Exact solutions of some nonlinear systems of partial differential equations by using the first integral method

In recent years, many approaches have been utilized for finding the exact solutions of nonlinear systems of partial differential equations. In this paper, the first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including, KdV, Kaup–Boussinesq and Wu–Zhang systems, analytically. By means of this method, some exact solutions for these systems of equations are formally obtained. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.     

A novel, one-pot, solvent-, and catalyst-free synthesis of 2-aryl/alkyl-4(3H)-quinazolinones

A novel and one-pot synthesis of 2-aryl/alkyl-4(3H)-quinazolinones is described. The in situ prepared amidoximes from the reaction between nitriles and hydroxylamine are condensed with anthranilic acids under solvent- and catalyst-free conditions to produce the title compounds in excellent yields.     

Mann type iterative methods for finding a common solution of split feasibility and fixed point problems

The purpose of this paper is to study and analyze three different kinds of Mann type iterative methods for finding a common element of the solution set ?? of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in the setting of infinite-dimensional Hilbert spaces. By combining Mann??s iterative method and the extragradient method, we first propose Mann type extragradient-like algorithm for finding an element of the set ${{{\rm Fix}}(S) \cap \Gamma}$ ; moreover, we derive the weak convergence of the proposed algorithm under appropriate conditions. Second, we combine Mann??s iterative method and the viscosity approximation method to introduce Mann type viscosity algorithm for finding an element of the ${{{\rm Fix}}(S)\cap \Gamma}$ ; moreover, we derive the strong convergence of the sequences generated by the proposed algorithm to an element of set ${{{\rm Fix}}(S) \cap \Gamma}$ under mild conditions. Finally, by combining Mann??s iterative method and the relaxed CQ method, we introduce Mann type relaxed CQ algorithm for finding an element of the set ${{{\rm Fix}}(S)\cap \Gamma}$ . We also establish a weak convergence result for the sequences generated by the proposed Mann type relaxed CQ algorithm under appropriate assumptions.     

Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity

Explicit expressions are given to study the biaxial buckling of monolayer graphene sheets. Based upon the continuum mechanics, a plate model is adopted in which the small length scale effect is incorporated into the governing equation through the nonlocal elasticity theory of Eringen. By employing the Galerkin method, analytical expressions are derived which allow quick and accurate calculation of the critical buckling loads of monolayer graphene sheets with various boundary conditions from the static deflection under a uniformly distributed load. The effectiveness of the present study is assessed by molecular dynamics simulations as a benchmark of good accuracy.     

Polynuclear Nickel(II) and Cobalt(II) Complexonates with Nitrilotrimethylenephosphonic Acid

Complexation in the Co(II)–H₆X–H₂O, Ni(II)–H₆X–H₂O, and Co(II)–Ni(II)–H₆X–H₂O systems (H₆X is nitrilotrimethylenephosphonic acid) was studied by spectrophotometry. The formation of binuclear complexonates Ni₂H₂X · 7H₂O, Co₂H₂X · 5H₂O, and NiCoH₂X · 6H₂O was demonstrated. These compounds were isolated from the solution, their composition was determined, the thermal stability was studied, and the kinetic parameters of dehydration were calculated.     

Evaluation of the thermal oxidative stability of polyimides via TGA techniques

Thermogravimetric analysis (TGA) has been used for many years to evaluate polymer thermal stability. The objective of this study is to determine if weight-loss curves from TGA and isothermal TGA (IGA) can be used to determine degradation activation energies and thus rank the thermal stability (TS) and thermooxidative stability (TOS) for selected polyimides. Two high-temperature stable addition-cured polyimides and two aromatic condensation polyimides, all four containing fluorinated connecting linkages in the dianhydride monomers, were compared. Three TGA kinetic methods (Coats/Redfern, Ingraham/Marier, Horowitz/Metzger) were used to determine the activation energy for decomposition in air. The results were then used to rank polyimide stability compared to more traditional rankings based on long-term isothermal air aging weight-loss (IWL) studies and thermal decomposition temperatures (T_d) from TGA data. Use of TGA coupled to a Fourier transform infrared (TGA–FTIR) spectrophotometer allowed for the simultaneous identification and relative quantification of evolved decomposition products (CO₂, CO, ArNCO, and CHF₃) of the four polyimides degraded in air or nitrogen. Isothermal TGA–FTIR (IGA–FTIR) was also done in air to determine the relative rate of product evolution at a constant temperature. Activation energies using TGA and IGA data were determined and then compared with IWL values for the degradation of the polyimide to examine for correlations of real-life thermal oxidative aging to accelerated aging techniques. The Coats/Redfern method and T_d were found to best reproduce stability rankings of those from long-term, high-temperature IWL studies. Together, they may provide a time-saving technique to evaluate polyimide thermal oxidative stability. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3943–3956, 1999     

Kinetics and mechanism of the photochemical reaction of Octacyanomolybdate (IV) and Diethylenetriamine

Photolysis of [Mo(CN)₈]⁴⁻ in the presence of diethylenetriamine (dien) leads to the complexation of ligand via hydrogen in the stoichiometry 2:1. The mechanism of the complexation was investigated by spectroscopy absorption and the rate constants and the quantum yield determined. Rate constants and quantum yields for the formation of the final products were found to depend on pH, ligand, and metal cyanide concentration. The values are a maximum at pH 7.4. At pH >7.4 the reverse reaction, generating octacyanomolybdate complex from the heptacyano species, is faster. At low pH, the ligand is protonated and less reactive; hence, the rate of reaction and quantum yield values decrease. The ionic strength does not affect the reaction rate, implying an associative mechanism for the photochemical reaction with dien, supported by the rate law. The observed rate law is: © 1999 John Wiley & Sons, Inc. J Chem Kinet 31: 89–93, 1999     

Different Dimensionalities,Morphological Advancements and Engineering of g-C3N4-Based Nanomaterials for Energy Conversion and Storage

Graphitic carbon nitride (g-C₃N₄) has gained tremendous interest in the sector of power transformation and retention, because of its distinctive stacked composition, adjustable electronic structure, metal-free feature, superior thermodynamic durability, and simple availability. Furthermore, the restricted illumination and extensive recombination of photoexcitation electrons have inhibited the photocatalytic performance of pure g-C₃N₄. The dimensions of g-C₃N₄ may impact the field of electronics confinement; as a consequence, g-C₃N₄ with varying dimensions shows unique features, making it appropriate for a number of fascinating uses. Even if there are several evaluations emphasizing on the fabrication methods and deployments of g-C₃N₄, there is certainly an insufficiency of a full overview, that exhaustively depicts the synthesis and composition of diverse aspects of g-C₃N₄. Consequently, from the standpoint of numerical simulations and experimentation, several legitimate methodologies were employed to deliberately develop the photocatalyst and improve the optimal result, including elements loading, defects designing, morphological adjustment, and semiconductors interfacing. Herein, this evaluation initially discusses different dimensions, the physicochemical features, modifications and interfaces design development of g-C₃N₄. Emphasis is given to the practical design and development of g-C₃N₄ for the various power transformation and inventory applications, such as photocatalytic H₂ evolution, photoreduction of CO₂ source, electrocatalytic H₂ evolution, O₂ evolution, O₂ reduction, alkali-metal battery cells, lithium-ion batteries, lithium–sulfur batteries, and metal-air batteries. Ultimately, the current challenges and potential of g-C₃N₄ for fuel transformation and retention activities are explored.