On the apparent molar volumes of nonelectrolytes in water

Apparent molar volumes of aqueous solutions of argon and xenon have been calculated using a previously developed comprehensive equation of state for nonelectrolyte systems. The equation consists of a virial expansion truncated after the fourth virial coefficient and a closed-form term approximating higher coefficients. Mixing rules are based on the composition dependence of virial coefficients, which is known from statistical mechanics. The equation accurately represents vapor-liquid and gas-gas equilibria for the Ar+H₂O and Xe+H₂O systems over wide ranges of pressure and temperature using two binary parameters. With the binary parameters determined from phase equilibrium data, the equation accurately predicts apparent molar volumes V in the near-critical and far-from-critical regions. Apart from reproducing experimental V data, the equation reveals remarkable maxima of V as a function of pressure and temperature in the near-critical region. The implications of this equation with respect to the Ar–H₂O potential are discussed via the second virial coefficient.     

Excess volumes for n-alkanols + n-alkanes I. Binary mixtures of methanol,ethanol, n-propanol,and n-butanol + n-heptane

Excess volumes V^E measured at 298.15 K in a successive-dilution dilatometer are reported for binary mixtures of the n-alkanols C₁ to C₄ + n-heptane. For ethanol +, and n-butanol + n-heptane, the measurements were extended to high dilutions of alkanol. V^E is positive for all of the mixtures but decreases rapidly in magnitude for increasing chain length of the n-alkanol. The results were used to estimate the excess partial molar volumes of the components.     

Multipeak distributions of first passage times in bistable dynamics in a model of a thermochemical system.

A master equation is used to study transitions between the stable limit cycle and stable focus in the two-variable bistable system. The distribution function of the mean first passage time between these attractors and the relative dispersion of the mean first return time from the stable focus to itself as a function of the intensity of fluctuations are calculated and discussed. A coherence resonance is observed for the return time from the focus to itself.     

Synthesis of porous vinylnaphthalene/divinylnaphthalene copolymers and their sorptive properties towards phenol and its derivatives

Four porous vinylnaphthalene/divinylnaphthalene (VN/DVN) polymers having three different nominal crosslinking degrees (60, 80 and 100 wt.%) have been synthesized using the suspension polymerization method in the presence of toluene and decane.The use of various crosslinking levels and inert diluents was aimed at changing the extent of polymeric network-diluent interactions. The resultant polymers have specific surface area in the range 450-700 m²/g depending on the DVN content. Two sets of pores were detected in all resins: one with the diameter of ≈2 nm and the second one in the range of 30-40 nm. Their sorptive properties have been studied using dilute (0.5 mmol/l) solutions of phenol and its derivatives (o-chlorophenol, 2-methylphenol, o-nitrophenol, m-nitrophenol and p-nitrophenol). It has been found that sorption, at low equilibrium concentration, follows the order: o-nitrophenol > o-chlorophenol > m-nitrophenol > o-methylphenol > p-nitrophenol > phenol. Full characteristics of the porous structure of resultant polymers was obtained by nitrogen adsorption at 77 K and their surface properties analyzed using Inverse Gas Chromatography.     

Semigroups of Jensen set-valued functions

A set-valued function F defined on a convex cone S in a real vector space X into the set n(Y) of all non-empty subsets of a real vector space Y is said to be the Jensen function iff $${1\over 2}\lbrack F(x)+F(x)\rbrack=F\lbrack{1\over 2}(x+y)\rbrack$$ for all x, y ∈ S. This note deals with iteration semigroups of Jensen set-valued functions on S.     

Affine selections of convex set-valued functions

Summary It is shown that every convex set-valued function defined on a cone with a cone-basis in a real linear space with compact values in a real locally convex space has an affine selection. Similar results can be obtained for midconvex set-valued functions.     

Natural calcium minerals as catalysts of oxidative conversion of methane

The studies of the influence of the kind of natural calcium mineral and the kind and amount of sodium promoter on the conversion degree of methane and oxygen, selectivity and yield of the oxidative conversion of methane have shown the usability of limestone as a basic component of the catalyst for this process.     

On measurable multifunctions in countably separated spaces

We use an idea of countable separability of points and sets in topological spaces to prove results on intersection of measurable multifunctions and an implicit function theorem. We generalize or extend in part some well known Himmelberg's theorems.