We present a computer assisted proof of existence of a family of Lyapunov orbits which stretches from L2 (the collinear libration point between the primaries) up to half the distance to the smaller primary in the Jupiter-Sun planar circular restricted three body problem. We then focus on a small family of Lyapunov orbits with energies close to comet Oterma and show that their associated invaria...

We describe a set of algorithms (and corresponding codes) that serve as a basis for an automated proof of existence of a certain dynamical behaviour in a given dynamical system. In particular it is in principle possible to automatically verify the presence of complicated dynamics using these tools. The Hénon map is used to illustrate these techniques.

In 1970, E. M. Andreev published a classification of all three dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles [3]. Given a combinatorial description of a polyhedron, C, Andreev’s Theorem provides five classes of linear inequalities, depending on C, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron real...

We determine the periodic cyclic homology of the Iwahori-Hecke algebras Hq, for q ∈ C∗ not a “proper root of unity.” (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a “weakly spectrum preserving” morphism of finite type algebras induces an isomorphism in periodic cyclic ...

The Apostolic Faith Mission (AFM) of South Africa is one the largest Pentecostal churches in Africa, with other denominational like Full Gospel and Assemblies God. Since its inception 1908, AFM has been divided into four main sections, namely: black, white, mixed race Indian, for about 88 years. church followed divisions under apartheid that people according to race, colour ethnicity, white at ...

amr bayn al-amrayn (principle of middle position) is amongst the fundamentals of the shī‘ī intellectual doctrines. it is attempted in this paper to demonstrate the genuineness and integrity of the theory of amr bayn al amrayn according to the principle of unity of divine acts and autonomous creatorship of god, the original principle of causality as well as the principle of analogical gradation ...