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.     

An Anionic Amido-Substituted Seven-Vertex Siliconoid Cluster

The silanide [Si₄{N(SiMe₃)Dipp}₃]⁻ ( 1 ) transforms into the anionic siliconoid cluster [Si₇{N(SiMe₃)Dipp}₃]⁻ ( 2 ) with four unsubstituted silicon atoms as a contact ion pair with [K([18]crown-6)] in C₆D₆ at room temperature within five weeks. Anion 2 was investigated by natural population analysis and visualization of intrinsic atomic orbitals. Magnetically induced current-density calculations of 2 revealed two distinct strong diatropic vortices that sum up in one direction and create a strongly shielded apical silicon atom in 2 .     

In Vitro Antineoplastic and Antiviral Activity and In Vivo Toxicity of Geum urbanum L. Extracts

This study evaluated the in vitro antineoplastic and antiviral potential and in vivo toxicity of twelve extracts with different polarity obtained from the herbaceous perennial plant Geum urbanum L. (Rosaceae). In vitro cytotoxicity was determined by ISO 10993-5/2009 on bladder cancer, (T-24 and BC-3C), liver carcinoma (HEP-G2) and normal embryonic kidney (HEK-293) cell lines. The antineoplastic activity was elucidated through assays of cell clonogenicity, apoptosis induction, nuclear factor kappa B p65 (NFκB p65) activation and total glutathione levels. Neutral red uptake study was applied for antiviral activity. The most promising G. urbanum extract was analyzed by UHPLC–HRMS. The acute in vivo toxicity analysis was carried out following OEDC 423. The ethyl acetate extract of aerial parts (EtOAc-AP) exhibited the strongest antineoplastic activity on bladder cancer cell lines (IC₅₀ = 21.33–25.28 µg/mL) by inducing apoptosis and inhibiting NFκB p65 and cell clonogenicity. EtOAc and n-butanol extracts showed moderate antiviral activity against human adenovirus type 5 and human simplex virus type I. Seventy four secondary metabolites (gallic and ellagic acid derivatives, phenolic acids, flavonoids, etc.) were identified in EtOAc-AP by UHPLC–HRMS. This extract induced no signs of acute toxicity in liver and kidney specimens of H-albino mice in doses up to 210 mg/kg. In conclusion, our study contributes substantially to the detailed pharmacological characterization of G. urbanum, thus helping the development of health-promoting phytopreparations.     

Synthesis and Crystal Structure of Fluoride K2(Ta0.9I0.1)F7 with the Micro-Isomorphic Substitution in the Ta Cationic Position

Crystallography Reports - Fluoride crystals K2(Ta0.9I0.1)F7 (sp. gr. Р21/c) complementary to the K2TaF7 and K2NbF7 fluoride family have been obtained by hydrothermal synthesis. Their...     

Interchange-turbulence-based radial transport model for SOLPS-ITER: A COMPASS case study

Mean-field plasma edge transport codes such as SOLPS-ITER heavily rely on ad-hoc radial diffusion coefficients to approximately model anomalous transport. Such coefficients are experimentally determined and vary between different machines, and also depend on the operational regime and plasma location within the same device. Therefore, to match experimental data the modeller is required to manually tune several free parameters in expensive simulations, and the code's predictive capabilities are significantly downgraded. As a solution, a new model has been developed for SOLPS-ITER, solving an additional transport equation for the turbulent kinetic energy k, derived by consistently time-averaging the Braginskii equations, and including a diffusive closure for the anomalous particle flux. This closure model relates the anomalous diffusion coefficient to the local k value. The resulting equation structure and its closure are inspired by TOKAM2D isothermal interchange turbulence simulation results. Within this model, fewer and hopefully more universal free parameters are retained, thus improving the code's predictive capabilities. The new model has been tested on a COMPASS case for which upstream plasma profiles were available. Experimental data and a reference solution, obtained by matching the profiles through manual tuning of radial diffusivities, have been used to estimate the parameters of our new transport model. A ballooned particle diffusivity profile is retrieved by the new radial transport model, thanks to the proposed interchange drive. The obtained upstream profiles qualitatively agree with the experiment and prove the new model is a promising first attempt to be further refined.     

