Abstract:
Several types of solid acid catalysts were prepared based on oxides like (ZrO_{2}, TiO_{2}, HfO_{2}, MCM-41 and SBA-15), using two main preparation methods: the precipitation and the sol-gel methods. Each catalyst was subjected to two types of impregnations: sulfate ions using sulfuric acid as precursor and niobium using niobium oxalate as precursor. These prepared catalysts were tested in the etherification reaction of 2-naphtol, where the catalysts showed both acidic and redox properties. The acidic character was manifested through the formation of 2-butoxynaphtalene (with moderate yields) when oxide is sulfated, and the redox character (when impregnated with niobium) manifested through the formation of the interesting product 2-ethylnaphtofuran (with low yields) and other products that were a result of oxidative coupling of two 2-naphtol molecules (binol and acetal of binol). However despite the effort, several attempts to increase the yield of 2-ethylnaphtofuran did not work. All products prepared were obtained in pure form and characterized by 1H and 13C NMR, GC and MS.

Abstract:
Several types of solid acid catalysts were prepared based on oxides like (ZrO_{2}, TiO_{2}, HfO_{2}, MCM-41 and SBA-15). Each catalyst was subjected separately to two types of impregnations: sulfate ions and niobium. The catalytic activity of these solids was tested in the oxidation reaction of 1-octanol. These catalysts showed acidic and redox characters. MCM-41 and SBA-15 materials showed higher redox catalytic activities through the formation of (octyl octanoate, peroxyacetal and octanal). Our interest was focused on obtaining the ester (octyl octanoate) with high yields.

Abstract:
We study the action of irreducible derivations X on some Hilbert's quasi-regular algebras QRH of germes at 0 of analytic functions on (U,0), where U is a semi-algebraic set: that is, we show that these algebras are X-finite or locally X-finite, ie. the degre of the integral projection is finite by restriction to fibers of elements of QRH, and the differential ideals are noetherian or locally noetherian. We then give an important application of this material to the Hilbert's 16th problem about limit cycles: there is no accumulation of limit cycles on hyperbolic polycycles, inside compact analytic families of vector fields on the 2-sphere. This is a highly non trivial result as it includes the case of polycycle that is an accumulation of cycles.

Abstract:
Let dH be a Hamiltonian one form on the real plane, of degre d. We show that, if H is a Morse function, generic at infinity, then there exists a number N(d) depending only on d, such that every small perturbation of dH has at most N(d) limit cycles on the hole real plane, assuming that it's of degre at most d, and that it has a non vanishing Abelian integral along real cycles of dH.

Abstract:
For $m \in \mathbb{N}$, we determine the irreducible components of the $m$-th Jet Scheme of a complex branch $C$ and give formulas for their number $N(m)$ and for their codimensions, in terms of $m$ and the generators of the semigroup of $C$. This structure of the Jet Schemes determines and is determined by the topological type of $C$.

Abstract:
For $m\in \IN, m\geq 1,$ we determine the irreducible components of the $m-th$ jet scheme of a toric surface $S.$ For $m$ big enough, we connect the number of a class of these irreducible components to the number of exceptional divisors on the minimal resolution of $S.$

Abstract:
Using the theory of jet schemes, we give a new approach to the description of a minimal generating sequence of a divisorial valuations on $\textbf{A}^2.$ For this purpose, we show how one can recover the approximate roots of an analytically irreducible plane curve from the equations of its jet schemes. As an application, for a given divisorial valuation $v$ centered at the origin of $\textbf{A}^2,$ we construct an algebraic embedding $\textbf{A}^2\hookrightarrow \textbf{A}^N,N\geq 2$ such that $v$ is the trace of a monomial valuation on $\textbf{A}^N.$ We explain how results in this direction give a constructive approach to a conjecture of Teissier on resolution of singularities by one toric morphism.

Abstract:
For $m\in \mathbb{N}, m\geq 1,$ we determine the irreducible components of the $m-th$ jet scheme of a normal toric surface $S.$ We give formulas for the number of these components and their dimensions. When $m$ varies, these components give rise to projective systems, to which we associate a weighted graph. We prove that the data of this graph is equivalent to the data of the analytical type of $S.$ Besides, we classify these irreducible components by an integer invariant that we call index of speciality. We prove that for $m$ large enough, the set of components with index of speciality $1,$ is in 1-1 correspondance with the set of exceptional divisors that appear on the minimal resolution of $S.$

Abstract:
this paper uses a sample of brazilian firms in the period 1997 to 2001 to investigate the effectiveness of alternative corporate governance mechanisms. the data show that firms can commit to protect their minority shareholders by issuing level ii adr' s or joining the novo mercado. in particular, firms with level ii adrs and firms in the novo mercado have larger stock returns in times of turmoil, and they are more likely to pay dividends. the study shows, however, that changes in corporate law affect the ability of private contracts like adrs to protect minority shareholders. as such, firms cannot completely overcome weaknesses in the brazil's legal system that harm minority shareholders.

Abstract:
In this paper, we study a new model of nonlocal geometric equations which appears in tomographic reconstruction when using the level-set method. We treat two additional difficulties which make the work original. On one hand, the level lines do not evolve along normal directions, and the nonlocal term is not of "convolution type". On the other hand, the speed is not necessarily bounded compared to the nonlocal term. We prove a existence and uniqueness results of our model.