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.     

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.     

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.     

Effects of large pyramidal surface roughness on spectral directional emittance

The spectral directional emittance of a roughened metal surface is presented for the case where the surface roughness is approximated by pyramidal undulations. The slope and height of the individual pyramids have been chosen to approximate the rms. slope and the rms. value of valley to peak distance of metal surfaces with random distribution of surface asperities. Each individual sloping surface is assumed to emit and reflect radiant energy according to Fresnel relationships.     

Positive solutions of nonlinear multi-point boundary value problems

This paper deals with the existence of positive solutions of nonlinear differential equation

$$\begin{aligned} u^{\prime \prime }(t)+ a(t) f(u(t) )=0,\quad 0<t <1, \end{aligned}$$

subject to the boundary conditions

$$\begin{aligned} u(0)=\sum _{i=1}^{m-2} a_i u (\xi _i) ,\quad u^{\prime } (1) = \sum _{i=1}^{m-2} b_i u^{\prime } (\xi _i), \end{aligned}$$

where \( \xi _i \in (0,1) \) with \( 0< \xi _1<\xi _2< \cdots<\xi _{m-2} < 1,\) and \(a_i,b_i \) satisfy   \(a_i,b_i\in [0,\infty ),~~ 0< \sum _{i=1}^{m-2} a_i <1,\) and \( \sum _{i=1}^{m-2} b_i <1. \) By using Schauder’s fixed point theorem, we show that it has at least one positive solution if f is nonnegative and continuous. Positive solutions of the above boundary value problem satisfy the Harnack inequality

$$\begin{aligned} \displaystyle \inf _{0 \le t \le 1} u(t) \ge \gamma \Vert u\Vert _\infty . \end{aligned}$$

     

Optical solitons and other solutions to the conformable space–time fractional complex Ginzburg–Landau equation under Kerr law nonlinearity

This study reveals the dark, bright, combined dark–bright, singular, combined singular optical solitons and singular periodic solutions to the conformable space–time fractional complex Ginzburg–Landau equation. We reach such solutions via the powerful extended sinh-Gordon equation expansion method (ShGEEM). Constraint conditions that guarantee the existence of valid solitary wave solutions are given. Under suitable choice of the parameter values, interesting three-dimensional graphs of some of the obtained solutions are plotted.