Substitution and Solvent Effect of Some Substituted Hydroxy Schiff Bases

Abstract

The uv-vis spectra of eight ortho-hydroxy- andpara-hydroxy schiff bases were recorded in different solvents. Inductive and resonance effect of the substituents affect the electronic spectra of those molecules, while, intra-molecular hydrogen bond formation or breakage have little effect on the uv-visible spectra.     

On a Class of Quasilinear Elliptic Equations

We consider a class of quasilinear elliptic boundary problems, including the following Modified Nonlinear Schrödinger Equation as a special case: $$\begin{cases} ∆u+ \frac{1}{2} u∆(u^2)−V(x)u+|u|^{q−2}u=0 \ \ \ in \ Ω, \\u=0 \ \ \ \ \ \ \ ~ ~ ~ on \ ∂Ω, \end{cases}$$ where $Ω$ is the entire space $\mathbb{R}^N$ or $Ω ⊂ \mathbb{R}^N$ is a bounded domain with smooth boundary, $q∈(2,22^∗]$ with $2^∗=2N/(N−2)$ being the critical Sobolev exponent and $22^∗= 4N/(N−2).$ We review the general methods developed in the last twenty years or so for the studies of existence, multiplicity, nodal property of the solutions within this range of nonlinearity up to the new critical exponent $4N/(N−2),$ which is a unique feature for this class of problems. We also discuss some related and more general problems.     

Comparison between standard and counterpoise-corrected optimization using some hydrogen and halogen bonded systems

The effect of the counterpoise correction on the geometries, stabilization energies, and vibrational harmonic frequencies of some hydrogen- and halogen-bonded systems (B?=?CH₃CN,?HCN,?NH₃,?N₂,?CO,?H₂O,?H₂S,?PH₃;?HX?=?HF,?HCl,?HBr,?HCN,?HCF₃; XY?=?Br₂,?BrCl,?BrF,?Cl₂,?ClF,?F₂) has been analysed at the MP2 level of theory using the popular 6-311++G(d,p) basis set. The optimized B?···?H and B?···?X bond lengths increase with counterpoise (CP) correction. In some cases standard values and in other cases CP-corrected values are close to experimental data. The absolute values of complexation energies of CP-corrected structures are higher than standard by inclusion of BSSE correction. The effect of CP correction on intermolecular bond lengths and complexation energies of B?···?XY series are usually higher than B?···?HX. Also, this effect is higher for H₂S and PH₃ groups. The CP correction changes the vibrational harmonic frequencies by 0–100%. The changes are frequently lower than 20% for frequencies higher than 300?cm^?1.     

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

This article concerns the analysis of an unsteady stagnation point flow of Eyring-Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme. A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme (RK-4) is available to show the credibility of the Galerkin method. The numerical exploration is carried out for various governing parameters, namely, Brownian motion, steadiness, thermophoresis, stretching ratio, velocity slip, concentration slip, thermal slip, and fluid parameters, and Hartmann, Prandtl and Schmidt numbers. The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing, but the behavior is reversed for assisting cases. The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases (assisting and opposing). The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter. All the outcomes and the behavior of emerging parameters are illustrated graphically. The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method. It is concluded that said method could be extended to other problems of a complex nature.     

不同堆构条件下颗粒柱有效质量的涨落

利用静态颗粒特性实验仪研究了不同堆构条件下颗粒柱有效质量的涨落.发现当只有一种颗粒堆构时涨落随着颗粒柱与颗粒的直径比的增大而减小,除此之外,当有不同颗粒堆构时涨落还随着不同大小颗粒的堆构位置而变化,可将这种现象的机理归结为颗粒柱中的颗粒数量的异同以及颗粒柱与限界之间摩擦力方向的不确定性.     

Efficient model order reduction for dynamic systems with local nonlinearities

In the nonlinear structural analysis, the nonlinear effects are commonly localized and the rest of the structure behaves in a linear manner. Considering this fact, this research work proposes a harmonic balance solution in order to determine the nonlinear response of the structures. The solution is simplified by using an exact dynamic reduction along with the modal expansion technique. This novel approach, which is applicable to both discrete and continuous systems, converts the system equations of motion in each harmonic to a small set of nonlinear algebraic equations. The full set of system equations is reduced to a discrete system with a few generalized degrees of freedom (DOFs) confined to the localized nonlinear regions. The resultant reduced order model is shown to be accurate enough for determining the periodic response. To demonstrate the capability of the proposed method, numerical case studies for continuous and discrete systems, including systems with internal resonance, have been studied and the outcomes are validated with benchmark studies. In addition, the method is applied in the identification process of an experimental test setup with unknown frictional support parameters, and the results are presented and discussed.     

Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua's circuit

The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are L(2) signals, an adaptive control incorporated with H(∞) control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua's circuits.