<abstract><p>Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel

In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

Elzaki Transform Adomian decomposition technique (ETADM), which an elegant combine, has been employed in this work to solve non-linear Riccati matrix differential equations. Solutions are presented to demonstrate the relevance of the current approach. With the use of figures, the results of the proposed strategy are displayed and evaluated. It is demonstrated that the suggested approach is effective, dependable, and simple to apply to a range of related scientific and technical problems.

   The potential application of granules of brick waste (GBW) as a low-cost sorbent for removal of Ni⁺²ions from aqueous solutions has been studied. The properties of GBW were determined through several tests such as X-Ray diffraction (XRD), Energy dispersive X-ray (EDX), Scanning electron microscopy (SEM), and BET surface area. In batch tests, the influence of several operating parameters including contact time, initial concentration, agitation speed, and the dose of GBW was investigated. The best values of these parameters that provided maximum removal efficiency of nickel (39.4%) were 1.5 hr, 50 mg/L, 250 rpm, and 1.8 g/100mL, respectively. The adsorption data obtained by batch experiments subjected to the Three i

The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

The nonlinear optical properties response of nematic liquid crystal (6CHBT) and the impact of doping with two kinds of nanoparticles; Fe₃O₄ magnetic nanoparticles and SbSI ferroelectric nanoparticles have been studied using the non-linear dynamic method through z-scan measurement technique. This was achieved utilizing CW He-Ne laser. The pure LC and magnetic LC nanoparticle composite samples had a maximum absorption while the ferroelectric LC nanoparticle composite had a minimum absorption of the incident light. The nonlinear refractive index was positive for the pure LC and the rod-like ferronematic LC composite samples, while it was negative for the ferroelectric LC composite. The studying of the nonlinear optical

Polyacrylamide Solutions of different concentrations (0.2, 0.4, 0.6, 0.8, 1.0 %) of Ag nanoparticles and ZnO nanoparticles were prepared, the viscosities and surface tension were measured for all solutions, where measurements indicated an increase in these properties with increased concentration, where the relative viscosity of polyacrylamide/zinc nanoparticles increased from 1.275 to 2.243, and the relative viscosity of polyacrylamide/silver nanoparticles increased from 1.178 to 1.934. Viscosity is significant parameters during electrospinning process. While the surface tension of the polyacrylamide/zinc nanoparticles has changed from 0.0343 Nm-1 to .0.0.0 Nm-1 and changed from .0.000Nm-1 to.0.0.0 Nm-1. Also the constants KH and KK were

Combining different treatment strategies successively or simultaneously has become recommended to achieve high purification standards for the treated discharged water. The current work focused on combining electrocoagulation, ion-exchange, and ultrasonication treatment approaches for the simultaneous removal of copper, nickel, and zinc ions from water. The removal of the three studied ions was significantly enhanced by increasing the power density (4–10 mA/cm2) and NaCl salt concentration (0.5–1.5 g/L) at a natural solution pH. The simultaneous removal of these metal ions at 4 mA/cm2 and 1 g NaCl/L was highly improved by introducing 1 g/L of mordenite zeolite as an ion-exchanger. A remarkable removal of heavy metals was reported