Equilibria of formation and dehydration of the carbinolamine intermediate in the reaction of benzaldehyde with hydrazine

Measurement of polarographic limiting currents at equilibria made it possible at pH 3-7 to simultaneously determine concentrations of benzaldehyde, of its hydrazone and of the carbinolamine derivative. The dependence of concentration of carbinolamine at equilibrium on pH indicated presence of its di-, mono-, and unprotonated forms. Acid dissociation constants of the formation (pK_a¹≈3.2) of the diprotonated form and of the dissociation of the monoprotonated form of carbinolamine (pK_a²≈4.7) were estimated. The equilibrium constants of formation (K₁) and dehydration (K₂) of the carbinolamine intermediate were determined.     

Copper(II) complexes of imino-bis(methyl phosphonic acid) with some bio-relevant ligands. Equilibrium studies and hydrolysis of glycine methyl ester through complex formation

Binary and ternary complexes of Cu(II) involving imino-bis(methyl phosphonic acid) (IdP) abbreviated as H₄A and some selected bio-ligands, amino acids, peptides and DNA constituents (L), were examined. Cu(II) forms CuA and CuAH complexes with IdP. Ternary complexes are formed in a stepwise mechanism whereby iminodiphosphonic acid binds to Cu(II), followed by coordination of amino acid, peptide or DNA. The concentration distribution of the various complex species has been evaluated. The kinetics of base hydrolysis of glycine methyl ester in the presence of Cu(II)-IdP was studied in aqueous solution at different temperatures, and in dioxane-water solutions of different compositions at 25°C. The activation parameters are evaluated and discussed.     

Dynamics of a two-strain vaccination model for polio

A new deterministic model for the transmission dynamics of two strains of polio, the vaccine-derived polio virus (VDPV) and the wild polio virus (WPV), in a population is designed and rigorously analysed. It is shown that Oral Polio Vaccine (OPV) reversion (leading to increased incidences of WPV and VDPV strains), together with the combined effect of vaccinating a fraction of the unvaccinated susceptible and missed susceptible children, could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. Furthermore, the model undergoes competitive exclusion, where the strain with the higher reproduction number (greater than unity) drives the other (with reproduction number less than unity) to extinction. In the absence of OPV reversions (leading to the co-existence of both strains in the population), it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated reproduction number is less than unity. Numerical simulations of the model suggest that the model undergoes the phenomenon of competitive exclusion, where the strain with the higher reproduction number (greater than unity) drives the other to extinction. Furthermore, co-existence of the two strains is feasible if their respective reproduction number are equal or approximately equal (and greater than unity).     

Stabilities and coordination modes of histidine in copper(II) mixed-ligand complexes with ethylenediamine,diethylenetriamine or N,N,N′,N″,N″-pentamethyldiethylenetriamine in aqueous solution

Solution equilibrium studies on the Cu(II)–polyamine–histidine ternary systems (polyamine: ethylenediamine (en), diethylenetriamine (dien), N,N,N′,N″,N″-pentamethyldiethylenetriamine (Me₅dien)) have been performed by pH-potentiometry, UV–Vis spectrophotometry and EPR methods. The obtained results suggest the formation of the mixed-ligand complexes with [Cu(A)(His)]⁺ stoichiometry in all studied systems. Additionally, in the systems with dien and Me₅dien protonated [Cu(A)(H–His)]²⁺ species also exists in acid solution. Our spectroscopic results indicate the tetragonal geometry for the [Cu(en)(His)]⁺, the geometry slightly deviated from square pyramidal for the [Cu(dien)(His)]⁺ and strongly deviated from square pyramidal towards trigonal bipyramidal for the [Cu(Me₅dien)(His)]⁺ species. The coordination modes in these mixed-ligand complexes are discussed.     

