Some elementary general principles of convex analysis

General principles of spectroscopy and spectroscopic analysis

where Z is the refractive index defined as the ratio of the speed of light in a vacuum to the speed of light in the given medium, date from this period. In more modern times, infrared, ‘‘beyond red,’’ radiation was discovered by William Herschel in 1800. He found that the temperature recorded by a thermometer increased from the violet to the red in the visible region. Going beyond the red he fo...

Some properties of convex hulls of integer points contained in general convex sets

In this paper, we study properties of general closed convex sets that determine the closed-ness and polyhedrality of the convex hull of integer points contained in it. We first present necessary and sufficient conditions for the convex hull of integer points contained in a general convex set to be closed. This leads to useful results for special class of convex sets such as pointed cones, stric...

Some Principles of Stratification: A Critical Analysis

McMullen's Conditions and Some Lower Bounds for General Convex Polytopes

Convex polytopes are the d-dimensional analogues of 2-dimensional convex polygones and 3-dimensional convex polyhedra. A polytope is a bounded convex set in R d that is the intersection of a finite number of closed halfspaces. The faces of a polytope are its intersections with supporting hyperplanes. The/-dimensional faces are called the i-faces and f i ( P ) denotes the number of i-faces of a ...

General Truthfulness Characterizations via Convex Analysis

We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, and a number of related settings that do not quite qualify as one or the other. Our main result is a characterization theorem, yielding characterizations for all of these settings, including a new characterization of scoring rules for non-convex sets of distributions. We generalize this model to ...