Since primary and secondary school, I have been very interested in mathematics and I had good marks without too much effort. So, it was natural for me to continue ... and stay in the area of mathematics.

To my uncle Georges Zangreyanogo who helped and supported me throughout my schooling.

To my family who spared no effort for my success in studies up to this level. To my uncle Georges Zangreyanogo who helped and supported me throughout my schooling. To the memory of my brother Victor.

My sincere thanks to Professor Albert Ouédraogo who kindly presided over the jury. We warmly thank Professor Daouda Sangaré for having accepted being a referee of our work and being a member of the jury. To Professor Akry Koulibaly who has supervised this work with great patience, competence and most of all advice, we simply say thank you, unable to find better ways to express our deep gratitude, as well as to Madame Koulibaly for her encouragement and her many advices. Our thanks are addressed equally to all the professors at the Faculty of Science, to my fellow students, for their advice, their encouragement and their constructive criticisms and to all those who in one way or another have supported this work.

We bring in this thesis our modest contribution to the study of Lie triple superalgebras. It is subdivided into three chapters. The first chapter recalls the definitions and properties known about superalgebras and Malcev superalgebras. In the second chapter, after having given the definitions of the notion of Lie triple superalgebras and of Lie triple supersystems, we study the weak super-representation of a Malcev superalgebra. We show that a Malcev super-representation is a weak super-representation, we give a condition for a weak super-representation to be a Malcev super-representation and we establish the cohomology groups related to the weak super-representation. In the third chapter, we define the notion of a projective relation between Lie triple superalgebras. We study the family of Lie superalgebras of projectivity of a Lie triple superalgebra. We show that a Lie superalgebra admits a family of Lie superalgebras of projectivity and we give a condition that a Lie triple superalgebra is in projective relation with a triple Lie super-system.

Good governance is generally accepted as the exercise of political, economic and administrative authority to manage the affairs of a State at all levels, with the participation of citizens through the framework of their expression. There are four areas of governance, namely: political governance, including security and human rights, administrative governance, economic governance and local governance.

Corruption has spread to all sectors of the economy of our country, including transport. However, hope is allowed since the highest authorities have for major concern to work to eradicate it. ... We must track down corruption wherever it occurs. ... We are waiting for proposals for relevant solutions in the direction of eradicating corruption to guide policy makers.

We extend Okikiolu's Campbell-Hausdorff formula for pseudo-differential operators to operators with non scalar leading symbol. For this we introduce conditioned traces for which we provide explicit formulae. This Campbell-Hausdorff formula is then applied to extend known local formulae for the multiplicative anomaly of zeta- and other regularised determinants.

This thesis is devoted to the study of the canonical trace and two types of determinants: on the one hand a determinant associated with the canonical trace on a class of pseudodifferential operators and on the other hand determinants associated with regularized traces. In the first part, in odd dimension, we revisit the uniqueness of the canonical trace on the space of classical pseudodifferential operators of odd class before extending it to log-polyhomogeneous operators of odd class. We classify the traces on the algebra of classical pseudodifferential operators of odd class and order zero. In the second part, we establish the locality of the multiplicative anomaly of the weighted determinant and the zeta determinant. These results are obtained thanks to the study of the locality of the weighted trace of the operator L(A;B). We then derive from these results the local expression of the multiplicative anomalies in terms of the noncommutative residue. In the third part, we classify multiplicative determinants on the grounds of the classification of traces on classical pseudodifferential operators of odd class and order zero in odd dimension. We also define the symmetrized determinant obtained from the canonical trace applied to the symmetrized logarithm of an odd class operator in odd dimension. We show the multiplicativy of this determinant under some restrictions on the spectral cuts of the operators.

... as you should expect, there are not many women professors in Africa. The African Mathematical Union Commission on Women in Mathematics in Africa, which is a commission of the African Mathematical Union, founded in 1986, is intended to correct and improve this weakness. Therefore, the AMUCWMA aims at:

1. generating activities and programs meant to encourage women to study and make careers in Mathematical Sciences;
2. mobilizing young girls all over the continent to show more interest in  Mathematics;
3. preparing and updating a directory of Women in Mathematics from all over the continent;
4. commissioning studies on various topics on Women in Mathematics in Africa; and
5. co-operating with other organizations with similar objectives.

As President of the African Mathematical Union Commission on Women in Mathematics in Africa, I was invited to the last congress of European Women in Mathematics in Barcelona. After several discussions with Professor Marie-Francoise Roy, the convenor of European Women in Mathematics, we decided to organize a workshop for African women mathematicians.

In Africa, among the holders of a doctorate in Mathematics, 11% are women. Some of the classical problems that have contributed to the scarcity and also underperformance of women in mathematics in some regions of Africa are given as follows:

1. The cultural and traditional bias: there is a bias in such developing countries and belief that mathematics and hard sciences are for boys and men, and you see it everywhere in implicit or explicit ways.

2. The lack of networking and mutual support between junior and the few senior women mathematicians. Sometimes lack of this association and networks where women can encourage one another, forces women to try join the male associations where there is limited acceptance and less opportunities for women to improve on their profession al development and growth as leaders in their own field.

3. The lack of role models and lack of a structured mentorship programme for young girls and emerging researchers within mathematics. These could involve matching interested young girls in mathematics and science to a senior mentor but such programmes work if they have structure and are funded. This is linked to the net for better networking amongst potential women mentors and developing such instruments.

4. The lack of government strategies and policies to promote mathematics and increase access for all genders. If governments have science policy and strategies which promote mathematics, for instance, then funding will be attached to programmes to ensure there are opportunities for bursaries, training and skills development. The link between maths and success in schooling and developing the economy have to be visible at national level and contribute to resourcing schools and learning institutions within every African region.