A SIRS epidemic model with infection-age dependence

Based on J. Mena-Lorca and H.W. Hethcote's epidemic model, a SIRS epidemic model with infection-age-dependent infectivity and general nonlinear contact rate is formulated. Under general conditions, the unique existence of its global positive solutions is obtained. Moreover, under more general assumptions than the existing, the existence and asymptotical stability of its equilibria are discussed. In the end, the condition on the stability of endemic equilibrium is verified by a special model.     

Azeotropic behaviour of (benzene + cyclohexane + chlorobenzene) ternary mixture using chlorobenzene as entrainer at 101.3 kPa

In this paper, the azeotropic behaviour of the (benzene + cyclohexane + chlorobenzene) ternary mixture was experimentally investigated with the aim of enhancing the knowledge for the feasible use of chlorobenzene as an entrainer for the azeotropic distillation of the binary azeotrope. Such a study has not been reported in the literature to the best of the authors’ knowledge. (Vapour + liquid) equilibria data for (benzene + cyclohexane + chlorobenzene) at 101.3 kPa were obtained with a Othmer-type ebulliometer. Data were tested and considered thermodynamically consistent. The experimental results showed that this ternary mixture is completely miscible and exhibits an unique binary homogeneous azeotrope, an unstable node at the conditions studied, and the propitious topological characteristics (residual curve map and relative volatility) to be separated. Satisfactory results were obtained for the correlation of equilibrium compositions with the UNIQUAC activity coefficients model and also for prediction with the UNIFAC method. In both cases, low root mean square deviations of the vapour mole fraction and temperature were calculated. The capability of chlorobenzene as a modified distillation agent at atmospheric condition is discussed in terms of the thermodynamic topological analysis. A conceptual distillation scheme with reversed volatility is proposed to separate the azeotropic mixture. In order to reduce the operational cost requirements of the sequence of columns proposed, the range for optimal reflux and the ratio for feed flow conditions were studied.     

The complementary unboundedness of dual feasible solution sets in convex programming

F.E. Clark has shown that if at least one of the feasible solution sets for a pair of dual linear programming problems is nonempty then at least one of them is both nonempty and unbounded. Subsequently, M. Avriel and A.C. Williams have obtained the same result in the more general context of (prototype posynomial) geometric programming. In this paper we show that the same result is actually false in the even more general context of convex programming — unless a certain regularity condition is satisfied.We also show that the regularity condition is so weak that it is automatically satisfied in linear programming (prototype posynomial) geometric programming, quadratic programming (with either linear or quadratic constraints),l _p -regression analysis, optimal location, roadway network analysis, and chemical equilibrium analysis. Moreover, we develop an equivalent regularity condition for each of the usual formulations of duality.Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR-73-2516.     

Equilibria effects in the dynamic ion-exchange separation of metal ions

Summary Equilibria occurring during the dynamic ion exchange separation of metal ions were examined, and their effect on the chromatography of the metal ions was evaluated. Bonded reversed-phase silica, pure organic reversed phase, and silica columns were used to differentiate between the role of silica and the reverse phase. The results show that system peaks had the most important influence on the applicability of dynamic exchangers to quantitative metal ion determinations. The response of system peaks to sample composition (pH, ionic strength, matrix effects) was complicated and could not be predicted easily. Equilibria effects that can cause analytical errors were identified and recommendations for elimination of such errors are given.Dedicated to Professor S. R. Lipsky on the occasion of his 60th birthday.     

Global asymptotic properties of an SEIRS model with multiple infectious stages

The paper presents a rigorous mathematical analysis of a deterministic model, which uses a standard incidence function, for the transmission dynamics of a communicable disease with an arbitrary number of distinct infectious stages. It is shown, using a linear Lyapunov function, that the model has a globally-asymptotically stable disease-free equilibrium whenever the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium when the threshold exceeds unity. The equilibrium is shown to be locally-asymptotically stable, for a special case, using a Krasnoselskii sub-linearity trick. Finally, a non-linear Lyapunov function is used to show the global asymptotic stability of the endemic equilibrium (for the special case). Numerical simulation results, using parameter values relevant to the transmission dynamics of influenza, are presented to illustrate some of the main theoretical results.