This paper deals with one of our research directions on software tools enhancing self-learning in computer science disciplines. In this study, we discuss an experiment on relational data bases learning using a tool for the edition and automated evaluation of learners‟ solutions given as relational algebra trees. Indeed, in addition to the interest of the graphic languages for any training, the ...

The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It led to the prediction and the observation of physical phenomena which confirm the important role of general relativity in physics. The understanding of the do...

We consider edge colourings of the complete r-uniform hypergraph K (r) n on n vertices. How many colours may such a colouring have if we restrict the number of colours locally? The local restriction is formulated as follows: for a fixed hypergraph H and an integer k we call a colouring (H, k)-local if every copy of H in the complete hypergraph K (r) n receives at most k different colours. We in...

Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as b...

Symmetry classification of two-body central potentials in a two-particle Schrödinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four different classes as for the point transformations. Thus in this problem contact transformations are not essentially different from point transformations. We have als...

Following the approach of Gromov and Witten [3, 20], we define invariants under deformation of stongly semipositive real symplectic manifolds provided essentially that their real locus is Pin. These invariants provide lower bounds in real enumerative geometry, namely for the number of real rational J-holomorphic curves which realize a given homology class and pass through a given real configura...

In this note, we discuss the complex-algebraic approach to the modular functor constructed from a finite group G. This can be considered as a “baby” case of a more interesting situation, modular functors related to orbifold conformal field theories, which we intend to pursue in a subsequent papers. We start by recalling some basic facts about the modular functor; detailed exposition can be foun...

Synonyms Transform methods, separation of variables, eigenfunction expansions, spectral representations. Transform methods replace differentiation in one variable with multiplication by a " transform " variable. Description The utility of transform methods essentially stems from the fact that they replace differentiation in one variable with multiplication by a transform variable. Hence, a PDE ...