To attack the Four Color Problem, in 1880, Tait gave a necessary and sufficient condition for plane triangulations to have a proper 4-vertex-coloring: a plane triangulation G has a proper 4-vertex-coloring if and only if the dual of G has a proper 3-edge-coloring. A cyclic coloring of a map G on a surface F 2 is a vertex-coloring of G such that any two vertices x and y receive different colors ...

Using Laskar’s frequency map analysis, we investigate the long-term stability of Venus Trojan orbits. By measuring the diffusion rate of proper frequencies, we outline in phase space the most stable region. It is located between 5 and 10 in proper inclination with libration amplitudes ranging from 50 to 110 . The proper eccentricity is lower than 0.13. The stable region is surrounded by secular...

background: production of solid waste is the result of the human’s different activities that today has changed a lot in comparison to the past due to the changing life styles and pervasive expansion. in isfahan province lots of wastes are produced daily. due to the importance of the waste and its recycling, the purpose is determining the production scopes of different wastes in order to find a ...

In [1], by using Fredholm index we developed a version of Quillen’s geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In [19], by using Quinn’s Transversality Theorem [23], it has been shown that this cobordism theory has a gra...

Abstract moment maps arise as a generalization of genuine moment maps on symplectic manifolds when the symplectic structure is discarded, but the relation between the mapping and the action is kept. Particular examples of abstract moment maps had been used in Hamiltonian mechanics for some time, but the abstract notion originated in the study of cobordisms of Hamiltonian group actions. In this ...

This paper presents a novel approach for creating a reliable map of an arbitrary indoor environment with a mobile robot. The map consists of a topological component representing rooms and doors and a grid map for obstacles within each room. Both maps are built via a SLAM approach based on distance measurements of two planar laser scanners. In order to get a proper overview of room and furniture...

Let f : X → Y be a Cohen-Macaulay map of finite type between Noetherian schemes, and g : Y ′ → Y a base change map, with Y ′ Noetherian. Let f ′ : X → Y ′ be the base change of f under g and g : X → X the base change of g under f . We show that there is a canonical isomorphism θ g : g ∗ ωf ≃ ωf ′ , where ωf and ωf ′ are the relative dualizing sheaves. The map θ g f is easily described when f is...

The phase flow method was originally introduced in [28] which can efficiently solve autonomous ordinary differential equations. In [13], the method was generalized to solve Hamiltonian system where the Hamiltonian function was discontinuous. However, both these methods require phase flow map constructed on an invariant manifold. This can increase computational cost when the invariant domain is ...