cost optimization of the reinforced concrete cantilever soil retaining wall of a given height satisfying some structural and geotechnical design constraints is performed utilizing harmony search and improved harmony search algorithms. the objective function considered is the cost of the structure, and design is based on aci 318-05. this function is minimized subjected to design constraints. a n...

In any Coxeter group, the set of elements whose principal order ideals are boolean forms a simplicial poset under the Bruhat order. This simplicial poset defines a cell complex, called the boolean complex. In this paper it is shown that, for any Coxeter system of rank n, the boolean complex is homotopy equivalent to a wedge of (n − 1)-dimensional spheres. The number of such spheres can be compu...

We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d + 3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88–91] and the second author [...

We consider an infeasible-interior-point algorithm, endowed with a nite termination scheme, applied to random linear programs generated according to a model of Todd. Such problems have degenerate optimal solutions, and possess no feasible starting point. We use no information regarding an optimal solution in the initialization of the algorithm. Our main result is that the expected number of ite...