Lump,soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics

This article investigates a nonlinear fifth-order partial differential equation (PDE) in two-mode waves. The equation generalizes two-mode Sawada-Kotera (tmSK), two-mode Lax (tmLax), and two-mode Caudrey–Dodd–Gibbon (tmCDG) equations. In 2017, Wazwaz [1] presented three two-mode fifth-order evolutions equations as tmSK, tmLax, and tmCDG equations for the integrable two-mode KdV equation and established solitons up to three-soliton solutions. In light of the research above, we examine a generalized two-mode evolution equation using a logarithmic transformation concerning the equation’s dispersion. It utilizes the simplified technique of the Hirota method to obtain the multiple solitons as a single soliton, two solitons, and three solitons with their interactions. Also, we construct one-lump solutions and their interaction with a soliton and depict the dynamical structures of the obtained solutions for solitons, lump, and their interactions. We show the 3D graphics with their contour plots for the obtained solutions by taking suitable values of the parameters presented in the solutions. These equations simultaneously study the propagation of two-mode waves in the identical direction with different phase velocities, dispersion parameters, and nonlinearity. These equations have applications in several real-life examples, such as gravity-affected waves or gravity-capillary waves, waves in shallow water, propagating waves in fast-mode and the slow-mode with their phase velocity in a strong and weak magnetic field, known as magneto-sound propagation in plasmas.

     

Nickel-catalyzed synthesis of benzocoumarins: application to the total synthesis of arnottin I

The ring-opening addition of methyl 2,3-dimethoxy-6-iodobenzoate to oxabenzonorbornadienes followed by cyclization in the presence of NiBr2(dppe) and Zn metal powder in acetonitrile at 80 degrees C to give the corresponding benzocoumarin derivatives is described. This methodology was then applied to the synthesis of natural product arnottin I, first isolated from Xanthoxylum arnottianum Maxim, using protecting group chemistry. After deprotection and subsequent ring closure, arnottin I was obtained in 21% overall yield after six steps starting from catechol.     

A randomized on–line algorithm for the k–server problem on a line

The k–server problem is one of the most important and well‐studied problems in the area of on–line computation. Its importance stems from the fact that it models many practical problems like multi‐level memory paging encountered in operating systems, weighted caching used in the management of web caches, head motion planning of multi‐headed disks, and robot motion planning. In this paper, we investigate its randomized version for which Θ(log k)–competitiveness is conjectured and yet hardly any <k competitive algorithms are known, even for the simplest of metric spaces of O(k) size. We present a –competitive randomized k–server algorithm against an oblivious adversary when the underlying metric space is given by n equally spaced points on a line . This algorithm is <k competitive for . Thus, it provides a super–linear bound for n with o(k)–competitiveness for the first time and improves the best results known so far for the range on . © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Temperature dependence of the field effect mobility of solution-grown germanium nanowires

The temperature dependence of the field effect mobility was measured for solution-grown single-crystal Ge nanowires. The nanowires were synthesized in hexane from diphenylgermane by the supercritical fluid-liquid-solid process using gold nanocrystals as seeds. The nanowires were chemically treated with isoprene to passivate their surfaces. The electrical properties of individual nanowires were then measured by depositing them on a Si substrate, followed by electrical connection with Pt wires using focused ion beam assisted chemical vapor deposition. The nanowires were positioned over TaN or Au electrodes covered with ZrO2 dielectric that were used as gates to apply external potentials to modulate the conductance. Negative gate potentials increased the Ge nanowire conductance, characteristic of a p-type semiconductor. The temperature-dependent source/drain current-voltage measurements under applied gate potential revealed that the field effect mobility increased with increasing temperature, indicating that the carrier mobility through the nanowire is probably dominated either by a hopping mechanism or by trapped charges in fast surface states.     

Synthesis of 1D β-MnO2 for high-performance supercapacitor application

Journal of Solid State Electrochemistry - Electrochemical supercapacitors (ESs) still need to overcome development obstacles in order to realize their full potential while being acknowledged as a...     

Hydrogen storage properties and neutron scattering studies of Mg2(dobdc)--a metal-organic framework with open Mg2+ adsorption sites

The hydrogen storage properties of Mg(2)(dobdc) (dobdc(4-) = 2,5-dioxido-1,4-benzenedicarboxylate), a metal-organic framework possessing hexagonal one-dimensional channels decorated with unsaturated Mg(2+) coordination sites, have been examined through low- and high-pressure adsorption experiments, infrared spectroscopy, and neutron scattering studies.     

A novel amino acid functionalized ionic liquid promoted one-pot solvent-free synthesis of 3,4-dihydropyrimidin-2-(1H)-thiones

An environmentally benign, cheap and reusable L-amino acid functionalized ionic liquid [L-AAIL]/AlCl₃ was found to be an effective catalyst for the synthesis of 3,4-dihydropyrimidine-2-(1H)-thione derivatives in good to excellent yield under solvent-free condition. Compared with the classical Biginelli reactions, this method consistently enjoys the advantages of mild reaction conditions, easy work-up, and short reaction time. These one-pot three-component Biginelli products could be separated easily from the catalyst–water system, and the catalyst could be reused at least five times without noticeably reducing catalytic activity.