On the existence of positive solutions of the p‐Laplacian dynamic equations on time scales

In this paper, we investigate the existence of positive solutions for a nonlinear m‐point boundary value problem for the p‐Laplacian dynamic equations on time scales, by applying a Krasnosel'skii's fixed point theorem. As an application, an example is included to demonstrate the main results. Copyright © 2017 John Wiley & Sons, Ltd.     

Synthesis and Comparison of Extraction Properties of p‐tert‐Butylcalix[n]arene Nitrile Derivatives for Selected Metals and Dichromate Anions

The article describes the syntheses and extraction properties of two p‐tert‐butylcalix[6]arene nitrile derivatives (3 and 4). The trinitrile derivative 3 has been synthesized from 5,11,17,23,29,35‐hexa‐tert‐butyl‐37,38,39,40,41,42‐hexahydroxycalix[6]arene 1. The compound 1 was directly converted to its hexanitrile derivative 4. In these syntheses, it was thought to explore the role of nitrile sites in the extraction of various metal cations and HCr₂O₇ ^?/Cr₂O₇ ^2? anions. The liquid‐liquid extraction properties of 3 and 4 towards selected alkali/transition metal cations and HCr₂O₇ ^?/Cr₂O₇ ^2? anions are reported. It has been observed that receptor 3 does not extract alkali/transition metal cations effectively, but shows affinity towards HCr₂O₇ ^?/Cr₂O₇ ^2? anions at low pH. The compound 4 is an effective form for transferring Ni²⁺ selectively, while it shows poor transferring ability for HCr₂O₇ ^?/Cr₂O₇ ^2? anions from an aqueous into a dichloromethane layer. It was observed that the cavity size of the calix[n]arenes and the cooperativity of the functionalities play important roles in two phase extraction systems.     

Synthetic Access to New Pyridone Derivatives through the Alkylation Reactions of Hydroxypyridines with Epoxides

General methods for the preparation of a variety of pyridone and oxypyridine derivatives are described. 2‐,3‐,4‐Hydroxy pyridine and 2‐pyridinemethanol were alkylated with ethylene‐, propylene‐, and stryrene‐oxide and epichlorohydrin in the presence of different Lewis acids as a catalyst. The best yield of 3a was achieved in the presence of CdI₂/BF₃ · OEt₂. The corresponding pyridone derivatives (3a–d, 7a–d) were obtained from the reaction of 2‐and 4‐hydroxypyridine with oxiranes in good yields, whereas oxypyridine derivatives (5a–d, 9a,b) were obtained from reactions of 3‐hydroxypyridine and 2‐pyridinemethanol with oxiranes. Chlorohydrines (3d, 5d, 7d) were easily converted to corresponding epoxy derivatives (10, 11, 12) in basic medium; then amino alcohols (13–17) were obtained from the reaction of these epoxy derivatives with amines.     

Redox reaction of N,N′-phenylenebis-(salicylideneiminato)iron(III) with hypophosphorous acid in mixed aqueous medium

Transition Metal Chemistry - The kinetics of redox reaction between N,N′-phenylenebis-(salicylideneiminato)iron(III), hereafter referred to as [FeSalphen]+, and hypophosphorous acid was...     

Global existence and decay of solutions for the generalized bad Boussinesq equation

In this paper,we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation.Moreover,we show that the supremum norm of the solution decays algebraically to zero as(1+t)(1/7)when t approaches to infnity,provided the initial data are sufciently small and regular.     

Log-Polynomial Period Functions for Hecke Groups

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups.     

On the solvability of initial boundary value problems for nonlinear time-dependent Schrödinger equations

In this paper, we study the initial boundary value problems for a nonlinear time-dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin’s method.     

Fabrication and characterization of calix[4]arene Langmuir–Blodgett thin film for gas sensing applications

Microwave irradiation has been found to be a highly efficient method for etherification of p-tert-butylcalix[4]arene with alkyl bromides or ditosylate. The corresponding products were obtained as a pure form in modest yield within short reaction time when the reactions were performed under microwave irradiation.     

Electronic and vibrational spectroscopy of intermediates in methane-to-methanol conversion by CoO+

At room temperature, cobalt oxide cations directly convert methane to methanol with high selectivity but very low efficiency. Two potential intermediates of this reaction, the [HO-Co-CH(3)](+) insertion intermediate and [H(2)O-Co=CH(2)](+) aquo-carbene complex are produced in a laser ablation source and characterized by electronic and vibrational spectroscopy. Reaction of laser-ablated cobalt cations with different organic precursors seeded in a carrier gas produces the intermediates, which subsequently expand into vacuum and cool. Ions are extracted into a time-of-flight mass spectrometer and spectra are measured via photofragment spectroscopy. Photodissociation of [HO-Co-CH(3)](+) in the visible and via infrared multiple photon dissociation (IRMPD) makes only Co(+) + CH(3)OH, while photodissociation of [H(2)O-Co=CH(2)](+) produces CoCH(2)(+) + H(2)O. The electronic spectrum of [HO-Co-CH(3)](+) shows progressions in the excited state Co-C stretch (335 cm(-1)) and O-Co-C bend (90 cm(-1)); the IRMPD spectrum gives ν(OH) = 3630 cm(-1). The [HO-Co-CH(3)](+)(Ar) complex has been synthesized and its vibrational spectrum measured in the O-H stretching region. The resulting spectrum is sharper than that obtained via IRMPD and gives ν(OH) = 3642 cm(-1). Also, an improved potential energy surface for the reaction of CoO(+) with methane has been developed using single point energies calculated by the CBS-QB3 method for reactants, intermediates, transition states and products.