A qualocation method for parabolic partial differential equations

In this paper a qualocation method is analysed for parabolicpartial differential equations in one space dimension. Thismethod may be described as a discrete H¹-Galerkin method inwhich the discretization is achieved by approximating the integralsby a composite Gauss quadrature rule. An O (h^4-i) rate of convergencein the W^i.p norm for i = 0, 1 and 1 p is derived for a semidiscretescheme without any quasi-uniformity assumption on the finiteelement mesh. Further, an optimal error estimate in the H² normis also proved. Finally, the linearized backward Euler methodand extrapolated Crank-Nicolson scheme are examined and analysed.     

Ultra-low-frequency dust-electromagnetic modes in self-gravitating magnetized dusty plasmas

Obliquely propagating altra-low-frequency dust-electromagnetic waves in a self-gravitating, warm, magnetized, two fluid dusty plasma system have been investigated. Two special cases, namely, dust-Alfvén mode propagating parallel to the external magnetic field and dustmagnetosonic mode propagating perpendicular to the external magnetic field have also been considered. It has been shown that effects of self-gravitational field, dust fluid temperature, and obliqueness significantly modify the dispersion properties of these ultra-low-frequency dust-electromagnetic modes. It is also found that in parallel propagating dust-Alfvén mode these effects play no role, but in obliquely propagating dust-Alfvén mode or perpendicular propagating dust-magnetosonic mode the effect of self-gravitational field plays destabilizing role whereas the effect of dust/ion fluid temperature plays stabilizing role.     

The role of folic acid in inducing of apoptosis by zinc(II) complex in ovary and cervix cancer cells

Molecular Diversity - Herein, the synthesis, structure, binding affinity, cytotoxicity, and apoptotic properties of the new Zn(II) complex composed of folic acid and bipyridine ligands are...     

An arc-search predictor-corrector infeasible-interior-point algorithm for P∗(κ)-SCLCPs

Numerical Algorithms - In this paper, we propose a new arc-search predictor-corrector infeasible-interior-point algorithm for linear complementarity problems over symmetric cones with the Cartesian...     

Structural characterization and magnetic properties of superparamagnetic zinc ferrite nanoparticles synthesized by the coprecipitation method

Single phase zinc ferrite (ZnFe₂O₄) nanoparticles have been prepared by the coprecipitation method without any subsequent calcination. The effects of precipitation temperature in the range 20–80 °C on the structural and the magnetic properties of zinc ferrite nanoparticles were investigated. The crystallite size, microstructure and magnetic properties of the prepared nanoparticles were studied using X-ray diffraction (XRD), Fourier transmission infrared spectrum, transmission electron microscope (TEM), energy dispersive X-ray spectrometer and vibrating sample magnetometer. The XRD results showed that the coprecipitated nanoparticles were single phase zinc ferrite with mixture of normal and inverse spinel structures. Furthermore, ZnFe₂O₄ nanoparticles have the crystallite size in the range 5–10 nm, as confirmed by TEM. The magnetic measurements exhibited that the zinc ferrite nanoparticles synthesized at 40 °C were superparamagnetic with the maximum magnetization of 7.3 emu/g at 10 kOe.     

An experimental investigation of substituent effects on the formation of 2,3‐dihydroquinazolin‐4(1H)‐ones: a kinetic study

The effect of different substituents on the kinetics of the reactions between 2‐amino‐benzamide and some of benzaldehyde derivatives have been spectrally investigated in the presence of formic acid. The proposed mechanism were challenged due to the determination of rate‐determining step (RDS) and also, to obtain the general rate law of the reaction. For all substituents, the reactions followed the second‐order kinetics and the partial orders of reactions were recognized with respect to each reactant. Electron withdrawing substituents on benzaldehyde ring increased the rate of reaction. Kinetic values (k and E_a) and associated activation parameters (ΔH^?, ΔG^? and ΔS^?) of the reactions were determined. Both the Arrhenius and the Eyring equations were used to calculate activation energy. Comparison of magnitude of and T showed that the reactions were enthalpy controlled. Isokinetic plots for the reactions were plotted and linear relationship between and recognized that relative contribution of enthalpy and entropy to the overall free energy was the same in the reactions.     

A Thermodynamic and Kinetic Insight into the Pathways Leading to a Highly Functionalized Ketenimine: A Computational Study

All steps of two mechanistic pathways for the synthesized ketenimine through a multicomponent reaction between cyclohexyl isocyanide 1 and acetylen ester 2 in the presence of CH‐acid 3 have been thermodynamically and kinetically evaluated. Intrinsic reaction coordinate calculations were performed for the optimized structures to verify the connectivity of all transition states with reactants and products. The kinetic data showed that the step 1 of the two proposed mechanisms was a rate‐determining step. Also, activation (ΔG^?, ΔH^?, ΔS^?) and thermodynamic (ΔG°, ΔH°, ΔS°) parameters confirmed that the second mechanism for generation product 4b was favored energetically. In addition, the single‐point ¹H and ¹³C NMR (GIAO) chemical shift calculations showed that the product obtained from the approval pathway was according to the experimental data.     

Two wide neighborhood interior-point methods for symmetric cone optimization

In this paper, we present two primal–dual interior-point algorithms for symmetric cone optimization problems. The algorithms produce a sequence of iterates in the wide neighborhood \(\mathcal {N}(\tau ,\,\beta )\) of the central path. The convergence is shown for a commutative class of search directions, which includes the Nesterov–Todd direction and the xs and sx directions. We derive that these two path-following algorithms have

$$\begin{aligned} \text{ O }\left( \sqrt{r\text{ cond }(G)}\log \varepsilon ^{-1}\right) , \text{ O }\left( \sqrt{r}\left( \text{ cond }(G)\right) ^{1/4}\log \varepsilon ^{-1}\right) \end{aligned}$$

iteration complexity bounds, respectively. The obtained complexity bounds are the best result in regard to the iteration complexity bound in the context of the path-following methods for symmetric cone optimization. Numerical results show that the algorithms are efficient for this kind of problems.