Contact numbers are natural extensions of kissing numbers. In this paper we give estimates for the number of contacts in a totally separable packing of n unit balls in Euclidean d-space for all n > 1 and d > 1.

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A finite set of vectors ${\cal S} \subseteq {R}^n$ is called a simplex iff ${\cal S}$ is linearly dependent but all its proper subsets are independent. This concept arises in particular from stoichiometry. We are interested in this paper in the number of simplexes contained in some ${\cal H} \subseteq R^n$, which we denote by $simp({\cal H})$. This investigation is particularly interesting for ${\cal H}$ spanning $R^n$ and containing no collinear vectors. Our main result shows that for any ${\cal H} \subseteq R^3$ of fixed size not equal to 3, 4 or 7 and such that ${\cal H}$ spans $R^3$ and contains no collinear vectors, $simp({\cal H})$ is minimal if and only if ${\cal H}$ is contained in two planes intersecting in ${\cal H}$, and one of which is of size exactly 3. The minimal configurations for $|{\cal H}|=3,4,7$ are also completely described. The general problem for $R^n$ remains open.

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Flexible agile and extreme project management methods have become increasingly popular among practitioners, particularly in the IT and R&D sectors. In contrast to the theoretically and algorithmically well-established and developed trade-off and multimode methods applied in traditional project management methods, flexible project scheduling methods, which are applied in agile, hybrid, and especially extreme project management, lack a principled foundation and algorithmic handling. The aim of this paper is to fill this gap. We propose a matrix-based method that provides scores for alternative project plans that host flexible task dependencies and undecided, supplementary task completion while also handling the new but unplanned tasks. In addition, traditional multimode resource-constrained project scheduling problems are also covered. The proposed method can bridge the flexible and traditional approaches.