The most promising and dominant data format for data processing and representation on the Internet is the semistructured data form termed XML. XML data has no fixed schema; it evolved and is self describing which results in management difficulties compared to, for example, relational data. It is therefore a major challenge for the database community to design query processing techniques and sto...

We solve the problem of computing the residual reliability (the RES problem) for all classes of P-threshold graphs for which efficient structural characterizations based on decomposition to indecomposable components have been established. In particular, we give a constructive proof of existence of linear algorithms for computing residual reliability of pseudodomishold, domishold, matrogenic and...

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.

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...

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we also propose a natural generalis...

Refinement operators for theories avoid the problems related to the myopia of many relational learning algorithms based on the operators that refine single clauses. However, the non-existence of ideal refinement operators has been proven for the standard clausal search spaces based on 0-subsumption or logical implication, which scales up to the spaces of theories. By adopting different generali...

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...