Exact solutions of nonlinear Schrödinger equation by using symbolic computation

The (G′/G,1/G)‐expansion method and (1/G′)‐expansion method are interesting approaches to find new and more general exact solutions to the nonlinear evolution equations. In this paper, these methods are applied to construct new exact travelling wave solutions of nonlinear Schrödinger equation. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. It is shown that the proposed methods provide a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Copyright © 2015 John Wiley & Sons, Ltd.     

On the concept of exact solution for nonlinear differential equations of fractional‐order

In this article, the new exact travelling wave solutions of the nonlinear space‐time fractional Burger's, the nonlinear space‐time fractional Telegraph and the nonlinear space‐time fractional Fisher equations have been found. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order in the sense of the Jumarie's modified Riemann–Liouville derivative. The ‐expansion method is effective for constructing solutions to the nonlinear fractional equations, and it appears to be easier and more convenient by means of a symbolic computation system. Copyright © 2016 John Wiley & Sons, Ltd.     

Dehydrophenylnitrenes: matrix isolation and photochemical rearrangements

The photochemistry of 3-iodo-2,4,5,6-tetrafluorophenyl azide 8 and 3,5-diiodo-2,4,6-trifluorophenyl azide 9 was studied by IR and EPR spectroscopy in cryogenic argon and neon matrices. Both compounds form the corresponding nitrenes as primary photoproducts in photostationary equilibria with their azirine and ketenimine isomers. In contrast to fluorinated phenylnitrenes, ring-opened products are obtained upon short-wavelength irradiation of the iodine-containing systems, indicative of C-I bond cleavage in the nitrenes or didehydroazepines under these conditions. Neither 3-dehydrophenylnitrene 6 nor 3,5-didehydrophenylnitrene 7 could be detected directly. The structures of the acyclic photoproducts were identified by extensive comparison with DFT calculated spectra. Mechanistic aspects of the rearrangements leading to the observed products and the electronic properties of the title intermediates are discussed on the basis of DFT as well as high-level ab initio calculations. The computations indicate strong through-bond coupling of the exocyclic orbital in the meta position with the singly occupied in-plane nitrene orbital in the monoradical nitrenes. In contrast to the ortho or para isomers, this interaction results in low-spin ground states for meta nitrene radicals and a weakening of the C1-C2 bond causing the kinetic instability of these species even under low-temperature conditions. 3,5-Didehydrophenylnitrenes, on the other hand, in which a strong C3-C5 interaction reduces coupling of the radical sites with the nitrene unit, might be accessible synthetic targets if the intermediate formation of labile monoradicals could be circumvented.     

Palladium‐catalyzed Suzuki reaction using 1,3‐dialkylbenzimidazol‐2‐ylidene ligands in aqueous media

From readily available starting compounds, six functionalized 1,3‐dialkylbenzimidazolium salts ( 2a–c and 4a–c ) have been prepared and characterized by conventional spectroscopic methods and elemental analyses. A highly effective, easy to handle, and environmentally benign process for palladium‐mediated Suzuki cross‐coupling was developed. The in situ prepared three‐component systems Pd(OAc)₂/1,3‐dialkylbenzimidazolium chlorides and Cs₂CO₃ catalyze quantitatively the Suzuki cross‐coupling of deactivated aryl chlorides. © 2004 Wiley Periodicals, Inc. Heteroatom Chem 15:419–423, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20034     

In vitro study on the competitive reactions between arsenite and selenite with glutathione

Exposure to arsenic can cause various biological effects by increasing the production of reactive oxygen species (ROS). Selenium acts as a beneficial element by regulating ROS and limiting heavy metal uptake and translocation. There are studies on the interactive effects of As and Se in plants, but the antagonistic and synergistic effects of these elements based on their binding to glutathione (GSH) molecules have not been studied yet. In this study, we aimed to investigate the antagonistic or synergistic effects of As and Se on the binding mechanism of Se and As with GSH at pH 3.0, 5.0, or 6.5. The interaction of As and Se in Se(SG)₂ + As(III) or As(SG)₃ + Se(IV) binary systems and As(III) + Se(IV) + GSH ternary system were examined depending on their ratios via liquid chromatography diode array detector/electrospray mass spectrometry (LC-DAD/MS) and liquid chromatography–electrospray ionization–tandem mass spectrometry (LC-ESI-MS/MS). The results showed that the formation of As(GS)₃ was not detected in the As(III) + Se(SG)₂ binary system, indicating that As(III) did not affect the stability of Se(SG)₂ complex antagonistically. However, in the Se(IV) + As(SG)₃ binary system, the addition of Se(IV) to As(SG)₃ affected the stability of As(SG)₃ antagonistically. Se(IV) reacted with GSH, disrupting the As(SG)₃ complex, and consequently, Se(SG)₂ formation was measured using LC-MS/DAD. In the Se(IV) + GSH + As(III) ternary system, Se(SG)₂ formation was detected upon mixing As(III), Se(IV), and GSH. The increase in the concentration of As(III) did not influence the stability of the Se(SG)₂ complex. Additionally, Se(IV) has a higher affinity than As(III) to the GSH, regardless of the pH of the solution. In both binary and ternary systems, the formation of the by-product glutathione trisulfide (GSSSG) was detected using LC-ESI-MS/MS.     

A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative

The modified simple equation method is an interesting technique to find new and more general exact solutions to the fractional differential equations in nonlinear sciences. In this paper, the method is applied to construct exact solutions of (2+1)-dimensional conformable time-fractional Zoomeron equation and the conformable space-time fractional EW equation.     

Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot

The electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s–1p, 1p–1d and 1d–1f transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states.     

The influence of moisture on deprotonation mode of imidazolinium chlorides with palladacycle acetate dimer

Deprotonation of 1,3-diorganyl imidazolinium salts, 1, with N,C-type palladacyclic acetate dimer 2 afforded novel NHC coordinated complexes 3 along with ring opening hydrolysis products 4, which may coordinate to palladium center via NH group to give 5a. The hydrolysis necessitates the study of NHC complex formation in anhydrous media. The new compounds were characterized by spectroscopic methods and three of them (3c, 4c, 5a) by X-ray single-crystal diffraction studies.     

Solitary wave solutions of two nonlinear physical models by tanh–coth method

In this work, we established the exact solutions for some nonlinear physical models. The tanh–coth method was used to construct solitary wave solutions of nonlinear evolution equations. The tanh–coth method presents a wider applicability for handling nonlinear wave equations.     

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.