In this paper, we define a new discrete curvature on two and three dimensional triangulated manifolds, which is modification of the well-known these manifolds. The definition more natural respects scaling exactly same way as Gauss does. Moreover, can be used to approximate surfaces. Then study corresponding constant problem, called combinatorial Yamabe by versions Ricci flow Calabi for surfaces...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

The paper briefly describes a basic set of special combinatorial engineering frameworks for solving complex problems in the field of hierarchical modular systems. The frameworks consist of combinatorial problems (and corresponding models), which are interconnected/linked (e.g., by preference relation). Mainly, hierarchical morphological system model is used. The list of basic standard combinato...

The ecologist H. T. Odum introduced a principle of physics, called Maximum Empower, in order to explain self-organization in a system (e.g. physical, biological, social, economical, mathematical, ...). The concept of empower relies on emergy, which is a second notion introduced by Odum for comparing energy systems on the same basis. The roots of these notions trace back to the 50’s (with the wo...

The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times, often rivaling and sometimes surpassing more tradit...