An adaptive and adaptable multi-purpose math-to-speech translation system is proposed in the paper. Along with the detailed presentation and design approach for the core math-to-speech translation system, exemplary output and tests are discussed. A scripting extension, providing flexibility of the system and enabling the user to adjust the output translations to his/hers preferences is incorporated into the presented solution. Some unit-tests and adaptable versions of translation rule sets are elaborated and evaluated by means of standard measures of machine translation quality. Designed as a flexible self contained solution, the presented system may be applied for various purposes such as e-learning audio presentation systems, educational tools for non-native speakers or visually impaired people, and may be easily adjusted to different national languages.

We investigate the commutators of elements of the group of infinite unitriangular matrices over an associative ring with and a commutative group of invertible elements. We prove that every unitriangular matrix of a specified form is a commutator of two other unitriangular matrices. As a direct consequence, we give a complete characterization of the lower central series of the group including the width of its terms with respect to basic commutators and Engel words. With an additional restriction on the ring , we show that the derived subgroup of coincides with the group . These results generalize the results obtained for triangular groups over a field.

Let K be a field and let UT_n(K) and T_n(K) denote the groups of all unitriangular and triangular matrices over field K, respectively. In the paper, the lattices of verbal subgroups of the above groups are characterized. Consequently, the equalities between certain verbal subgroups and their verbal width are determined. The considerations bring a series of verbal subgroups with exactly known finite width equal to 2. An analogous characterization and results for the groups of infinitely dimensional triangular and unitriangular matrices are established in the last part of the paper.