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

We provide cubature formulas for the calculation of derivatives of expected values in the spririt of Terry Lyons and Nicolas Victoir. In financial mathematics derivatives of option prices with respect to initial values, so called Greeks, are of particular importance as hedging parameters. The proof of existence of Cubature formulas for Greeks is based on an argument, which leads to the calculat...

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...

The design of underground spaces is mainly carried out using empirical, analytical, and numerical methods. The convergence confinement method (CCM) is an analytical technique that is widely utilized in analyzing the stability of underground spaces. However, the main challenge in the stability analysis is the selection of an accurate constitutive model for rock mass, and particularly, its post-f...