Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

The dynamics of a two-component fluid in the presence of capillary forces

In the present paper we study the qualitative behavior ast→∞ of the solution of the Cauchy problem for a system of equations describing a dynamics of a two-component viscous fluid. The model under consideration takes into account the mutual diffusion of the fluid components as well as their capillary interaction. We describe the ω-limit set of trajectories of the dynamical system generated by the problem. It is proved that the stationary solution of the problem, is a homogeneous stationary distribution of one of the components, is asymptotically stable. Any other stationary solution is not asymptotically stable and is even unstable if there are no close stationary solutions corresponding to a smaller energy level. Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 293–305, August, 1997. Translated by A. M. Chebotarev     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.     

关于均值KIRCHHOFF板非线性边界镇定问题的几点注记

对于均值K IRCHHOFF板非线性边界镇定问题给出几点注记.首先应用G reen公式对具有非线性边界反馈控制的均值K IRCHHOFF板所决定的非线性系统的能量衰减速度进行了重新推导,从而修正了前人的结果.然后应用极大单调函数的定义和分部积分技巧,对均值K IRCHHOFF板非线性边界镇定问题所决定的非线性算子A的极大单调性给出了重新证明,进而更正了已有文献中相应证明的欠妥之处.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.     

Conductance Study of the Binding of K+ by Dibenzo-pyridino-18-crown-6 and 1,10-N,N′-didecyl-diaza-18-crown-6 in Acetonitrile

The binding of K+ by dibenzo-pyridino-18-crown-6 (B2-py-18-C-6) and1,10-N,N-didecyl-diaza-18-crown-6 (22-DD) has been studiedconductometrically at 10, 15, 20 and 25 °C in acetonitrile. Thecomplexes formed were assumed to have 1 : 1 stoichiometry. The complexes ofK+ with 18-crown-6 (18-C-6) and dibenzo-18-crown-6 (B2-18-C-6) were alsostudied for comparison purposes. The stability constant, K, of a givencomplex and its molar conductance, c, were obtained by subjectingthe conductance data to a non-linear least-squares curve fitting procedure.The values of the enthalpy change, H, the entropy change, Sand the Gibbs free energy, G, associated with the formation of the 1: 1 complexes were derived and compared with relevant literature data. Thevalues of G at 25 °C indicate that the binding capacity of thefour macrocycles follows the order 18-C-6 > 22-DD > B2-18-C-6 >B2-py-18-C-6. The difference between the molar ionic conductance of the freeK+ cation and that of the bound cation, KL+, was estimated and the trend insuch differences correlates with the molecular size of the macrocycle, L.     

Surface forces in foam films from ABA block copolymer: a dynamic method study

The thinning of foam films from aqueous solutions of an ABA triblock copolymer of polyethylene oxide and polypropylene oxide (average molecular weight 14,000 g/mol) is studied experimentally. The dependence of the surface forces on film thickness is obtained by the dynamic method of Scheludko and Exerowa.The total surface force measured in foam films (radius 60–70 m) from 10^–5 M (0.014 wt%) polymer solution with 0.1 M NaCl is positive at thicknesses from about 800 down to 460 . The electrostatic repulsion is negligible while the contribution of van der Waals attraction is small (within 15%). Therefore a positive surface force component predominates. Most probably it arises from steric interactions between the hydrophilic polyethylene oxide tails of the polymer. The dynamic method appears to be a suitable technique for exploring the stabilization of foam films from ABA copolymers.     

Electrical Conductance Studies in Aqueous Solutions with Ascorbate Ions

Conductivity measurements in dilute aqueous solutions of L-ascorbic acid, sodium-L-ascorbate, magnesium-L-ascorbate, calcium-L-ascorbate and ferrous-L-ascorbate were performed in the (288.15 to 323.15) K temperature range. The limiting molar conductances of the ascorbic anion, λ^∘(HAsc⁻, T), and the dissociation constants of ascorbic acid, K(T), were derived by the use of the Debye-Hückel equation for the activity coefficients and the Onsager and Quint and Viallard conductivity equations.     

Equilibrium studies of Mn(II), Mg(II), Ca(II), Sr(II) and Ba(II) withp-fluoro-,p-chloro-,p-bromo-,p-methyl-benzoylacetones and 1-(4-fluorophenyl)-1,3-pentanedione

The rawpH-data, obtained from the potentiometric titrations of the titled ligands with NaOH in 75% (v/v) dioxane-water mixture performed at 20, 30 and 40°C at constant ionic strength (=0.1M-NaClO₄), have been adequately corrected for dilution, and solvent effects in order to evaluate thermodynamic dissociation constants. Variance of the latter as a function of temperature has also been accounted for. The differing magnitudes of thermodynamic dissociation constants of the titled ligands have been explained on the basis of the non coplanar orientation of the phenyl ring in the ligands and a comparison has been made with those of unsubstituted benzoylacetone, dibenzoylmethane and acetylacetone.Following similar technique, thermodynamic stepwise and overall formation constants of the titled metal-ligand systems have been obtained and the results correlated with ligand basicity inverse metal crystal radii and second potentials of metals. Decrease in the free enthalpy (–G) of complexation reaction has also been evaluated.

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Untersuchung der Gleichgewichte von Mn(II), Mg(II), Ca(II), Sr(II) und Ba(II) mit p-Fluor-, p.-Chlor-, p-Brom-, p-Methyl-benzoylaceton und 1-(4-Fluorphenyl)-1,3-pentanedion

Zusammenfassung Aus der potenitometrischen Titration der Titelverbindungen mit NaOH in 75 (v/v) Dioxan—Wasser bei, 20, 30 und 40°C bei konstanter Ionenstärke (=0,1M-NaClO₄) wurden die thermodynamischen Dissoziationskonstanten ermittelt. Verdünnungs-, Lösungsmittel-und Temperatureffekte wurden berücksichtigt. Die unterschiedlichen Dissoziationskonstanten werden mit der Nichtplanarität des Phenylrings in den Liganden erklärt. Außerdem wurden die Komplexbildungskonstanten bestimmt; sie sind in die Diskussion miteinbezogen.

     

Study on the stability of noradrenaline and on the determination of its acidity constants

Noradrenaline is a catecholamine which has been largely recognised to play a very important role in biological systems. In view of the neurotransmitter's alleged importance, this work aimed at showing the influence of time on its spectral behaviour using different analytical methods and determining its acidity constants through spectrophotometric titration and by the so-called point-by-point analysis, where the samples are freshly prepared for each pH value investigated at the instant required. Because the catecholamines are light-sensitive and likely to react with the oxygen in the surrounding air, both methods used preclude its incidence onto the samples being analysed under the presence of a nitrogen atmosphere maintained over the solutions. The constants obtained through point-by-point analysis were log beta1 = 30.71+/-0.16, log beta2 = 22.00+/-0.15 and log beta3 = 11.69+/-0.16.