In conclusion, I may point out that Theorem II may be generalized by a weakening of the hypothesis (d) . (1) In the first place, continuity of [a, g] f with respect to the pair of variables a, /3 may be replaced by upper semi-continuity . This generalization requires no change in the proof . (2) This continuity (or upper semi-continuity) with respect to (a, /3) is used only to show that the set...

In some past works by the author and collaborators, the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed. Generally, the ageing function turns out to be a semi-copula. Here we focus attention on the special class of survival models whose ageing function is actually a copula. For pairs of models in this class we define a notion...

The paper deals with the propagation of singularities of semi-convex functions. We obtain lower bounds on the degree of the singularities and on the size of the singular set in a neighborhood of a singular point. These results apply to viscosity solutions of HamiltonJacobi-Bellman equations. In particular, they provide sufficient conditions for the propagation of singularities, depending only o...

This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximizat...

We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we improve the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem. We also present a lower bound, wit...

A class of skew products over irrational rotations of the circle is defined which contains some systems which have strange nonchaotic attractors. The global attractor of these systems is characterized: it lies between an upper semi-continuous curve and a lower semi-continuous curve. With additional assumptions on the class of maps considered more detail of the attractor can be given. Mathematic...

The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients a are assumed to be measurable in one direction and have small BMO semi-norms in the other directions. For equations in a bounded domain, additionally we assume...

where x stands for the three coordinate functions, ^(w , u)} ff (#\ u), x{u, u), and X stands for their three Jacobians. Various theorems of the following general type have been proved by McShane, Caccioppoli, Cimmino, and Radó: If (i) the triples of functions xn{u , u), i = 1, 2; n = 0, 1, 2, • • • , satisfy certain conditions; (ii) the surfaces defined by x = xn(u , u), i = l,2;n = l,2, • • •...

This problem is about to schedule a number of jobs of different lengths on two uniform machines with given speeds 1 and s ≥ 1, so that the overall completion time, i.e., the makespan, is earliest possible. We consider a semi-online variant (introduced for equal speeds) by Azar and Regev, where the jobs arrive one after the other, while the scheduling algorithm knows the optimum value of the cor...