)(BCl₂) (1: m = 1; 2: m = 2) at 196 °C leads to the borazine derivates [(SiCl_mMe_3?m)NB(Cl_nMe_1?n)]₃ (3: m = 1, n = 0.185; 4: m = 2, n = 0.111) characterized by NMR and IR spectroscopy and mass spectrometry. Single‐crystal X‐ray diffraction structure analyses reveal (BN)₃ units with unusual twisted boat conformations in both compounds. Additionally, more detailed studies are done to clear up the function of the by‐products (SiCl_mMe_3?m)N(SiClMe₂)(BClMe) formed during the cyclization step leading to asymmetrically boron substituted borazine derivatives. The single‐source precursors 3 and 4 were cross‐linked with methylamine producing polymers 3P and 4P, which were transformed into black amorphous materials with ceramic yields of 20.8 % and 50.3 %, respectively. Ceramic 4C (Si_1.00B_0.98 N_2.55 C_1.37O_0.05) was further investigated by ¹¹B and ²⁹Si magic angle spinning (MAS) NMR spectroscopy. A combined study of high‐temperature TG analyses and X‐ray powder diffraction analyses confirms the thermal stability of 4C up to 1670 °C. Copyright © 2012 John Wiley & Sons, Ltd.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

Quantum Pfaffians and hyper-Pfaffians

The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Plücker relations for the quantum linear transformations, and then use them to give an optimal set of relations required for the quantum Pfaffian. We then give the formula between the quantum determinant and the quantum Pfaffian and prove that any quantum determinant can be expressed as a quantum Pfaffian. Finally the quantum hyper-Pfaffian is introduced, and we prove a similar result of expressing quantum determinants in terms of quantum hyper-Pfaffians at modular cases.     

Synthesis of diaryl sulfides via nickel ferrite‐catalysed C─S bond formation in green media

NiFe₂O₄ magnetic nanoparticles (MNPs) were synthesized, characterized and applied as an air‐stable, inexpensive and magnetically separable nanocatalyst for the synthesis of structurally diverse sulfides. Efficient methodologies were developed for the synthesis of unsymmetric diaryl sulfides via odourless and one‐pot reactions of triphenyltin chloride/S₈ or arylboronic acid/S₈ as thiolating agents with aryl halides or nitroarenes as starting materials in the presence of base (K₂CO₃ or NaOH) and NiFe₂O₄ MNPs as a catalyst in water or poly (ethylene glycol) as solvent at 80–110 °C. Free from ligand and the unpleasant smell of thiols and with the use of magnetically reusable nanocatalyst, green solvents and commercially available and cheap sulfur source and starting materials, these methods are more eco‐friendly and practical than available protocols for the synthesis of sulfides.     

On solitary wave solutions to the nonlinear Schrödinger equations with two parameters

In this paper, we discuss the existence and multiplicity of positive solitary wave solutions for nonlinear Schrödinger equations with two parameters. The proof is based on the method of upper and lower solutions and the fixed point index.     

Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations

A new ordinary differential inequality without global solutions is proposed. Comparison with similar differential inequalities in the well‐known concavity method is performed. As an application, finite time blow up of the solutions to nonlinear Klein–Gordon equation and generalized Boussinesq equation is proven. The initial energy is arbitrary high positive. The structural conditions on the initial data generalize the assumptions used in the literature for the time being. Copyright © 2015 John Wiley & Sons, Ltd.     

Metabolic profiles and pharmacokinetics of goitrin in rats through liquid chromatography combined with electrospray ionization–tandem mass spectrometry

Several chemical and biological studies have revealed R,S‐goitrin as the main bioactive constituent of Isatis indigotica Fort., responsible for antiviral antiendotoxin activity; however, few pharmacokinetic studies have been conducted. To comprehend the kinetics of R,S‐goitrin and promote its curative application, a rapid and sensitive UHPLC–MS/MS method was developed. The selected reaction monitoring transitions were m/z 130.0 → 70.0 for R,S‐goitrin and m/z 181.1 → 124.0 for the internal standard in a positive‐ion mode. The established UHPLC–MS/MS method achieved good linearity for R,S‐goitrin at 10–2000 ng/mL. The intra‐ and interday accuracy levels were within ±9.7%, whereas the intraday and interday precision levels were <11.3%. The extraction recovery, stability and matrix effect were within acceptable limits. The validated method was successfully applied for the pharmacokinetic analysis of R,S‐goitrin in rats after oral administration. Moreover, a total of six metabolites were structurally identified through UHPLC–Q/TOF–MS. The proposed metabolic pathways of R,S‐goitrin in rats involve demethylation, acetylation, glutathionylation and oxygenation.     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.