Thermodynamics of molecular interactions in ethyl iodide+toluene mixtures

The excess Gibb's free energy of mixing, G^E, for ethyl iodide+toluene at 25°C have been obtained from the measured vapor pressuure data. The H^E and G^E values for ethyl iodide+toluene are positive throughout the ethyl iodide concentration range and G^E>H^E. The results have been analyzed in terms of Flory and ideal associated model theory of nonelectrolyte solutions. It has been observed that the ideal associated model approach which assumes the presence of AN and A₂B molecular species describes well (within±10 J-mol^–1 in the worst case) the general dependence of H^E on X_A (mole fraction of ethyl iodide) over the whole composition range for ethyl iodide+toluene mixtures. The equilibrium constants for A+A AB and 2A+BA₂B reactions along with the enthalpies of formation of AB and A₂B molecular species have been calculated.     

A study of preferential solvation of N-alkyl pyridinium iodides in mixed solvents containing acetonitrile

The charge transfer (CT) band maximum of N-alkyl pyridinium iodide (NAPI) has been studied as a function of the composition of binary mixed dipolar aprotic solvents. The deviation from linearity of the energy maximum (E₁₂) and the mole fraction (of a component solvent) plot is explained as due to a preferential solvation by the more polar cosolvent in the binary mixture. The extent of preferential solvation has been observed to vary with the composition, the maximum being towards the less-polar end. The role of hydrogen bond donating ability of a solvent in preferential solvation is discussed.     

Superized Troesch complexes and cohomology for strict polynomial superfunctors

We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We apply these complexes to construct injective resolutions of the even and odd Frobenius twist functors, to investigate the structure of the Yoneda algebra of the Frobenius twist functor, and to compute other extension groups between strict polynomial superfunctors. By an equivalence of categories, this also provides cohomology calculations in the category of left modules over Schur superalgebras.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Trigonometric wavelets for Hermite interpolation

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.

     

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

Quantitative weight of evidence method for combining predictions of quantitative structure-activity relationship models

ABSTRACT

A method for combining statistical-based QSAR predictions of two or more binary classification models is presented. It was assumed that all models were independent. This facilitated the combination of positive and negative predictions using a quantitative weight of evidence (qWoE) procedure based on Bayesian statistics and the additivity of the logarithms of the likelihood ratios. Previous studies combined more than one prediction but used arbitrary strengths for positive and negative predictions. In our approach, the combined models were validated by determining the sensitivity and specificity values, which are performance metrics that are a point of departure for obtaining values that measure the weight of evidence of positive and negative predictions. The developed method was experimentally applied in the prediction of Ames mutagenicity. The method achieved a similar accuracy to that of the experimental Ames test for this endpoint when the overall prediction was determined using a combination of the individual predictions of more than one model. Calculating the qWoE value would reduce the requirement for expert knowledge and decrease the subjectivity of the prediction. This method could be applied to other endpoints such as developmental toxicity and skin sensitisation with binary classification models.     

A view and a review of the melting of alkali metal halide crystals

Summary A representational model, proposed to account for the physical changes that accompany the melting of alkali halides, was described in Part 1 [1]. The liquid is portrayed as undergoing continual dynamic structural reorganization of its constituent ions between individual small domains, zones of various regular, crystal-type arrays. These alternative arrangements are stabilized by the enthalpy of melting, which, in liquids, relaxes the restriction for solids that only the single, most stable, crystal structure can be present. The dynamic character of the melt accounts for its fluid character and the loss of long-range order [1, 2]. This model is extended here to consider the phase diagrams of binary, common ion, alkali halide mixtures comprehensively reviewed in [3]. Factors determining whether each of these yields a eutectic, or a solid solution, on cooling are discussed and several trends in the 70-phase diagrams are identified. Eutectic formation, involving maintenance of the liquid state below the melting points of the pure components, is ascribed to the participation, in an extended dynamic equilibrium, of additional domains having the regular structures characteristic of double salts. The known crystalline double binary halides [3], Li/Cs or Rb/F, Cl, Br or I, melt at temperatures well below those of the simpler pure component salts. It is concluded that the set/liq model for melting, proposed in [1, 2], accounts for some important properties of the phase diagrams presented in [3].     

Solubility of benzil in binary alkane + dibutyl ether solvent mixtures. Comparison of predictive expressions derived from the nearly ideal binary solvent model

Experimental solubilities are reported for benzil dissolved in six binary mixtures containing dibutyl ether with hexane, heptane, octane, cyclohexane, methylcyclohexane, and 2,2,4-trimethylpentane at 25°C. Results of these measurements are compared to the predictions of equations developed previously for solubility in systems of nonspecific interactions. The most successful equation in terms of goodness of fit involved a volume fraction average of the excess Gibbs energies relative to the Flory-Huggins model, and predicted the experimental solubilities in the six systems studied to within an overall average absolute deviation of 3.4% and with a maximum deviation of 6.0%.