Finite convergence analysis and weak sharp solutions for variational inequalities

In this paper, we study the weak sharpness of the solution set of variational inequality problem (in short, VIP) and the finite convergence property of the sequence generated by some algorithm for finding the solutions of VIP. In particular, we give some characterizations of weak sharpness of the solution set of VIP without considering the primal or dual gap function. We establish an abstract result on the finite convergence property for a sequence generated by some iterative methods. We then apply such abstract result to discuss the finite termination property of the sequence generated by proximal point method, exact proximal point method and gradient projection method. We also give an estimate on the number of iterates by which the sequence converges to a solution of the VIP.     

Analytical Investigation of Soliton Solutions to Three Quantum Zakharov-Kuznetsov Equations

In the present paper, the two-dimensional quantum Zakharov-Kuznetsov (QZK) equation, three-dimensional quantum Zakharov-Kuznetsov equation and the three-dimensional modified quantum Zakharov-Kuznetsov equation are analytically investigated for exact solutions using the modified extended tanh-expansion based method. A variety of new and important soliton solutions are obtained including the dark soliton solution, singular soliton solution, combined dark-singular soliton solution and many other trigonometric function solutions. The used method is implemented on the Mathematica software for the computations as well as the graphical illustrations.     

A Spectrofluorimetric Sequential Injection Method for the Determination of Penicillamine Using Fluorescamine in the Presence of β-cyclodextrins

A simple, robust and sensitive sequential injection spectrofluorimetric method for the determination of penicillamine (PA) in pharmaceutical formulations is developed. The method is based on the formation of a highly fluorescent derivative when penicillamine is reacted with fluorescamine (FL) in borate buffer of pH 9.3. The derivative produced is monitored at an emission wavelength of 495 nm using an excitation wavelength of 355 nm. The optimum conditions for the determination of PA with FL were: 3 mM FL, pH 9.3, 5 mM methyl-β-cyclodextrin, sample volume of 75 μL and reagent volume of 75 μL. Furthermore, the effect of various media on the fluorescence intensity of the PA–FL derivative was studied and methyl-β-cyclodextrin was found to give the largest enhancement. A linear dynamic range for the determination of PA of 5–80 ppm was obtained with a sampling frequency of 50 h⁻¹ and a relative standard deviation of less than 2.5%. The method was applied to the determination of PA in pharmaceutical formulations with reasonable recoveries ranging from 101.0–103.1%, indicating that no interference is observed from concomitants usually present in dosage forms.     

Flow injection colorimetric method for the assay of vitamin C in drug formulations using tris,1-10-phenanthroline-iron(III) complex as an oxidant in sulfuric acid media

A simple, fast and accurate colorimetric flow injection (FI) method suitable for the assay of vitamin C in drug formulations was proposed. In the method, vitamin C was injected into a flowing stream of iron(III) and then mixed with 1,10-phenanthroline in 0.05M sulphuric acid media. The mixture was allowed to react in a 45-cm long coil and the resulting solution of tris, 1-10-phenanthroline-iron(II) complex was monitored at 510 nm. The method was adopted by fully investigating the kinetics of the reaction and proposing a suitable mechanism. A throughput of 100 samples per hour was achieved with a relative standard deviation of 0.88% for vitamin C concentration range of 100-400 ppm.     

Mechanistic Insight into Binding of Huperzine A with Human Serum Albumin: Computational and Spectroscopic Approaches

Human serum albumin (HSA) is the most abundant protein in plasma synthesized by the liver and the main modulator of fluid distribution between body compartments. It has an amazing capacity to bind with multiple ligands, offering a store and transporter for various endogenous and exogenous compounds. Huperzine A (HpzA) is a natural sesquiterpene alkaloid found in Huperzia serrata and used in various neurological conditions, including Alzheimer’s disease (AD). This study elucidated the binding of HpzA with HSA using advanced computational approaches such as molecular docking and molecular dynamic (MD) simulation followed by fluorescence-based binding assays. The molecular docking result showed plausible interaction between HpzA and HSA. The MD simulation and principal component analysis (PCA) results supported the stable interactions of the protein–ligand complex. The fluorescence assay further validated the in silico study, revealing significant binding affinity between HpzA and HSA. This study advocated that HpzA acts as a latent HSA binding partner, which may be investigated further in AD therapy in experimental settings.     