Synthesis and Crystal Structure of New Indium Iodate (K<Subscript>0.6</Subscript>Na<Subscript>0.4</Subscript>Ba)In[IO<Subscript>3</Subscript>]<Subscript>6</Subscript>

Crystals of new indium iodate (K_0.6Na_0.4Ba)In[IO₃]₆ were prepared by the hydrothermal synthesis. The unit-cell parameters are a = 11.3984(3) Å, с = 11.3817(3) Å, sp. gr. R3?. The chemical formula of the compound was derived from the structure determination and refinement with anisotropic displacement parameters to R = 0.0284. In the structure the InO₆ octahedra share vertices with six umbrella-like [IO₃]–groups typical of iodates and form isolated 3?-symmetric charged \(\rm{In[IO_{3}]_6^{3-}}\) clusters. Large Ba, K, and Na cations occupy a common site on a threefold axis due to the isomorphous substitution and compensate the charge of the clusters. The new structure extends the family of the recently discovered alkali-metal and barium iodates containing Ti and Zr atoms in octahedral sites. The iodate K₂Ge[IO₃]₆ containing Ge atoms in the centers of octahedra is the parent compound of this structural family.     

Charge-transfer photochemistry of the ternary complex (dithio-diseleno-carbamato)copper(II)

Photolysis of the ternary system consisting of diethyldithiocarbamate (Et2dtc), diethyldiselenocarbamate (Et2dsc) and copper(II) (1:1:1) has been studied in isobutylmethylketone (IBMK), toluene, chloromethane and chloromethane/ROH solutions (chloromethane = CCl4, CHCl3 or CH2Cl2 and ROH = EtOH or i-PrOH). The results obtained by EPR techniques and UV-Vis data indicate that a homolytic Cu-S bond cleavage involving the dithiocarbamate (dtc) ligand appears as the primary photo-process in Cu(Et2dtc)(Et2dsc) photolysis. Further conversion of the primary photoproduct Cu(I)(Et2dsc) is discussed in terms of a specific interaction with the solvent. In chloromethanes and chloromethane/ROH Cu(I)(Et2dsc) is oxidised by the solvent to give the corresponding paramagnetic mixed-ligand Cu(II)(Et2dsc)Cl complex and/or its chloride-bridged and EPR silent dimer Cu2(Et2dsc)2Cl2. The formation of the monomeric species occurs through a co-ordination of the alcohol molecule in the xy plane of the complex. Because of its co-ordination inertness, toluene poorly stabilises the primary photoproduct Cu(I)(Et2dsc), thus providing an effective primary recombination process and lower efficiency of Cu(Et2dtc)(Et2dsc) photolysis. The formation of the bis-solvated mixed-ligand complex Cu(II)(Et2dsc)+ in IBMK is also discussed.     

Infrared catastrophe in a two-quasiparticle collision integral

Relaxation of a nonequilibrium state in a disordered metal with a spin-dependent electron energy distribution is considered. The collision integral due to the electron-electron interaction is computed within the approximation of a two-quasiparticle scattering. It is shown that the spin-flip scattering processes with a small energy transfer may lead to the divergence of the collision integral for a quasi one-dimensional wire. This divergence is present only for a spin-dependent electron energy distribution that corresponds to the total electron spin magnetization M = 0 and only for nonzero interaction in the triplet channel. In this case, a nonperturbative treatment of the electron-electron interaction is needed to provide an effective infrared cutoff. The text was submitted by the authors in English. An erratum to this article is available at .     

Existence and Asymptotic Behavior of Positive Solutions of Neutral Impulsive Differential Equations

In this article, we consider first-order neutral impulsive differential equations with constant coefficients and constant delays. We study the asymptotic behavior of eventually positive solutions of these equations and establish necessary and sufficient conditions for the existence of such solutions. __________ Published in Neliniini Kolyvannya, Vol. 8, No. 3, pp. 304–318, July–September, 2005.