A sharper decay rate for a viscoelastic wave equation with power nonlinearity

We consider a viscoelastic wave equation with power nonlinearity. First, we construct a local solution by the Faedo-Galerkin approximation scheme and contraction mapping theorem. Next, we continue the local solution to the global one by a priori estimates obtained from a decreasing energy. Finally, we discuss the decay rate of the global solution by assuming that the kernel function is convex.     

Weinstein positive definite functions

Positivity - In this paper, we introduce the notion of the Weinstein positive definite functions and we state a version of Bochner’s theorem. Furthermore, we study the strictly Weinstein...     

The Littlewood-Paley g-function Associated with the Spherical Mean Operator

First we study the Gauss and Poisson semigroups connected with the spherical mean operator. Next, we define and study the Littlewood– Paley g-function associated with the spherical mean operator for which we prove the L ^p -boundedness for ${p \in]1, 2]}$ .     

Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation

The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation. The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives KleinGordon equation. This method introduces a promising tool for solving many space-time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Investigation of electrostatic charge distribution within the reactor wall fouling and bulk regions of a gas–solid fluidized bed

The distribution of charge within the wall fouling region and bulk of a fluidized bed reactor was investigated. Experiments were conducted in a 0.1 m in diameter carbon steel fluidization column under atmospheric conditions. Polyethylene particles were fluidized with extra dry air at 1.5 the minimum fluidization velocity (bubbling flow regime) for 1 h. Using an online Faraday cup measurement technique, the net charge-to-mass ratio (q/m), as well as the size distribution of all particles adhered to the column wall and those in the bulk of the bed was determined. The wall particles were found to be predominantly negatively charged while those which did not adhere to the wall were predominantly positively charged. The charge distribution within each region was then investigated by a custom made charged particle separator that separated the particles according to their charge magnitude and polarity. It was determined that although the net charge of the wall layer particles was negative, a significant amount of positively charged particles existed within each sample and therefore the entire wall particle layer. This suggests that the wall layer was formed through layering between positively and negatively charged particles. Particles in the bulk of the bed also consisted of bipolarly charged particles.     

Efficient Access to Deuterated and Tritiated Nucleobase Pharmaceuticals and Oligonucleotides using Hydrogen‐Isotope Exchange

A general approach for the efficient hydrogen‐isotope exchange of nucleobase derivatives is described. Catalyzed by ruthenium nanoparticles, using mild reaction conditions, and involving either D₂ or T₂ as isotopic sources, this reaction possesses a wide substrate scope and a high solvent tolerability. This novel method facilitates the access to essential diagnostic tools in drug discovery and development: tritiated pharmaceuticals with high specific activities and deuterated oligonucleotides suitable for use as internal standards during LC‐MS quantification.     

Graft copolymerization of hydroxyethyl cellulose with solketal acrylate: Preparation and characterization for moisture absorption application

In this work, we reported the preparation of a novel biomaterial, by graft-polymerization of 2-2-dimethyl-1-3-dioxolan-4-yl methyl acrylate (solketalacrylate, DMDMA) on hydroxyethyl cellulose (HEC) using KPS as initiator. Several experiments were performed to found the optimum conditions for the preparation of this biopolymer, by varying the time of the reaction as well as the initiator and the monomer ratio. Results showed that the highest grafting yield was 25%, obtained after 72?minutes at 65?°C, using THF as solvent. The structure of the grafted copolymer was confirmed by X-ray diffraction patterns which showed, besides the characteristic peaks of HEC at 2θ?=?31.74° and 44.63° a new peak at 2θ?=?30.72° related to an organized structure of the grafted polymer on the HEC backbone. The DSC analysis showed a single glass transition temperature Tg, intermediate between the corresponding values for HEC and neat poly(solketal acrylate). Moreover, the grafted biomaterial presented two-fold more moisture absorption ability by comparison with HEC, making this new synthetic biomaterial highly promising for dryness applications. In our knowledge, the synthesized monomer: 2-2-dimethyl-1-3-dioxolan-4-yl methyl acrylate, (solketal acrylate, DMDMA), has never been grafted on the HEC backbones before that is what makes the novelty of the present work.