Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations

This study proposes two derivative-free approaches for solving systems of large-scale nonlinear equations, where the underlying functions of the systems are continuous and satisfy a monotonicity condition. First, the framework generates a specific direction then employs a backtracking line search along this direction to construct a new point. If the new point solves the problem, the process will be stopped. Under other circumstances, the projection technique constructs an appropriate hyperplane strictly separating the current iterate from the solutions of the problem. Then the projection of the new point onto the hyperplane will determine the next iterate. Thanks to the low memory requirement of derivative-free conjugate gradient approaches, this work takes advantages of two new derivative-free conjugate gradient directions. Under appropriate conditions, the global convergence result of the recommended procedures is established. Preliminary numerical results indicate that the proposed approaches are interesting and remarkably promising.     

Facile catalyst-free pseudo five-component domino reactions in the expedient synthesis of 5-aroyl-1,3-diarylhexahydropyrimidines

The pseudo five-component domino reactions of (E)-3-(dimethylamino)-1-arylprop-2-en-1-one, formaldehyde and aniline afford 5-aroyl-1,3-diarylhexahydropyrimidines in good yields under catalyst-free conditions. This transformation involving 4 C-N and 1 C-C bond formations in a one pot operation presumably proceeds via Michael addition-elimination-Mannich type reaction-condensative annulation-reduction sequence.     

Synthesis of Ag nanoparticle-decorated 2,4,6-tris(2-pyridyl)-1,3,5-triazine nanobelts and their application for H2O2 and glucose detection

The present paper reports on the first preparation of 2,4,6-tris(2-pyridyl)-1,3,5-triazine nanobelts (TPTNBs) by adjusting the pH value of the solution and the subsequent synthesis of Ag nanoparticle (AgNP)-decorated TPTNBs (AgNP-TPTNBs) by mixing an aqueous AgNO(3) solution with preformed TPTNBs without use of any external reducing agent. It is found that the resultant AgNP-TPTNBs exhibit notable catalytic performance for H(2)O(2) reduction. A glucose biosensor was fabricated by immobilizing glucose oxidase (GOD) onto a AgNP-TPTNBs-modified glassy carbon electrode (GCE) for glucose detection. The constructed glucose sensor has a wide linear response range from 3 mM to 20 mM (r: 0.999) with a detection limit of 190 μM. It is further shown that this glucose biosensor can be used for glucose detection in human blood serum.     

Kinetic spectrophotometric determination of the macrolide antibiotic josamycin in formulations

A simple kinetic spectrophotometric method was developed for the determination of josamycin in its dosage forms. The method is based on oxidation of the drug with alkaline potassium permanganate at room temperature for a fixed time of 20 min and measuring the produced green color at 611 nm. The absorbance-concentration plot is rectilinear over the range of 2-10 microg/mL (2.4 x 10(6)-1.2 x 10(-5)M) with minimum detectability of 1.0 microg/mL (1.2 x 10(-6)M). The determination of josamycin by fixed concentration and the rate-constant methods is also feasible with the calibration equations obtained, but the fixed-time method proved to be more applicable. The procedure was applied successfully to commercial tablets, and statistical analysis showed that the results compared favorably with those obtained by reference methods. The effect of sensitizers and surfactants on the performance of the proposed method was also studied. A proposal of the reaction pathway was presented.     

Kinetics and Mechanism of the Autocatalytic Oxidation of L-Asparagine in a Moderately Concentrated Sulfuric Acid Medium

The reaction kinetics of the Autocatalytic Oxidation of L-asparagine by permanganate ions has been investigated in moderately strong acid medium using the spectrophotometric technique. In all cases studied, an autocatalytic effect due to Mn²⁺ ions formed as a reaction product was observed. Both catalytic and noncatalytic processes were determined to be first order with respect to the permanganate ions while a first and a fractional order with respect to the amino acid for noncatalytic and catalytic reactions were obtained, respectively. The overall rate equation for this process may be written asd[MO₄ ^–]/dt= k´₁[MnO₄ ^–]+k´₂[MnO₄ ^–][Mn⁺²],where k´₁ and k´₂ are rate pseudoconstants for noncatalytic and catalytic reactions, respectively. The influence of some factors such as temperature and reactant concentration on the rate constants has been studied, and the activation parameters have been calculated. Reaction mechanisms satisfying observations for both catalytic and noncatalytic routes have been presented.     

ZrCl4 as an Efficient Catalyst for Crossed‐Aldol Condensation of Cyclic Ketones with Aromatic Aldehydes in Refluxing Ethanol

The aldol condensation reaction of cyclic ketones with aromatic aldehydes in ethanol under reflux conditions using ZrCl₄ as a catalyst to afford the corresponding α,α′‐bis(substituted benzylidene and cinnamylidene)cycloalkanones in excellent yields has been described. No self‐condensation product was produced.     

Investigation of sol-gel matrices containing crude metallothionein from <Emphasis Type="Italic">Scchizosaccharomyces pombe</Emphasis> for water treatment applications

The application of silica sol–gel particles containing crude metallothionein (MT) was investigated for cadmium removal from water. The metallothionein was first extracted from the yeast Scchizosaccharomyces pombe, and entrapped in the sol–gel matrices. Then sol–gel particles with the different sizes (ranging from 45 to 225 μm) were made. The effect of different flow rates as well as different particle sizes on adsorption of cadmium was investigated. The particle size has a greater effect on Cd adsorption than flow rate in the system studied. The breakthrough curves in the column were modeled using an empirical two parameter fixed-bed adsorption model. The model relates the changes of cadmium concentration in effluent to the standard deviation (σ) and characteristic of time (t ₀).     

Uniqueness for an overdetermined boundary value problem for the p-Laplacian

For set , and let be a measure with compact support. Suppose, for , there are functions and (bounded) domains , both containing the support of with the property that in (weakly) and in the complement of . If in addition is convex, then and .