Using language of dg PROPs we give a new short proof of existence of star products on (formal) germs of Poisson manifolds.

Using language of dg PROPs we give a new proof of existence of star products on (formal) germs of Poisson manifolds.

In 1984, Raoult proposed a formalization of graph rewritings using pushouts in the category of graphs and partial functions. This note generalizes his method and formulates algebraic graph structure to introduce a more general framework for graph rewritings and to give a simple proof of existence theorem of pushouts using relational calculus.

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...

Abstract The existence of monopoles is a characteristic signature Kaluza–Klein multidimensional theories. topology these solutions extremely interesting. dipole solution, which we have associated to monopole–anti-monopole bound state, the leitmotiv this investigation. in its lowest energy here call also monopolium, electromagnetically inert free space interacting only gravitationally. Monopoliu...

Let G be a string graph (an intersection graph of continuous arcs in the plane) with m edges. Fox and Pach proved that G has a separator consisting of O(m √ logm) vertices, and they conjectured that the bound of O( √ m) actually holds. We obtain separators with O( √ m logm) vertices. Let G = (V,E) be a graph with n vertices. A separator in G is a set S ⊆ V of vertices such that there is a parti...