Quasi-Periodic Solutions and Stability for a Weakly Damped Nonlinear Quasi-Periodic Mathieu Equation

Quasi-Periodic (QP) solutions are investigated for a weakly dampednonlinear QP Mathieu equation. A double parametric primary resonance(1:2, 1:2) is considered. To approximate QP solutions, a double multiple-scales method is applied to transform the original QP oscillator to anautonomous system performing two successive reductions. In a first step,the multiple-scales method is applied to the original equation to derive afirst reduced differential amplitude-phase system having periodiccomponents. The stability of stationary solutions of this reduced systemis analyzed. In a second step, the multiple-scales method is applied again tothe first reduced system (RS) to obtain a second autonomous differentialamplitude-phase RS. The problem for approximating QP solutions of theoriginal system is then transformed to the study of stationary regimesof the induced autonomous second RS. Explicit analytical approximationsto QP solutions are obtained and comparisons to numerical integrationare provided.     

Enhanced transport properties and thermal stability of agro-based RO-membrane for desalination of brackish water

This present work focused on preparation of economic and high performance reverse osmosis membranes, characterized by high transport properties (salt rejection and flux) towards desalination of brackish water. In this respect cellulose acetate from sugar-cane bagasse (BCA) and polymethyl methacrylate (PMMA) wastes were used as the substrates of membrane. The function of PMMA for enhancing the performance of bagasse-based cellulose acetate RO-membranes was investigated at operating pressure 35.85 bar and feed temperature 25 °C. The effects of casting solution, percentage of polymer and treatment of polymer by alkali (HPMMA) on the performance of RO-membrane were discussed. The preferable composition (wt.%) of the 90% BCA and 10% HPMMA was achieved salt rejection 92.18% and flux 325.9 l h⁻¹ m⁻². High water purity was obtained by pre-passing the salted water through membrane made from dissolved bagasse (methylol cellulose) together with PMMA, instead of ion exchanger, followed by passing the accepted water through BCA–HPMMA membrane, whereas the salt rejection increased to 98%. Also, by this approach we obtained high thermal stability membrane compared to CA-RO-membrane. This data gives highlight on possibility of application such type of membrane with high temperature operation conditions.     

The thermal behaviour of lignins from wasted black pulping liquors

The thermal degradation of lignins separated from black liquor waste from pulping of bagasse and cotton stalks has been investigated. Thermal gravimetric analysis (TGA), differential thermal analysis (DTA) and derivative thermogravimetry (DTG), between 20 and 1000°C, have been used. Activation energies of treated lignins were calculated. Lignins separated from liquors obtained at low pulping temperature have higher activation energies than high-temperature lignins. The use of anthraquinone (AQ) as an additive for accelerating the pulping process raises the activation energy of the lignin in the black liquors waste.     

Comparative DFT Computational Studies with Experimental Investigations for Novel Synthesized Fluorescent Pyrazoline Derivatives

A novel series of pyrazoline derivatives were synthesized and their spectral properties were characterized via FT-IR, ¹H, and ¹³C NMR. The electronic transitions and fluorescence properties were tracked via UV-Vis and emission spectrometry. The density functional theory (DFT) calculations have been also computed to get spot onto the geometry, electronic transitions and spectroscopic properties theoretically that has been compared with the encountered experimental ones. Moreover, the dipole moment, optimized energy, HOMO - LUMO energies and band gaps were calculated for novel candidates pyrazoline derivatives with highly fluorescence quantum yield.     

Asymptotics of Homoclinic Bifurcation in a Three-Dimensional System

An analytical approach to predicting a critical parameter valueof homoclinic bifurcation in a three-dimensional system is reported. Themultiple scales method is first performed to construct a higher-orderapproximation of the periodic solution. A criterion based on a collisionbetween the periodic orbit and the fixed point involved in thebifurcation is applied. This criterion developed initially to predicthomoclinic bifurcations in planar autonomous systems, is adapted here toderive a critical value of the homoclinic bifurcation in a specificthree-dimensional system. To support our analytical predictions and todescribe the dynamical behaviour of the system, a complete numericalstudy is provided.     

Metal chelates with some cellulose derivatives; part IV. Structural chemistry of HEC complexes

Reactions of hydroxyethyl cellulose (HEC) with Cr ^III, Ni^II, Co^II, or Cu^II chlorides in aqueous medium yielded complexes with formulae [M(HEC)Cl _m .n H ₂O], wherem =1 or 2 and n=2 or 3. HEC acted as a uninegatively charged bidentate ligand in the case of Cr^III and Ni^II, and as a neutral ligand in the case of Co^II and Cu^II complexes. The spectra showed that the binding sites in Cr^III and Ni^II complexes were the ether oxygen between two ethoxyl groups and the oxygen of the hydroxyl group; while in the Co^II and Cu^II complexes the binding sites were the oxygen of ethoxyl groups and the primary alcoholic O atom of glucopyranose rings. These complexes would most likely exhibit octahedral geometry with Cr^III, Ni^II, and Co^II, but square planar configuration in the case of the Cu^II complex. The ligand parameters of the Cr^III, Ni^II, and Co^II metal chelates were calculated in different solvents and at different temperatures. The thermal stability of the above complexes was investigated and the overall thermodynamics functions G⁰, H⁰, and S⁰, associated with complex formation, were estimated.     

Quasi-Periodic Oscillations,Chaos and Suppression of Chaos in a Nonlinear Oscillator Driven by Parametric and External Excitations

An analysis is given of the dynamic of a one-degree-of-freedom oscillator with quadratic and cubic nonlinearities subjected to parametric and external excitations having incommensurate frequencies. A new method is given for constructing an asymptotic expansion of the quasi-periodic solutions. The generalized averaging method is first applied to reduce the original quasi-periodically driven system to a periodically driven one. This method can be viewed as an adaptation to quasi-periodic systems of the technique developed by Bogolioubov and Mitropolsky for periodically driven ones. To approximate the periodic solutions of the reduced periodically driven system, corresponding to the quasi-periodic solution of the original one, multiple-scale perturbation is applied in a second step. These periodic solutions are obtained by determining the steady-state response of the resulting autonomous amplitude-phase differential system. To study the onset of the chaotic dynamic of the original system, the Melnikov method is applied to the reduced periodically driven one. We also investigate the possibility of achieving a suitable system for the control of chaos by introducing a third harmonic parametric component into the cubic term of the system.