We show that the number of topologically different orthographic views of a polyhedral terrain with n edges is O(n 5 +~), and that the number of topologically different perspective views of such a terrain is O(nS+0, for any e > 0. Both bounds are almost tight in the worst case. The proofs are simple consequences of the recent almost-tight bounds of [11] on the complexity of lower envelopes in hi...

A binary three-dimensional (3D) image I is well-composed if the boundary surface of its continuous analog is a 2D manifold. In this paper, we present a method to locally “repair” the cubical complex Q(I) (embedded in R3) associated to I to obtain a polyhedral complex P (I) homotopy equivalent to Q(I) such that the boundary surface of P (I) is a 2D manifold (and, hence, P (I) is a well-composed ...

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, ...

In this study, we propose a robust bi-objective optimization model of the green closed-loop supply chain network considering presorting, heterogeneous transportation system, and carbon emissions. The proposed is an uncertain mixed-integer linear that maximizes profit minimizes emissions by costs, selling price, approach implemented using combined interval polyhedral, “Interval+ Polyhedral,” unc...

The traditional use of organic chemistry as the mainstay of all aspects of contemporary biomedical chemistry has provided truly miraculous results. However, advances in the closely related area of aromatic polyhedral borane chemistry (polyhedral ions, carboranes, metallacarboranes, metallaboranes and other heteroatom derivatives) has now provided the basic discoveries necessary for the assembly...

In the paper [9], Mangasarian introduced a new approach in order to give dual characterizations for different set containment problems. He succeeded to characterize the containment of a polyhedral set in another polyhedral set and in a reverse convex set defined by convex quadratic constraints and the containment of a general closed convex set in a reverse convex set defined by convex nonlinear...

Extant research has examined the process of decision making under uncertainty, specifically in situations of ambiguity. However, much of this work has been conducted in the context of semantic and low-level visual processing. An open question is whether ambiguity in social signals (e.g., emotional facial expressions) is processed similarly or whether a unique set of processors come on-line to r...

We propose and characterize a model of preferences over acts such that the decision maker prefers act f to act g if and only if Eμφ(Eπu ◦ f ) ≥ Eμφ(Eπu ◦ g), where E is the expectation operator, u is a von Neumann–Morgenstern utility function, φ is an increasing transformation, and μ is a subjective probability over the set Π of probability measures π that the decision maker thinks are relevant...