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Interval disjunctions arise in scheduling problems when the durations of some jobs are constrained not to overlap. Such situations are found in production scheduling, project scheduling, traffic light scheduling, etc. A general class of deterministic scheduling problems with interval disjunctions is defined in the paper. The structure of its solution set is studied in connection with the theory of potentials on a graph. A branch-and-bound algorithm is described for the case where the objective function is to minimize the total duration; optimal and heuristic variants of the algorithm are discussed. (Author).

The work deals with the circumstances under which a linear complementarity problem has a ray of complementary solutions emanating from a given complementary solution.

Problems of the form: Find w and z satisfying w = q + Mz, w = or> 0, z = or> 0, zw = 0 play a fundamental role in mathematical programming. This paper describes the role of such problems in linear programming, quadratic programming and bimatrix game theory and reviews the computational procedures of Lemke and Howson, Lemke, and Dantzig and Cottle. (Author).

Two proofs are given for a conjecture of Bela Martos concerning conditions under which a quasi-convex quadratic function of nonnegative variables is actually a pseudo-convex function. (Author).

It is well known that quasi-convexity and pseudo-convexity play a 'natural' role in nonlinear programming theory. Despite this, it is said that these notions lack utility because they have defining conditions involving infinitely many inequalities and are not easily checked. The aim of the paper is to prove that testing the quasi-convexity (pseudo-convexity) of a quadratic function on the nonnegative (semipositive) orthant can be reduced to an examination of finitely many conditions.

An unoriented, irreflexive graph G is a proper circular-arc graph if there exists a proper family F of circular arcs ('proper' means no arc of F contains another) and a 1-1 correspondence between the vertices of G and the circular arcs in F such that two distinct vertices of G are adjacent if and only if the corresponding circular arcs in F intersect. The family F is called a proper circular-arc model for G. The fundamental problem is: Given a graph G, under what conditions can one construct a proper circular-arc model for G. Two characterizations of proper circular-arc graphs are given, one in terms of a circular property of the adjacency matrix and the other in terms of forbidden subgraphs (like Kuratowski's famous characterization of planar graphs). (Author).