In this paper, we study concave compositions, an extension of partitions that were considered by Andrews, Rhoades, and Zwegers. They presented several open problems regarding the statistical structure compositions including distribution perimeter tilt, number summands, shape graph a typical composition. We present solutions to these applying Fristedt’s conditioning device on uniform measure.

In this paper the turnpike property is established for convex optimal control problems, involving undiscounted utility function and differential inclusions defined by multi-valued mapping having convex graph. Utility function is concave but not necessarily strictly concave. The turnpike theorem is proved under the main assumption that over any given line segment, either multi-valued mapping is ...

This is a variation of the two-sided market model of [10]: Demand D is concave in D̃ in (16) of [10]. So, in (5) of [10] and after Theorem 2, take the parametric case 0 < a ≤ 1. Thus, demand D is both decreasing and concave in price p, and so the utilities (U = pD) are also concave in price. Also, herein a simpler illustrative demandresponse model is used in Appendix A and B.

w. N. Street Computer Science Department Oklahoma State University 205 Mathematical Sciences Stillwater, OK 74078 email: nstreet@es. okstate. edu The problem of assigning m points in the n-dimensional real space Rn to k clusters is formulated as that of determining k centers in Rn such that the sum of distances of each point to the nearest center is minimized. If a polyhedral distance is used, ...

The notion of Lehrer-concave integral is generalized taking instead of the usual arithmetical operations of addition and multiplication of reals more general real operations called pseudo-addition and pseudomultiplication.