Single‐Particle Spectroscopy on Large SAPO‐34 Crystals at Work: Methanol‐to‐Olefin versus Ethanol‐to‐Olefin Processes

The formation of hydrocarbon pool (HCP) species during methanol‐to‐olefin (MTO) and ethanol‐to‐olefin (ETO) processes have been studied on individual micron‐sized SAPO‐34 crystals with a combination of in situ UV/Vis, confocal fluorescence, and synchrotron‐based IR microspectroscopic techniques. With in situ UV/Vis microspectroscopy, the intensity changes of the λ=400 nm absorption band, ascribed to polyalkylated benzene (PAB) carbocations, have been monitored and fitted with a first‐order kinetics at low reaction temperatures. The calculated activation energy (E_a) for MTO, approximately 98 kJ mol^?1, shows a strong correlation with the theoretical values for the methylation of aromatics. This provides evidence that methylation reactions are the rate‐determining steps for the formation of PAB. In contrast for ETO, the E_a value is approximately 60 kJ mol^?1, which is comparable to the E_a values for the condensation of light olefins into aromatics. Confocal fluorescence microscopy demonstrates that during MTO the formation of the initial HCP species are concentrated in the outer rim of the SAPO‐34 crystal when the reaction temperature is at 600 K or lower, whereas larger HCP species are gradually formed inwards the crystal at higher temperatures. In the case of ETO, the observed egg‐white distribution of HCP at 509 K suggests that the ETO process is kinetically controlled, whereas the square‐shaped HCP distribution at 650 K is indicative of a diffusion‐controlled process. Finally, synchrotron‐based IR microspectroscopy revealed a higher degree of alkylation for aromatics for MTO as compared to ETO, whereas high reaction temperatures favor dealkylation processes for both the MTO and ETO processes.     

Weak Sharp Solutions for Nonsmooth Variational Inequalities

In this paper, we study the weak sharp solutions for nonsmooth variational inequalities and give a characterization in terms of error bound. Some characterizations of solution set of nonsmooth variational inequalities are presented. Under certain conditions, we prove that the sequence generated by an algorithm for finding a solution of nonsmooth variational inequalities terminates after a finite number of iterates provided that the solutions set of a nonsmooth variational inequality is weakly sharp. We also study the finite termination property of the gradient projection method for solving nonsmooth variational inequalities under weak sharpness of the solution set.     

The Application of 7-Chloro-4-nitrobenzoxadiazole (NBD-Cl) for the Analysis of Pharmaceutical-Bearing Amine Group Using Spectrophotometry and Spectrofluorimetry Techniques

Abstract

Many papers have been presented in recent years regarding the field of application of 7-chloro-4-nitrobenzoxadiazole (NBD-Cl) as a fluorogenic and chromogenic reagent for the determination of pharmaceutical amines using spectrophotometry and spectrofluorimetry techniques. In this review article, various spectrophotometric and spectrofluorimetric methods using NBD-Cl as a labeling reagent for determination of pharmaceutical amines are covered. The application of these methods for the determination of drugs in pharmaceutical and real samples is also discussed.     

Structure methods for solving the nearest correlation matrix problem

The nearest correlation matrix problem is to find a positive semidefinite matrix with unit diagonal, that is, nearest in the Frobenius norm to a given symmetric matrix A. This problem arises in the finance industry, where the correlations are between stocks. In this paper, we formulate this problem as a smooth unconstrained minimization problem, for which rapid convergence can be obtained. Other methods are also studied. Comparative numerical results are reported.