Free energies of transfer of complexes of the type MCl2py4 between pyridine and other solvent media

Solubility isotherms are reported for the NiCl₂·4py, MnCl₂·4py, and MnCl₂·2py solid pyridinates in a number of pyridine+diluent mixtures at 25°C. Activity coefficients of the solvent components have been derived from the total vapor pressures measured by a static method. The standard free energies of transfer for the NiCl₂py₄ and MnCl₂py₄ complexes are the same, within the experimental error, in the pyridine+aprotic diluent mixtures, while marked differences are observed in the pyridine+chloroform mixtures. Marked deviations are observed for chloroform and 1,2-dichloroethane from a correlation between the standard free energy of transfer of the complexes, on one hand, and the Hildebrand's solubility parameter of the solvent, on the other, the latter correlation being roughly valid for aprotic solvents. The deviations are tentatively ascribed to hydrogen bond formation of the type H... between the protic solvents and the coordinated pyridine molecules, enhanced by the d electron delocalization.     

Binding and chemical fractionation of heavy metals in typical peat matter

Laboratory batch studies were conducted to evaluate the binding capacity and the mobility of metal species bound to typical humus peat matter. The identification of phase composition of mineral fractions and functional groups in the organic matter was assessed. The results showed generally high, but different retention capacity and binding strength, suggesting distinct diversity in binding mechanisms, phases and chemical nature of binding sites, depending on the metal species and their input concentrations. In general, the binding capacity of peat for the metal ions studied follows the order: Cr(3+) > Cu(2+) > Zn(2+) > Cd(2+) and results in the decrease of pH in the same order, due to displacement of H(3)O(+) from the peat by metal ions. The highest metal enrichment occurs in fractions F1(EXC), F2(CARB), F4(MRO) and F5(OM) of different binding strength adequate to exchangeable, carbonatic, moderately reducible amorphous Fe-oxide and organic/ sulphidic fractions in soils and sediments. In relation to species distribution in peats, the prevailing part of Cr(3+) is strongly bound in oxidizable organic substrate, while Cu(2+) is highly enriched in the moderately reducible F4(MRO) and the most labile F2(EXC) fractions. Cd(2+) and Zn(2+) are predominantly bound in the labile F1(EXC) and F2(CARB) fractions. Diversity of the predominant binding phases for the studied metals suggests rather weak competition for binding sites between chromium and copper ions; the strongest competition between the sorbed metal ions is anticipated for F1(EXC) and F2(CARB) fractions.     

An approximation theorem of wong-zakai type for nonlinear stochastic partial differential equations

We present an extension of the Wong-Zakai approximation theorem for nonlinear 984 given by the Wiener process and a martingale. By approximating these disturbances we obtain in the limit equation the Ito correction term for the infinite dimensional case. Such form of the correction term connected with the Wiener process was proved in the author's papers [21] and [22], where the approximation theorem for semilinear stochastic evolution equations in Hilbert spaces was studied. Our model here is similar as the one considered by Pardoux [17]     

Binding and chemical fractionation of heavy metals in typical peat matter

Laboratory batch studies were conducted to evaluate the binding capacity and the mobility of metal species bound to typical humus peat matter. The identification of phase composition of mineral fractions and functional groups in the organic matter was assessed. The results showed generally high, but different retention capacity and binding strength, suggesting distinct diversity in binding mechanisms, phases and chemical nature of binding sites, depending on the metal species and their input concentrations. In general, the binding capacity of peat for the metal ions studied follows the order: Cr³⁺ > Cu²⁺ > Zn²⁺ > Cd²⁺ and results in the decrease of pH in the same order, due to displacement of H₃O⁺ from the peat by metal ions. The highest metal enrichment occurs in fractions F1(EXC), F2(CARB), F4(MRO) and F5(OM) of different binding strength adequate to exchangeable, carbonatic, moderately reducible amorphous Fe-oxide and organic/ sulphidic fractions in soils and sediments. In relation to species distribution in peats, the prevailing part of Cr³⁺ is strongly bound in oxidizable organic substrate, while Cu²⁺ is highly enriched in the moderately reducible F4(MRO) and the most labile F2(EXC) fractions. Cd²⁺ and Zn²⁺ are predominantly bound in the labile F1(EXC) and F2(CARB) fractions. Diversity of the predominant binding phases for the studied metals suggests rather weak competition for binding sites between chromium and copper ions; the strongest competition between the sorbed metal ions is anticipated for F1(EXC) and F2(CARB) fractions.     

Thermal and Spectral Studies of Y(III) and Lanthanide(III) Complexes with Mesaconic Acid

Y(III) and lanthanide(III) mesaconates were prepared as crystalline solids with general formula Ln₂(C₅H₄O₄)₃⋅nH₂O, where n=7 for La−Pr, n=4 for Y,Nd−Ho, n=8 for Er−Lu. IR spectra of the prepared mesaconates suggest that carboxylate groups are bidentate bridging anf chelating. During heating the hydrated complexes are dehydrated in one (Y, Nd−Lu) or two steps (La−Pr) and then decompose directly to oxides (Y, Ce, Pr, Sm, Gd−Lu) or with intermediate formation Ln₂O₂CO₃ (La, Nd, Eu). This revised version was published online in August 2006 with corrections to the Cover Date.     

An extension of the Wong-Zakai theorem for stochastic evolution equations in Hilbert spaces

In this paper we examine an approximation theorem of the Wong–Zakai type for stochastic evolution equations in a Hilbert space with the noise being the generalized derivative of the Wiener process with values in another Hilbert space. As a consequence of the approximation of the Wiener process we get in the limit equation the Ito correction term for the infinite dimensional case. The obtained result includes the case of stochastic delay equations. The uniqueness and existence of solutions are guaranteed by known theorems for the mild solutions     

Wong-Zakai approximations for stochastic differential equations

The aim of this paper is to give a wide introduction to approximation concepts in the theory of stochastic differential equations. The paper is principally concerned with Zong-Zakai approximations. Our aim is to fill a gap in the literature caused by the complete lack of monographs on such approximation methods for stochastic differential equations; this will be the objective of the author's forthcoming book. First, we briefly review the currently-known approximation results for finite- and infinite-dimensional equations. Then the author's results are preceded by the introduction of two new forms of correction terms in infinite dimensions appearing in the Wong-Zakai approximations. Finally, these results are divided into four parts: for stochastic delay equations, for semilinear and nonlinear stochastic equations in abstract spaces, and for the Navier-Stokes equations. We emphasize in this paper results rather than proofs. Some applications are indicated.The author's research was partially supported by KBN grant No. 2 P301 052 03.     

On the approximation method of solving integral equations in diffusion problems

In this paper we consider the one-dimensional problem of heat or mass transport in the system with moving ends. We show that without solving the heat transfer equation, the heat flux flowing out from the system can be found when temperature on the boundary of this system is known. We make use of the Banach contraction theorem for appropriate integral equations. Our method also enables us to find the distribution of temperature in the whole domain that forms the physical system.