Boundedness properties in function spaces

Some boundedness properties of function spaces (considered as topo- logical groups) are studied.     

Synthesis of phenanthridine and phenanthridinone derivatives based on Pd‐catalyzed C–H activation

This review article provides an overview of the most recent and exciting developments in palladium‐catalyzed C–H activation and mechanistic aspects of these catalytic reactions as the fast‐growing field for the synthesis of phenanthridine derivatives.     

A note on commutators of Hardy operators

Fu and Lu et al. 7 showed that the commutator $\mathcal {H}_{\beta ,b}$ generated by the fractional Hardy operator and a locally integrable function b is bounded on the homogenous Herz spaces if and only if b is a central bounded mean oscillation function. We show that their result is optimal by giving a counterexample.     

Bis(4‐pyridylamino)triazine‐stabilized magnetite nanoparticles: preparation,characterization and application as a retrievable catalyst for the green synthesis of 4H‐pyran, 4H‐thiopyran and 1,4‐dihydropyridine derivatives

Synthesis of bis(4‐pyridylamino)triazine stabilized on silica‐coated nano‐Fe₃O₄ particles, and their feasibility as a reusable heterogeneous basic catalyst are reported. The catalytic performance of this novel material was studied for the green synthesis of highly functionalized 4H ‐pyran, 4H ‐thiopyran and 1,4‐dihydropyridine derivatives via one‐pot multicomponent reactions. Eco‐friendly method, high yield and purity of desired products, short reaction time along with ease of workup procedure outline the advantages of these new methodologies over earlier ones. Surface and magnetic properties of the core–shell hybrid nanoparticles were characterized via transmission and scanning electron microscopies, X‐ray diffraction, energy‐dispersive X‐ray and Fourier transform infrared spectroscopies and vibrating sample magnetometry. Copyright © 2016 John Wiley & Sons, Ltd.     

Liouville–Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations

A Liouville–Green (or WKB) asymptotic approximation theory is developed for a class of almost-diagonal (‘asymptotically diagonal’) linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.     

Preparation,characterization and heterogeneous catalytic applications of GO/Fe3O4/HPW nanocomposite in chemoselective and green oxidation of alcohols with aqueous H2O2

Graphene oxide ‐ Fe₃O₄ ‐ NH₃⁺H₂PW₁₂O₄₀ ^‐ magnetic nanocomposite (GO/Fe₃O₄/HPW) was prepared by linking amino ‐ functionalized Fe₃O₄ nanoparticles (Fe₃O₄ ‐ NH₂) on the graphene oxide (GO), and then grafting 12 ‐ tungstophosphoric acid (H₃PW₁₂O₄₀) on the graphene oxide ‐ magnetite hybrid (GO ‐ Fe₃O₄ ‐ NH₂). The obtained GO/Fe₃O₄/HPW nanocomposite was well characterized with different techniques such as FT ‐ IR, TEM, SEM, XRD, EDX, TGA ‐ DTA, AGFM, ICP and BET measurements. The used techniques showed that the graphene oxide layers were well prepared and the various stages of preparation of the GO/Fe₃O₄/HPW nanocomposites successfully completed. This new nanocomposite displayed excellent performance as a heterogeneous catalyst in the oxidation of alcohols with H₂O₂. The as ‐ prepared GO/Fe₃O₄/HPW catalyst was more stable and recyclable at least five times without significantly reducing its catalytic activity.     

Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator

The paper deals with second order nonlinear evolution inclusions and their applications. We study evolution inclusions involving a Volterra-type integral operator, which are considered within the framework of an evolution triple of spaces. First, we deliver a result on the unique solvability of the Cauchy problem for the inclusion by combining a surjectivity result for multivalued pseudomonotone operators and the Banach contraction principle. Next, we provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Finally, we consider a dynamic frictional contact problem of viscoelasticity for materials with long memory and indicate how the result on evolution inclusion is applicable to the model of the contact problem.     

Dihedral angle study in Hesperidin using NMR Spectroscopy

Hesperidin is flavonoid molecule found in citrus fruits (Citrus reticulata), especially difficult to extract, classify and characterize. Present work is to study the unresolved relative configuration of Hesperidin through the dihedral angle, coupling constant and different NMR techniques. The Karplus equation and its modifications have been originated from the valence bond theory and associated with dihedral angle and coupling constant. The result data set of calculated dihedral angle can probe significant method to assign the virtual configuration of natural products and also resolved stereochemistry of Hesperidin at C‐2 position in. Copyright © 2016 John Wiley & Sons, Ltd.