Freezing temperatures of aqueous solutions of methyl formate and ethyl acetate with a variety of nonelectrolytes. Gibbs energy of interaction of the ester group with other functional groups

Freezing temperatures of dilute aqueous solutions of ethyl acetate and mixtures with myo-inositol, D-mannitol, formamide, 1,3,5-trioxane, 1,4-dioxane, acetamide, hexamethylenetetramine, and methyl formate have been measured. In addition, freezing temperatures of dilute aqueous solutions of methyl formate and mixtures with the above solutes have been measured. From these data, the pairwise molecular Gibbs energies of interaction between the molecules were calculated. Using the additivity principle, the pairwise functional group Gibbs energies of interaction were calculated for ester group interactions with a variety of other functional groups.     

Equations describing lamellar structure parameters and melting points of polyethylene-<Emphasis Type="Italic">co</Emphasis>-(butene/octene)s

Time- and temperature-dependent SAXS-experiments were used to determine the effect of octene and butene co-units on the lamellar structure and the melting properties of polyethylene. As expected, melting points decrease with increasing co-unit content, but crystal thicknesses are not affected and depend on the crystallization temperature only. Results can be cast into some simple equations which describe the dependence:

Analysis of critical points on the potential energy surface

A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L ^T gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture.     

The generalized order complementarity problem

Given an ordered Banach Space (E,K) andm functionsf ₁,f ₂,...,f _m:EE, the generalized order complementarity problem associated with {f _i} andK is to findx ₀K such thatf _i(x ₀)K,i=1,...,m, and (x ₀,f ₁(x ₀),...,f _m(x ₀))=0. The problem is shown to be equivalent to several fixed-point problems and equivalent to the order complementarity problem studied by Borwein and Dempster and by Isac. Existence and uniqueness of solutions and least-element theory are shown in the spacesC(, ) andL _p(, ). For general locally convex spaces, least-element theory is derived, existence is proved, and an algorithm for computing a solution is presented. Applications to the mixed lubrication theory of fluid mechanics are described.     

Existence of maximal points with respect to ordered bipreference relations

The maximality of a point with respect to an ordered pair of arbitrary preference relations is introduced. Necessary and sufficient conditions for the existence of maximal points are given.The authors are grateful for the referee's comments which led to an improved presentation of the paper.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

Critical Points in a Crystal and Procrystal

The critical points in the model electron density distributions of LiF, NaF, NaCl, and MgO crystals, constructed from accurate X-ray diffraction data, are determined. For LiF and MgO they are compared with those obtained from a Hartree–Fock electron density calculation. Both experiment and theory show the same type of critical points on the bond lines. The topological features in areas between structural units, where the electron density is low and near-uniform, turn out to be model dependent and cannot be established well with the data available. Topological analysis of procrystals (hypothetical systems consisting of spherical atoms or ions placed on the same sites as atoms in real crystal) show that (3, –1) critical points, usually connected with bonding interaction, are observed on interatomic lines in these nonbonded systems as well.     

Surfactants having polyfluoroalkyl chains. II. Syntheses of anionic surfactants having two polyfluoroalkyl chains including a trifluoromethyl group at each tail and their flocculation-redispersion ability for dispersed magnetite particles in water

Anionic surfactants having two polyfluoroalkyl chains per molecule, i.e. the sodium salt of bis(1H, 1H, 2H,2H-heptadeca-fluorodecyl)-2-sulfosuccinate, CF₃(CF₂)₇(CH₂)₂OCOCH₂CH(SO₃Na)COO(CH₂)₂(CF₂)₇CF₃, the sodium salt of bis(1H, 1H, 2H, 2H-tridecafluoro-octyl)-2-sulfosuccinate, CF₃(CF₂)₅(CH₂)₂OCOCH₂CH(SO₃Na)COO(CH₂)₂(CF₂)₅CF₃, and the sodium salt of bis(1H, 1H, 2H, 2H-nonafluorohexyl)-2-sulfosuccinate, CF₃(CF₂)₃(CH₂)₂OCOCH₂CH(SO₃Na)COO(CH₂)₂(CF₂)₃CF₃, have been prepared from maleic anhydride, the corresponding alcohols possessing a polyfluoroalkyl chain and sodium hydrogen sulfite. The flocculation and redispersion abilities of these surfactants for dispersed magnetic particles in water have been examined to investigate the effect of the chain length. It was found that this ability was enhanced by an increase in the chain length. The contact angles for water for pelleted surface-modified magnetite have been measured. In order to compare this ability and the contact angles, data for other fluorinated surfactant have been obtained. The Kraff point, the surface tension and the pNa of the aqueous surfactant solutions have also been measured.     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.     

Low-energy points on the sphere and the real projective plane

We present a generalization of a family of points on ${\mathbb{S}}^2$, the Diamond ensemble, containing collections of N points on ${\mathbb{S}}^2$ with very small logarithmic energy for all $N\in \mathbb{N}$. We extend this construction to the real projective plane ${\mathbb{RP}}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.