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 ...

In [8], Dontchev and Hager have shown that a monotone set-valued map defined from a Banach space to its dual which satisfies the Aubin property around a point (x, y) of its graph is actually single-valued in a neighbourhood of x. We prove a result which is the counterpart of the above for quasimonotone set-valued maps, based on the concept of single-directional property. As applications, we pro...

The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose that a non-negative monotone submodular function f : Z+ → R+ is given via an evaluation oracle. Assume further that f satisfies the diminishing return propert...

Abstract Is it always beneficial to create a new relationship (have follower/friend) in social network? This question can be formally stated as property of the centrality measure that defines importance actors network. Score monotonicity means adding an arc increases score target arc; rank improves relatively remaining nodes. It is known most centralities are both and monotone on directed, stro...

The employment of proper codings, such as the base-2 coding, has allowed to establish the universal approximation property of Boolean functions: if a sufficient number b of inputs (bits) is taken, they are able to approximate arbitrarily well any real Borel measurable mapping. However, if the reduced set of monotone Boolean functions, whose expression involves only and and or operators, is cons...

A continuum means comp6lct, connected metric space. A hereditarily unicoherent and arcwise connected continuum is called a dendroid. It follows that it is hereditarily decomposable ([2], (47), p. 239). A hereditarily unicoherent and hereditarily decomposable continuum is said to be a A.-dendroid. Thus, every dendroid is a }.-dendroid and an arcwise connected A.-dendroid is a dendroid. Note that...

We prove a removal lemma for infinitely-many forbidden hypergraphs. It affirmatively settles a question on property testing raised by Alon and Shapira (2005) [2, 3]. All monotone hypergraph properties and all hereditary partite hypergraph properties are testable. Our proof constructs a constant-time probabilistic algorithm to edit a small number of edges. It also gives a quantitative bound in t...

In this paper we provide necessary and sufficient conditions for the distribution of demand in the future to be stochastically increasing in the demand that has been observed in the past. We base our analysis on the multiperiod inventory model examined by Eppen and Iyer (1997). In the process of establishing the necessary and sufficient conditions we develop a new property called the sequential...

For a graph property P, the edit distance of a graph G from P, denoted EP(G), is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying P. What is the furthest graph on n vertices from P and what is the largest possible edit distance from P? Denote this maximal distance by ed(n,P). This question is motivated by algor...

High utility itemsets mining extends frequent pattern mining to discover itemsets in a transaction database with utility values above a given threshold. However, mining high utility itemsets presents a greater challenge than frequent itemset mining, since high utility itemsets lack the anti-monotone property of frequent itemsets. Transaction Weighted Utility (TWU) proposed recently by researche...