Some basic concepts for functions defined on subsets of the unit sphere, such as s-directional derivative, s-gradient and s-Gateaux s-Frechet differentiability etc, are introduced investigated. These different from usual ones Euclidean spaces, however, results obtained here very similar. Then, applications, we provide some criterions s-convexity spheres which improvements or refinements known r...

Solution symmetries in integer linear programs often yield long Branch-and-Bound based solution processes. We propose a method for finding elements of the permutation group of solution symmetries, and two different types of symmetry-breaking constraints to eliminate these symmetries at the modelling level. We discuss some preliminary computational results.

Community detection is one of the most investigated problems in the field of complex networks. Although several methods were proposed, there is still no precise definition of communities. As a step towards a definition, I highlight two necessary properties of communities, separation and internal cohesion, the latter being a new concept. I propose a local method of community detection based on t...

We give geometric and algorithmic criterions in order to have of a proper Galois closure for a codimension one germ of quasi-homogeneous foliation. We recall this notion recently introduced by B. Malgrange, and describe the Galois envelope of a group of germs of analytic diffeomorphisms. The geometric criterions are obtained from transverse analytic invariants, whereas the algorithmic ones make...

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...

in recent decades, as a result of population growth, industrial developments, scarcity of sources, etc. more attention has been paid to spatial planning. spatial planning needs the consideration of different goals, scenarios, criterions and constraints, which leads us to the usage of spatial multi-criteria decision analysis (mcda) methods. the mail goal of this research is to develop a novel mo...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

in a military organization, the role of transportation should be much more strong and strategic character for the organization. in this context, the evaluation of operating ability of transportation and eliminate defects and problems, can help the managers to improve performance and increase the effectiveness and efficiency of transportation in the assigned missions. in this study, a model is p...