We discuss coloring and partitioning questions related to Sperner’s Lemma, originally motivated by an application in hardness of approximation. Informally, we call a partitioning of the (k − 1)-dimensional simplex into k parts, or a labeling of a lattice inside the simplex by k colors, “Sperner-admissible” if color i avoids the face opposite to vertex i. The questions we study are of the follow...

We discuss the ab initio rendering four-dimensional (4-d) spacetime of Maxwell’s equations on random (irregular) lattices. This rendering is based on casting Maxwell’s equations in the framework of the exterior calculus of differential forms, and a translation thereof to a simplicial complex whereby fields and causative sources are represented as differential p-forms and paired with the oriente...

The problem of spherical packing and the distribution points on a sphere are well-known unsolved mathematical problems. In particular, is included in list problems Steve Smale. Accordingly, significant interest for study both direct search solutions to research areas related known dense coating directly regular, irregular layered lattices, noise-resistant coding, synthesis analysis broadband si...

The dual simplex method is frequently the most efficient technique for solving linear programming (LP) problems. This thesis describes an efficient implementation of the sequential dual simplex method and the design and development of two parallel dual simplex solvers. In serial, many advanced techniques for the (dual) simplex method are implemented, including sparse LU factorization, hyper-spa...

Based on recent studies, the ethanolic extract of Kembang Bulan leaves (Tithonia diversifolia[A.Gray]) has an anti-keloid effect. This study aims to determine optimum formula for cream preparations with paraffinum liquidum, cetyl alcohol, and stearyl alcohol. Inappropriate comparison additional ingredients results in physical properties preparation becoming unstable during storage. The was obta...

This paper introduces a new shortest path simplex pivot rule choosing a subset of non-basic arcs to simultaneously enter into the basis. The term multiple pivot for this operation is used. From this concept, a generic shortest path simplex algorithm with multiple pivots is described. In addition, a simplex multiple pivot rule is provided to design a shortest path simplex algorithm requiring O(n...