We prove that if a pure simplicial complex of dimension d with n facets has the least possible number of (d − 1)-dimensional faces among all complexes with n faces of dimension d, then it is vertex decomposable. This answers a question of J. Herzog and T. Hibi. In fact, we prove a generalization of their theorem using combinatorial methods.

A formal notion of a Boolean-function decomposition was introduced recently and used to provide lower bounds on various representations of Boolean functions, which are subsets of decomposable negation normal form (DNNF). This notion has introduced a fundamental optimization problem for DNNF representations, which calls for computing decompositions of minimal size for a given partition of the fu...

The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and mat...

The classical Jordan decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper explores the effective version of Jordan decomposition. We give a sufficient and necessary condition for those computable real functions of bounded variation which can be expressed as a difference of two computable increasing functi...

In the paper, a natural class of logical calculi is fixed for which we formulate the notion of a ∆–decomposable set of formulas. We demonstrate that the property of uniqueness of signature decompositions holds in those calculi of this class that have the Craig interpolation property. In conclusion, we give a sufficient condition for the ∆–decomposability property to be decidable.

In our previous work [1], a divide-and-conquer approach was proposed for cooperative tasking among multi-agent systems. The basic idea is to decompose a requested global specification into subtasks for individual agents such that the fulfillment of these subtasks by each individual agent leads to the satisfaction of the global specification as a team. It was shown that not all tasks can be deco...