We study the problem of placing guard towers on a terrain such that the terrain can be seen from at least one tower. This problem is important in many applications, and has an extensive history in the literature (known as, e.g., multiple observer siting). In this paper, we consider the problem on polyhedral terrains, and we allow the guards to see only a fixed fraction of the terrain, rather th...

in this paper a certain class of polyhedral semigroups which has a presentation $$ is examined‎. ‎the completeness of the presentation and solvability of word problem of this class of semigroups is determined‎. ‎moreover the combinatorial distance between two words is determined‎.

 Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...

I’m trying to understand which Riemannian manifolds can be Lipschitz approximated by polyhedral spaces of the same dimension with curvature bounded below. The necessary conditions I found consist of some special inequality for curvature at each point (the geometric curvature bound). This inequality is also sufficient condition for local approximation. I conjecture that it is also a sufficient c...

iii Acknowledgments iv Chapter 1. A Hierarchy of Polyhedral Arrangements 1 1.1. Polyhedral Arrangements 1 1.2. Polyhedral Dissections 1 1.3. Polyhedral Complexes 5 1.4. Polyhedral Triangulations 8 1.5. A Hierarchy of Polyhedral Arrangements 9 Chapter 2. Computation on Polyhedral Arrangements 12 2.1. Bucket Method 12 2.2. Sage Code 13 2.3. Experiments 16 Chapter 3. Regular Triangulations 22 3.1....

The linear viscoelastic behavior of thermoplastic hybrid inorganic-organic polymers synthesized through radical copolymerization of styrene and styryl-based polyhedral oligosilsesquioxane (POSS), R7(Si8O12) (C6H4CHdCH2), with R ) isobutyl (iBu), cyclopentyl (Cp), and cyclohexyl (Cy), was studied to reveal a significant influence of the vertex group, R. The glass transition temperatures were fou...