Concave compositions are compositions (i.e. ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function disco...

We study a class of left-invertible operators which we call weakly concave operators. It includes the and some subclasses expansive strict $m$ -isometries with $m > 2$ . prove Wold-type decomposition for also obtain Berger–Shaw-type theorem analytic finitely cyclic The proofs these results rely heavily on spectral dichotomy provides fairly close relationship, written in terms reciprocal auto...

There is a fundamental relation between the capacity of a set and energy integrals of probability measures supported on that set. If the capacity is small the energy integral will be large; in particular sets of capacity zero cannot support probability measures of …nite energy. Here we develop similar ideas relating capacity to Carleson measures. We show that if a set has small capacity then an...

We treat uncertain linear programming problems by utilizing the notion of weighted an-alytic centers and notions from the area of multi-criteria decision making. After introducing ourapproach, we develop interactive cutting-plane algorithms for robust optimization, based on concaveand quasi-concave utility functions. In addition to practical advantages, due to the flexibility of our...

In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...