The delay effect on reaction–diffusion equations

In this work we study a reaction–diffusion problem with delay and we make an analysis of the stability of solutions by means of bifurcation theory. We take the delay constant as a parameter. Special conditions on the vector field assure existence of a spatially nonconstant positive equilibrium U_k , which is stable for small values of the delay. An increase of the delay destabilizes the equilibrium of U_k and leads to super or subcritical Hopf bifurcation.     

Second-Order Modified Contingent Epiderivatives in Set-Valued Optimization

In this article, we introduce a second-order modified contingent cone and a second-order modified contingent epiderivative. We discuss some properties of the second-order cone and the epiderivative, respectively. Moreover, a Fritz John type necessary optimality condition is obtained for the set-valued optimization problems with constraints by using the second-order modified contingent epiderivative and an example is proposed to explain the Fritz John type necessary optimality condition. In particular, we obtain a unified second-order sufficient and necessary optimality condition for the set-valued optimization problems with constraints under twice differentiable L-quasi-convex assumption.     

Nonlinear Leray–Schauder Alternatives for Decomposable Operators in Dunford–Pettis Spaces and Application to Nonlinear Eigenvalue Problems

We present some new variants of Leray–Schauder type fixed point theorems and eigenvalue results for decomposable single-valued nonlinear weakly compact operators in Dunford-Pettis spaces.     

Optical damage resistance of Mg:Ce:Fe:LiNbO3 crystals

Mg:Ce:Fe:LiNbO₃ crystals were prepared with fixed concentrations of Fe₂O₃ and CeO₂, and differing concentrations of MgO by the Czochralski technique. Their infrared transmission spectra were measured in order to investigate their defect structures and their optical damage resistance was characterized by the photoinduced birefringence change and transmission facula distortion method. The optical damage resistance of Mg:Ce:Fe:LiNbO₃ crystals increases remarkably when the concentration of MgO exceeds a threshold concentration. The dependence of the optical damage resistance on the defect structure of Mg:Ce:Fe:LiNbO₃ crystals is discussed in detail. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of clay suspensions on the precipitation of CaCO3 in seawater

The effect of montmorillonite and kaolinite, most common clay in marine water, on nucleation and growth of calcium carbonate in standard sea water was studied. Crystallization was induced by the degasification of the dissolved carbonic gas. It was shown by XRD and SEM analysis that CaCO₃ crystallize under its aragonite polymorph some either the clay concentration or type. It was also found that tested clays inhibited significantly the crystallization of calcium carbonate, especially for concentrations higher than 25 mgL^–1. From the fine analyses of the formed solid, it was suggested that the tested clays have an indirect effect on nucleation and growth of aragonite by increasing the Mg ions concentration, strong inhibitor of CaCO₃ formation, in the neighbourhood of clay particles where supersaturation is the higher and than crystallization can occur. In addition to its indirect role, kaolinite can interact with aragonite by adsorbing on their faces and blocking growth sites (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystal Structure of 3-(4-Methoxy-benzylidene)-isothiochroman-4-one

Abstract  

The title compound, 3-(4-methoxy-benzylidene)-isothiochroman-4-one (C₁₇H₁₄O₂S) was prepared from the reaction of isothiochroman-4-one with benzaldehyde in the presence of small amount of HCl. The structure of the synthesised compound was determined by IR, ¹H NMR and X-ray crystallography. The structure was solved in monoclinic, space group P2₁/n with a = 3.9773 (7) Å, b = 10.918 (2) Å, c = 30.609 (6) Å, β = 90.615 (3)°, V = 1329.1 (4) Å³, Z = 4 and with R _int = 0.047. The bicyclic ring of isothiochroman-4-one moiety does not adopt a planar geometry. The molecular conformation is stable via C10–H···O1 and C16–H···S1 intramolecular hydrogen-bonding interactions. These contacts involve molecules in an extended two-dimensional sheet to the bc plane.     

Crystal Structure of Cuprate (II) Complex of Tetradentate ONNO Ligand: 4-[(2-{[(1<Emphasis Type="Italic">E</Emphasis>)-1-Methyl-3-oxobutylidene]amino}ethyl)imino]pentan-2-one

Abstract  

The title copper complex, Cu[CH₃CO–CH=C(CH₃)N(CH₂–CH₂)N(CH₃)C=CHCO CH₃], has been synthesized by the reaction of ligand, 4-[2-(1-methyl-3-oxo-but-1-enylamino)-ethylamino]-pent-3-en-2-one (ONNO) and copper chloride. The structure of the synthesized complex was determined by IR, NMR, mass spectroscopic data and X-ray crystallography. The structure was solved in monoclinic, space group P2₁/n with a = 10.971 (4), b = 8.988 (3), c = 12.830 (5) ?, β = 93.512 (5), V = 1,262.7 (6) ?³, Z = 4 and with R _int = 0.047. The geometry around the copper atom displays a distorted square-planner structure by coordinating with two oxygen atoms from carbonyl moiety and two nitrogen heteroatom from the central moiety of the ligands and thus established two 6-membered rings and one 5-membered ring. The two nitrogen atoms form two anionic–cationic bonds to complete the coordination sphere around the copper metal atom.     

Determination of inorganic arsenic species in natural waters—Benefits of separation and preconcentration on ion exchange and hybrid resins

A simple method for the separation and determination of inorganic arsenic (iAs) species in natural and drinking water was developed. Procedures for sample preparation, separation of As(III) and As(V) species and preconcentration of the total iAs on fixed bed columns were defined. Two resins, a strong base anion exchange (SBAE) resin and a hybrid (HY) resin were utilized. The inductively-coupled plasma-mass spectrometry method was applied as the analytical method for the determination of the arsenic concentration in water. The governing factors for the ion exchange/sorption of arsenic on resins in a batch and a fixed bed flow system were analyzed and compared. Acidity of the water, which plays an important role in the control of the ionic or molecular forms of arsenic species, was beneficial for the separation; by adjusting the pH values to less than 8.00, the SBAE resin separated As(V) from As(III) in water by retaining As(V) and allowing As(III) to pass through. The sorption activity of the hydrated iron oxide particles integrated into the HY resin was beneficial for bonding of all iAs species over a wide range of pH values from 5.00 to 11.00. The resin capacities were calculated according to the breakthrough points in a fixed bed flow system. At pH 7.50, the SBAE resin bound more than 370 μg g⁻¹ of As(V) while the HY resin bound more than 4150 μg g⁻¹ of As(III) and more than 3500 μg g⁻¹ of As(V). The high capacities and selectivity of the resins were considered as advantageous for the development and application of two procedures, one for the separation and determination of As(III) (with SBAE) and the other for the preconcentration and determination of the total arsenic (with HY resin). Methods were established through basic analytical procedures (with external standards, certified reference materials and the standard addition method) and by the parallel analysis of some samples using the atomic absorption spectrometry-hydride generation technique. The analytical properties of both procedures were similar: the limit of detection was 0.24 μg L⁻¹, the limit of quantification was 0.80 μg L⁻¹ and the relative standard deviations for samples with a content of arsenic from 10.00 to 300.0 μg L⁻¹ ranged from 1.1 to 5.8%. The interference effects of anions commonly found in water and some organic species which can be present in water were found to be negligible. Verification with certified reference materials proved that the experimental concentrations found for model solutions and real samples were in agreement with the certified values.