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.

     

Thermodynamics of Hydrogen Adsorption on Metal‐Organic Frameworks

Interaction between adsorbed hydrogen and the coordinatively unsaturated Mg²⁺ and Co²⁺ cationic centres in Mg‐MOF‐74 and Co‐MOF‐74, respectively, was studied by means of variable‐temperature infrared (VTIR) spectroscopy. Perturbation of the H₂ molecule by the cationic adsorbing centre renders the H? H stretching mode IR‐active at 4088 and 4043 cm^?1 for Mg‐MOF‐74 and Co‐MOF‐74, respectively. Simultaneous measurement of integrated IR absorbance and hydrogen equilibrium pressure for spectra taken over the temperature range of 79–95 K allowed standard adsorption enthalpy and entropy to be determined. Mg‐MOF‐74 showed ΔH⁰=?9.4 kJ mol^?1 and ΔS⁰=?120 J mol^?1 K^?1, whereas for Co‐MOF‐74 the corresponding values of ΔH⁰=?11.2 kJ mol^?1 and ΔS⁰=?130 J mol^?1 K^?1 were obtained. The observed positive correlation between standard adsorption enthalpy and entropy is discussed in the broader context of corresponding data for hydrogen adsorption on cation‐exchanged zeolites, with a focus on the resulting implications for hydrogen storage and delivering.     

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     

Development of a validated high-throughput LC-ESI-MS method for determination of sirolimus on dried blood spots

A high‐throughput liquid chromatography–electrospray ionization mass spectrometric (LC–ESI‐MS) method for screening of sirolimus on dried blood spots (DBS) was developed and validated. It involves solvent extraction of a punch of DBS followed by reversed‐phase LC on a relatively new monolithic column consisting of a silica rod with bimodal pore structure and detection by ESI‐MS. The run time was less than 3 min with a very low backpressure at a flow rate of 0.5 mL/min. The method can analyze more than 100 samples in an 8 h working day, including sample preparation. The assay was linear from 1 to 100 ng/mL. The mean recovery was 92.42%. The mean inter‐day and intra‐day precisions were 1.23 and 1.41%, respectively. The developed method is simple, rapid and useful for clinical applications. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

An efficient and direct route to the synthesis of diaryl sulfoxides catalyzed by heteropoly acid

Heteropoly acid tungstophosphoric acid (H₃PW₁₂O₄₀) was found to be an excellent catalyst for the synthesis of symmetrical diaryl sulfoxides. The reaction was carried out in various organic solvents or ionic liquids and under solventfree condition. The reaction exhibited better results in terms of the yield and rate under solventfree condition. The catalyst was efficiently recovered from the reaction mixture and reused. The highlighting features of the present protocol are short reaction times, high yields of the products, ambient conditions, and simple workup.     

Emulsion electrospinning: composite fibers from drop breakup during electrospinning

We evaluate the feasibility of electrospinning oil‐in‐water type emulsions. The emulsions had an aqueous solution of polyethylene oxide (PEO) as the continuous phase, and either mineral oil or a polystyrene (PS) in toluene solution as the drop phase. The Taylor cones and electrified liquid jets were stable even when the emulsion drops were as large as a few‐ten microns in diameter. The resulting electrospun PEO fibers incorporated the dispersed phase of the emulsion in the form of drops (in case of mineral oil), or in the form of solid particles (in case of PS). Mineral oil drops appear to be completely encapsulated in the PEO fibers, whereas the PS particles are either incompletely encapsulated, or covered by only a very thin layer of PEO. Calculations show that in both cases, the initially large emulsion drops are broken during the electrospinning process. Copyright © 2007 John Wiley & Sons, Ltd.