If & ^ 1 for each v, then by reasoning analogous to that of the preceding example, it may be shown, for any set (a), that there is no point p such that tp implies that log St(a, £) is concave. Hence Theorem 4 applies to all such functions log St(a, £). However, for this case the conclusion of the general theorem is weaker than the...

G. SZEKERES We shall deal with real functions which have continuous second derivatives in some open interval (a, b), — » ^a(x) is called convex (from below) if "(x)^0 in I(<p). If <p(x) is monotone increasing and convex, and ^i(x) is monotone increasing and concave such that the range of <p(x) is contained ...

We study the minimum concave cost flow problem over a two-dimensional grid network (CFG), where one dimension represents time (1 ≤ t ≤ T ) and the other dimension represents echelons (1 ≤ l ≤ L). The concave function over each arc is given by a value oracle. We give a polynomial-time algorithm for finding the optimal solution when the network has a fixed number of echelons and all sources lie a...

We study the problem of how to detect interesting objects appeared in a given image I Our approach is to treat it as a function approximation problem based on an over redundant basis Since the ba sis a library of image templates is over redundant there are in nitely many ways to decompose I To select the best decomposition we rst propose a global optimization procedure that considers a concave ...

Murota et al. have recently developed a theory of discrete convex analysis which concerns M -convex and L-convex functions on jump systems. We introduce here a family of M -concave functions arising naturally from polynomials (over the field of Puiseux series) with prescribed non-vanishing properties. This family contains several of the most studied M -concave functions in the literature. We al...

We study the problem of how to detect \interesting objects" appeared in a given image, I. Our approach is to treat it as a function approximation problem based on an over-redundant basis. Since the basis (a library of image templates) is over-redundant, there are innnitely many ways to decompose I. To select the \best" decomposition we rst propose a global optimization procedure that considers ...

Suppose the agent has preferences over consumption and labor represented by the utility function u (c, l) that we assume separable and quasi-linear such that u (c, l) = c v (l). We assume that v0 (l) > 0 and v00 (l) 0. Each agent earns income z = nl when supplying l hours of labor and consumes c = nl T (nl) after taxes. Individuals are heterogeneous in the salary n that represents their type an...

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