Prediction of latent heat of vaporization of multicomponent mixtures

A very simple method has been developed for predicting the differential latent heat of vaporization involved in vapor-liquid equilibria of multicomponent mixtures. The technique uses the UNIFAC method for predicting activity coefficients.In order to establish this method, 88 binary systems and 13 ternary systems, both nonazeotropic and azeotropic, were tested successfully. On the basis of the 101 systems investigated, the mean overall deviation between the observed and predicted values was found to be 4.6%. Despite the fact that the majority of the systems tested were azeotropic, a consequence of the small amount of data available for the differential heats of nonazeotropic systems, the method proposed is equally applicable to nonazeotropic systems.For azeotropic mixtures, it is possible to predict the latent heat (integral or differential) by means of an analytical equation which involves only the parameters of Antoine's equation, with a mean overall deviation of 6.1%.From the differential heats obtained by the proposed method, it is possible to calculate integral heats by applying equations derived here which relate these quantities.     

Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem

The Fermat—Weber location problem is to find a point in ⁿ that minimizes the sum of the weighted Euclidean distances fromm given points in ⁿ . A popular iterative solution method for this problem was first introduced by Weiszfeld in 1937. In 1973 Kuhn claimed that if them given points are not collinear then for all but a denumerable number of starting points the sequence of iterates generated by Weiszfeld's scheme converges to the unique optimal solution. We demonstrate that Kuhn's convergence theorem is not always correct. We then conjecture that if this algorithm is initiated at the affine subspace spanned by them given points, the convergence is ensured for all but a denumerable number of starting points.     

Improved algorithms for several network location problems with equality measures

We consider single facility location problems with equity measures, defined on networks. The models discussed are, the variance, the sum of weighted absolute deviations, the maximum weighted absolute deviation, the sum of absolute weighted differences, the range, and the Lorenz measure. We review the known algorithmic results and present improved algorithms for some of these models.     

Aggregation error for location models: survey and analysis

Location problems occurring in urban or regional settings may involve many tens of thousands of “demand points,” usually individual private residences. In modeling such problems it is common to aggregate demand points to obtain tractable models. We survey aggregation approaches to a large class of location models, consider and compare various aggregation error measures, identify some effective (and ineffective) aggregation error measures, and discuss some open research areas.     

Wetting properties of the multiscaled nanostructured polymer and metallic superhydrophobic surfaces

A superhydrophobic surface is produced from industrial grade polymer materials. The surface comprises partly disordered triple-scaled arrays of polyvinylidene fluoride (PVDF) globules. An inherently superhydrophobic metallic surface is produced with polymer template. The mathematical model based on the Cassie-Baxter hypothesis of air trapping under a water drop is built, which gives the apparent contact angle on the manifold-scaled interface. The presence of several scales itself is not a sufficient condition of hydrophobicity of inherently wettable surfaces. The geometrical features favoring the increase of the vapor-water interface fraction are necessary for this phenomenon.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.     

Cyclic permutations and nearly symmetric integer vectors

Given an integer vector x^T=(x₁,…,x_n) with the property x₁>x₂>? >x_n>0, it is shown that the convex hull of the n cyclic permutations of x contains all the nearly symmetric integer vectors majorized by x. A generalization to noninteger vectors and an application to a class of integer symmetric optimization problems are also given.     

1,1‐Diamino‐2,2‐dinitroethylenes are always zwitterions

The nitration of tetraiodoethylene (7) yields 1,1‐diiodo‐2,2‐dinitroethylene (8). The latter reacts with alkylamines 9 or alkyldiamines 11 to give the corresponding acyclic 1,1‐diamino‐2,2‐dinitroethylenes 10 or their cyclic analogs 12, respectively. On the basis of liquid and solid‐state ¹³C and ¹⁵N NMR data, x‐ray analysis and ab initio calculations, we suggest that the title compounds are always zwitterionic and that the C_A–C_N bond is not a true double bond. Copyright © 2012 John Wiley & Sons, Ltd.