Linear and Bilinear Multiplier Operators for the Dunkl Transform

The main purpose of this article is to study the L _p -boundedness of linear and bilinear multiplier operators for the Dunkl transform in the one dimensional case.     

New notions in derived categories of local rings

In the derived category of a local commutative noetherian ring, we define irreducible chain complexes, atomic chain complexes, minimal atomic chain complexes and chain complexes having no mod m detectable homology. Also, we define nuclear chain complexes and core of chain complexes. After defining these notions, we establish the connection between them.     

Microstructural and optical properties of europium-doped zinc oxide nanowires

Single-crystal Eu³⁺-doped wurtzite ZnO micro- and nanowires were synthesized by chemical vapor deposition. The nanostructures grew via a self-catalytic mechanism on the walls of an alumina boat. The structure and properties of the doped ZnO were characterized using X-ray diffraction, energy-dispersive X-ray spectroscopy, scanning and transmission electron microscopy, and photoluminescence (PL) methods. A 10-min synthesis yielded vertically grown nanowires of 50–400 nm in diameter and several micrometers long. The nanowires grew along the ±[0001] direction. The Eu³⁺ concentration in the nanowires was 0.8 at.%. The crystal structure and microstructure of were compared for Eu³⁺-doped and undoped ZnO. PL spectra showed a red shift in emission for Eu³⁺-doped (2.02 eV) compared to undoped ZnO nanowires (2.37 eV) due to Eu³⁺ intraionic transitions. Diffuse reflectance spectra revealed widening of the optical bandgap by 0.12 eV for Eu³⁺-doped compared to undoped ZnO to yield a value of 3.31 eV. Fourier-transform infrared spectra confirmed the presence of europium in the ZnO nanowires.     

Free vibration analysis of linear particle chain impact damper

Impact dampers have gained much research interest over the past decades that resulted in several analytical and experimental studies being conducted in that area. The main emphasis of such research was on developing and enhancing these popular passive control devices with an objective of decreasing the three parameters of contact forces, accelerations, and noise levels. To that end, the authors of this paper have developed a novel impact damper, called the Linear Particle Chain (LPC) impact damper, which mainly consists of a linear chain of spherical balls of varying sizes. The LPC impact damper was designed utilizing the kinetic energy of the primary system through placing, in the chain arrangement, a small-sized ball between each two large-sized balls. The concept of the LPC impact damper revolves around causing the small-sized ball to collide multiple times with the larger ones upon exciting the primary system. This action is believed to lead to the dissipation of part of the kinetic energy at each collision with the large balls.     

Effective synthesis of carbon nanotubes via catalytic decomposition of methane: Influence of calcination temperature on metal–support interaction of Co–Mo/MgO catalyst

The present work investigated the influence of calcination temperature for bimetallic Co–Mo/MgO catalyst on the synthesis of carbon nanotubes (CNTs) via catalytic chemical vapor deposition (CCVD) of methane. The experimental results showed that variation in the catalyst calcination temperature affected carbon yield, diameter distribution and quality of the CNTs. Increasing the catalyst calcination temperature enabled Co–Mo/MgO catalysts in growing CNTs at higher yield, narrower diameter distribution and better degree of graphitization, credited to the strong metal–support interaction (MSI) formed between CoO species and MgO support. We also discovered that the catalysts of weak MSI were beneficial to the nucleation and growth of CNTs, meanwhile the catalysts with strong MSI provoked the growth of CNTs with narrow diameter distribution. The catalyst calcined at 700 °C, possessing moderate MSI, was found to be the most suitable catalyst for the growth of high quality CNTs with the diameter of 7.70±0.77 nm and the carbon yield of as high as 647.4%.     

Influence of gamma radiation on morphology structure,electrochemical corrosion behavior and hardness of Ni–Cr based alloys

This study evaluates the effects of gamma radiation on structure, electrochemical corrosion behavior and Vickers hardness of commercial dental Nikkeli–Kromi–Polttosekoitus [Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn)] alloy. The corrosion rate of Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn) alloy with 0.5 M HCl is increased with increasing the exposure rate of gamma radiation. The corrosion resistance of Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn) is varied and reaches a minimum value at 30 KGy. The corrosion potential value also is varied and reaches its highest value at 30 KGy. The Vickers hardness value of Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn) alloy is decreased by increasing the gamma radiation dose. Also it is obvious from our results that the effects of gamma radiation at the surface are much higher as compared with deeper parts and the structure of the alloy is changed due to its exposure to gamma radiation.     

On existence and asymptotic behaviour of solutions of a fractional integral equation

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions, defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.     

Existence and uniqueness of the solution,separation for certain second order elliptic differential equation

In this paper, we study conditions under which Schrodinger type operators with a matrix potential is separated and Schrodinger equation has a unique solution in the weighted space L_2,k(Rⁿ)^l, where l is any natural number and k ε C¹(Rⁿ) is a positive function