Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”     

Validated liquid chromatography–tandem mass spectrometry method for simultaneous quantitation of bendamustine and copanlisib in mouse plasma: Application to a pharmacokinetic study in mice

In this study, we report the development and validation of an LC–tandem mass spectrometry method for the simultaneous quantitation of bendamustine and copanlisib in mouse plasma as per the US FDA regulatory guidelines. The sample processing involves extraction of bendamustine and copanlisib along with internal standard (IS; warfarin) from 50 μL mouse plasma using a liquid–liquid extraction method. The chromatographic separation of bendamustine, copanlisib and the IS was achieved on an Atlantis dC₁₈ column using an isocratic mobile phase (5 mM ammonium acetate:methanol, 20:80 v/v). Bendamustine, copanlisib and the IS eluted at 0.88, 1.39 and 0.74 min, respectively, with a total run time of 2.5 min. The calibration curve ranged from 3.99–2996 and 4.33–3248 ng/mL for bendamustine and copanlisib, respectively. Inter- and intra-day precision and accuracy, stability in processed samples and upon storage, dilution integrity and incurred sample reanalysis were investigated for both the analytes. The intra- and inter-day precisions were in the ranges of 2.01%–5.05% and 2.74%–6.13% and 1.98%–7.64 and 8.62%–9.04% for bendamustine and copanlisib, respectively. Stability studies showed that both analytes were stable on bench top for 6 h, in auto-sampler for 24 and at −80°C for 30 days. The validated method was successfully applied to a pharmacokinetic study in mice.     

Polymerization-induced self-assembly of amino-acid-based nano-objects by reversible addition–fragmentation chain-transfer dispersion polymerization

A series of amino-acid-based amphiphilic diblock copolymer nano-objects having different morphologies were developed by reversible addition–fragmentation chain-transfer (RAFT) dispersion polymerization of styrene (St) in methanol. This was mediated by six different hydrophilic poly(N-acryloyl amino acid) macro-chain transfer agents (CTAs), including three carboxylic-acid-containing ones, poly(N-acryloyl-l -proline) (PAProOH), poly(N-acryloyl-4-trans-hydroxy-l -proline) (PAHypOH), and poly(N-acryloyl-l -threonine) (PAThrOH) prepared by RAFT polymerization, and their methyl ester forms, PAProOMe, PAHypOMe, and PAThrOMe. The effects of polymerization conditions on RAFT dispersion polymerization of St using a dithiocarbamate-terminated PAProOH was investigated. A systematic study of the effects of monomer conversion and concentration afforded the formation of various morphologies (i.e., spheres, worms, and vesicles). The effects of hydrogen-bonding and ionic interactions of the macro-CTAs on the assembled structures of the nano-objects were evaluated using six different macro-CTAs. Transforming the products from methanol to water via dialysis produced amino-acid-based block copolymer nano-objects, exhibiting pH-responsive morphological change, in aqueous solution.     

FeNi Alloy Nanoparticles Encapsulated in Carbon Shells Supported on N-Doped Graphene-Like Carbon as Efficient and Stable Bifunctional Oxygen Electrocatalysts

The development of cost-effective and durable oxygen electrocatalysts remains highly critical but challenging for energy conversion and storage devices. Herein, a novel FeNi alloy nanoparticle core encapsulated in carbon shells supported on a N-enriched graphene-like carbon matrix (denoted as FeNi@C/NG) was constructed by facile pyrolyzing the mixture of metal salts, glucose, and dicyandiamide. The in situ pyrolysis of dicyandiamide in the presence of glucose plays a significant effect on the fabrication of the porous FeNi@C/NG with a high content of doped N and large specific surface area. The optimized FeNi@C/NG catalyst displays not only a superior catalytic performance for the oxygen reduction reaction (ORR, with an onset potential of 1.0 V and half-wave potential of 0.84 V) and oxygen evolution reaction (OER, the potential at 10 mA cm⁻² is 1.66 V) simultaneously in alkaline, but also outstanding long-term cycling durability. The excellent bifunctional ORR/OER electrocatalytic performance is ascribed to the synergism of the carbon shell and FeNi alloy core together with the high-content of nitrogen doped on the large specific surface area graphene-like carbon.     

Chemoselective Hydrogenation of 6-Alkynyl-3-fluoro-2-pyridinaldoximes: Access to First-in-Class 6-Alkyl-3-Fluoro-2-pyridinaldoxime Scaffolds as New Reactivators of Sarin-Inhibited Human Acetylcholinesterase with Increased Blood–Brain Barrier Permeability

Novel 6-alkyl- and 6-alkenyl-3-fluoro-2-pyridinaldoximes have been synthesised by using a mild and efficient chemoselective hydrogenation of 6-alkynyl-3-fluoro-2-pyridinaldoxime scaffolds, without altering the reducible, unprotected, sensitive oxime functionality and the C−F bond. These novel 6-alkyl-3-fluoro-2-pyridinaldoximes may find medicinal application as antidotes to organophosphate poisoning. Indeed, one low-molecular-weight compound exhibited increased affinity for sarin-inhibited acetylcholinesterase (hAChE) and greater reactivation efficiency or resurrection for sarin-inhibited hAChE, compared with those of 2-pyridinaldoxime (2-PAM) and 1-({[4-(aminocarbonyl)pyridinio]methoxy}methyl)-2-[(hydroxyimino)methyl]pyridinium chloride (HI-6), two pyridinium salts currently used as antidote by several countries. In addition, the uncharged 3-fluorinated bifunctional hybrid showed increased in vitro blood–brain barrier permeability compared with those of 2-PAM, HI-6 and obidoxime. These promising features of novel low-molecular-weight alkylfluoropyridinaldoxime open up a new era for the design, synthesis and discovery of central non-quaternary broad spectrum reactivators for organophosphate-inhibited cholinesterases.     

Generalization of the Kelvin equation for arbitrarily curved surfaces

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equation's applicability for arbitrarily curved surface has been long debated and is severe problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to the vapor/fluid interfaces in chemical equilibrium conditions nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.