New results on q-positivity

In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original bilinear form. The notion of q-positivity generalizes the classical notion of the monotonicity of a subset of a product of a Banach space and its dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss concepts generalizing the representations of monotone sets by convex functions, as well as the number of maximally q-positive extensions of a q-positive set. We also discuss symmetrically self-dual Banach spaces, in which we add a Banach space structure, giving new characterizations of maximal q-positivity. The paper finishes with two new examples.Comment: 18 page

Response of CdWO4 crystal scintillator for few MeV ions and low energy electrons

The response of a CdWO4 crystal scintillator to protons, alpha particles, Li, C, O and Ti ions with energies in the range 1 - 10 MeV was measured. The non-proportionality of CdWO4 for low energy electrons (4 - 110 keV) was studied with the Compton Coincidence Technique. The energy dependence of the quenching factors for ions and the relative light yield for low energy electrons was calculated using a semi-empirical approach. Pulse-shape discrimination ability between gamma quanta, protons, alpha particles and ions was investigated.Comment: 20 pages, 8 figs, accepted in Nucl. Instrum. Meth.

Ordered Incidence geometry and the geometric foundations of convexity theory

An Ordered Incidence Geometry, that is a geometry with certain axioms of incidence and order, is proposed as a minimal setting for the fundamental convexity theorems, which usually appear in the context of a linear vector space, but require only incidence, order (and for separation, completeness), and none of the linear structure of a vector space.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42995/1/22_2005_Article_BF01227810.pd

Bounding separable recourse functions with limited distribution information

The recourse function in a stochastic program with recourse can be approximated by separable functions of the original random variables or linear transformations of them. The resulting bound then involves summing simple integrals. These integrals may themselves be difficult to compute or may require more information about the random variables than is available. In this paper, we show that a special class of functions has an easily computable bound that achieves the best upper bound when only first and second moment constraints are available.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44185/1/10479_2005_Article_BF02204821.pd