Mixed strategy solutions forN-person quadratic games

Mixed strategy -equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Thermodynamics of saturated lanthanide nitrate-water systems

The thermodynamic properties of saturated aqueous lanthanide nitrate solutions were determined using recently published critically evaluated solubility and activity data. The variation of the thermodynamic functions and congruent melting points as a function of atomic number are interpreted in terms of changes in inner sphere coordination number in both the solid hexahydrates and in the aquo ions, and in terms of the double-double effect.Inconsistencies in experimental solubility data are generally caused by uncertainties in solid phase composition which is shown to be due to the very small Gibbs energies accompanying transitions from stable to metastable systems differing in the number of hydrating water molecules.Presentation to First International Symposium on Solubility Phenomena, University of Western Ontario, London, Ontario, August 21–23, 1984.     

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.