A note on strong β-I-sets and strongly β-I-continuous functions

Summary In [6], we introduced and investigated the notions of strong β-I-open sets and strong β-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties.     

Idealization of a decomposition theorem

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A _I-sets and A _I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A _I-continuous. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Hydrolytic Stability of Organic Ligands in Al-, Ti- and Zr-Alkoxide Complexes

The complexation degrees of Al-, Ti- and Zr-butoxide (M) with unsaturated and saturated -diketones (3-allylpentane-2.4-dione-APD, acetylacetone-ACAC) and -ketoesters (methacryloxyethyl-acetoacetate-MEAA, allylacetoacetate-AAA, ethylacetoacetate-EAA) as organic ligands (L) were examined by IR and ¹³ C NMR spectroscopy and were found to be L:M 1.5. The hydrolytic stability of the ligands of the metal alkoxide complexes (L:M = 1) during hydrolysis/condensation reactions at the molar ratio h (H₂O : OR) = 0.5–2.0 decreases with increasing H$$₂O:complex ratio. Furthermore, the ligand stability depends on the type of metal in the complexes and decreases in the order Al- > Zr- > Ti-butoxide complexes at h=1. The ACAC ligand likewise shows in the Al-, Ti- and Zr-butoxide complexes a high hydrolytic stability (95–100%) at h=1 within 7 days. The Ti- and Zr-butoxide complexes with -ketoesters as ligand show at h=1> a release to a different extent e.g., up to 60% in the case of the MEAA-ligand in the Ti-butoxide complex after 2 days. In general, the hydrolytic stability of the ligands in the Ti-butoxide complexes (L:M = 1, h=1) decreases in the order ACAC > APD > AAA > EAA MEAA. The hydrolysis/condensation reaction of complexes having a weak ligand stability leads to larger particle sizes in the sols than those with stable ACAC ligands. The results contribute to a more controlled synthesis of sols and of new inorganic-organic hybrid polymers via the sol-gel process.     

Influences of Crystal-Field and Interlayer Coupling Interactions on Dynamic Phase Diagrams of a Mixed-Spin(3/2,2) Bilayer System

Influences of crystal-fields(D_A and D_B) and interlayer coupling interactions(J_3) on dynamic magnetic critical behaviors of a mixed-spin(3/2, 2) bilayer system under an oscillating magnetic field are investigated by the Glauber-type stochastic dynamics based on the mean-field theory. For this purpose, dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane for the ferromagnetic/ferromagnetic(FM/FM),antiferromagnetic/ferromagnetic(AFM/FM) and AFM/AFM interactions in detail. We observe that the influences of D_A, D_B and J_3 interactions parameters on the behavior of the dynamic phase diagrams are very much.     

Generalizations of Lifting Modules

The notion of -supplemented modules is a proper generalization of lifting modules. As a proper generalization of -supplemented modules, we introduce (D ₁₂)-modules and obtain some properties, characterizations and decompositions of -supplemented modules and (D ₁₂)-modules.     

Voltammetry of Benzo[a]pyrene in Aqueous and Nonaqueous Media: Adsorptive Stripping Voltammetric Determination at Pencil Graphite Electrode

A detailed study of the electrochemical oxidation of Benzo[a]pyrene (BaP) at the glassy carbon and pencil graphite electrodes was carried out in aqueous and nonaqueous media. Using square‐wave stripping mode, the compound yielded a well‐defined voltammetric response at pencil graphite electrode in acetate buffer, pH 4.8 at +1.13 V (vs. Ag/AgCl) (a preconcentration step being carried out at a fixed potential of +0.70 V for 180 s). The process could be used to determine BaP concentrations in the range 0.25–1.25 μM, with a detection limit of 0.027 μM (6.82 μg L^?1). The applicability to assay of spiked human urine samples was also illustrated.     

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in N′eel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.