The research in this thesis involves the synthesis and characterization of nanoparticle catalysts for oxidation reactions. It includes two projects: 1) polymer-stabilized Au, Pd and bimetallic AuPd nanoparticle catalysts for alcohol oxidation reactions, and 2) oxidative stabilities and catalytic activities of thiolate- and dithiolate-protected Au monolayer-protected clusters (MPCs).<p>n the first project, alcohol oxidations under mild conditions using polyvinylpyrrolidone (PVP)-stabilized Au, Pd and bimetallic AuPd nanoparticle catalysts in aqueous solutions have been investigated. The catalytic activities of the nanoparticles towards the oxidation of benzyl alcohol, 1-butanol, 2-butanol, 2-buten-1-ol and 1,4-butanediol indicate that bimetallic 1:3 Au:Pd nanoparticles have higher catalytic activities than Au, Pd and other bimetallic AuPd nanoparticles, and that selectivities towards specific products can often be tuned using bimetallic particles. In addition, advantages and disadvantages for the use of such nanoparticle catalysts as mild, environmentally-friendly oxidation catalysts have been examined. This work has recently been published in the Journal of Catalysis.<p>In the second project, 1-dodecanethiolate-, dithiolate-, and 1:1 mixed 1-dodecanethiolate/dithiolate-protected Au MPCs have been synthesized and their thermal stability, oxidative stability in the presence of oxygen and cyanide anions have been studied. These systematic investigations reveal the stability of Au MPCs can be tuned by choosing different thiolate ligands and oxidation conditions. Partially-oxidized thiolate-protected Au MPCs which have substrate-accessible surfaces and are stabilized by residual thiolate ligands show indications they will be promising catalysts. The catalytic activities of 1-dodecanethiolate-, dithiolate-, and 1:1 mixed 1-dodecanethiolate/dithiolate-protected Au MPCs for catalytic 4-nitrophenol reduction with sodium borohydride were investigated, and all the Au MPCs showed high catalytic activity for this reaction.

The research in this thesis involves the synthesis and characterization of nanoparticle catalysts for oxidation reactions. It includes two projects: 1) polymer-stabilized Au, Pd and bimetallic AuPd nanoparticle catalysts for alcohol oxidation reactions, and 2) oxidative stabilities and catalytic activities of thiolate- and dithiolate-protected Au monolayer-protected clusters (MPCs).<p>n the first project, alcohol oxidations under mild conditions using polyvinylpyrrolidone (PVP)-stabilized Au, Pd and bimetallic AuPd nanoparticle catalysts in aqueous solutions have been investigated. The catalytic activities of the nanoparticles towards the oxidation of benzyl alcohol, 1-butanol, 2-butanol, 2-buten-1-ol and 1,4-butanediol indicate that bimetallic 1:3 Au:Pd nanoparticles have higher catalytic activities than Au, Pd and other bimetallic AuPd nanoparticles, and that selectivities towards specific products can often be tuned using bimetallic particles. In addition, advantages and disadvantages for the use of such nanoparticle catalysts as mild, environmentally-friendly oxidation catalysts have been examined. This work has recently been published in the Journal of Catalysis.<p>In the second project, 1-dodecanethiolate-, dithiolate-, and 1:1 mixed 1-dodecanethiolate/dithiolate-protected Au MPCs have been synthesized and their thermal stability, oxidative stability in the presence of oxygen and cyanide anions have been studied. These systematic investigations reveal the stability of Au MPCs can be tuned by choosing different thiolate ligands and oxidation conditions. Partially-oxidized thiolate-protected Au MPCs which have substrate-accessible surfaces and are stabilized by residual thiolate ligands show indications they will be promising catalysts. The catalytic activities of 1-dodecanethiolate-, dithiolate-, and 1:1 mixed 1-dodecanethiolate/dithiolate-protected Au MPCs for catalytic 4-nitrophenol reduction with sodium borohydride were investigated, and all the Au MPCs showed high catalytic activity for this reaction.

The aim of this work is to generalize the results given by Domitrz, Janeczko and Zhitomirskii in [10]. In this article they classify in the symplectic manifold (R2, w) where w = dx1 &Lambda; dx2 + · · · + dx2n-1 &Lambda; dx2n is the symplectic form given by Darbouxs Theorem, all the set which are symplectomorphic to a fixed quasi homogeneous curve . To do this classification they defined the algebraic restrictions. We develop a new method called the method of exact algebraic restrictions and show that this classification is solved for the non quasi homogeneous case N = {(x1, x2) = x&ge;3 = 0} in the symplectic manifold (C2, w ), where f(x1, x2) = x41 + x52 + x21 x32. / Este trabalho tem como objetivo generalizar os resultados feitos por Domitrz, Janeczko e Zhitomirskii em [10]. Neste artigo eles clasificaram na variedade simplética (R2, w) onde w = dx1 &Lambda; dx2 + ... + dx2n-1 &Lambda; dx2n é a forma simpléctica dada pelo Teorema de Darboux, todos os conjuntos que são simplectomorfos a uma curva quase homogênea fixada . Para fazer a classificação eles definem as restrições algebraicas. Nós desenvolvemos um novo método o qual chamamos de método das restrições algebraicas exatas e provamos que a classificação é resolvida para o caso não quase homogêneo N = {f(x1, x2) = x&ge;3 = 0} na variedade simplética (C2, w ), onde f(x1, x2) = x41 + x52 + x21 x32.

The aim of this work is to generalize the results given by Domitrz, Janeczko and Zhitomirskii in [10]. In this article they classify in the symplectic manifold (R2, w) where w = dx1 &Lambda; dx2 + · · · + dx2n-1 &Lambda; dx2n is the symplectic form given by Darbouxs Theorem, all the set which are symplectomorphic to a fixed quasi homogeneous curve . To do this classification they defined the algebraic restrictions. We develop a new method called the method of exact algebraic restrictions and show that this classification is solved for the non quasi homogeneous case N = {(x1, x2) = x&ge;3 = 0} in the symplectic manifold (C2, w ), where f(x1, x2) = x41 + x52 + x21 x32. / Este trabalho tem como objetivo generalizar os resultados feitos por Domitrz, Janeczko e Zhitomirskii em [10]. Neste artigo eles clasificaram na variedade simplética (R2, w) onde w = dx1 &Lambda; dx2 + ... + dx2n-1 &Lambda; dx2n é a forma simpléctica dada pelo Teorema de Darboux, todos os conjuntos que são simplectomorfos a uma curva quase homogênea fixada . Para fazer a classificação eles definem as restrições algebraicas. Nós desenvolvemos um novo método o qual chamamos de método das restrições algebraicas exatas e provamos que a classificação é resolvida para o caso não quase homogêneo N = {f(x1, x2) = x&ge;3 = 0} na variedade simplética (C2, w ), onde f(x1, x2) = x41 + x52 + x21 x32.

Les grassmanniennes symplectiques impaires sont une famille d'espaces quasi-homogènes très proches des grassmanniennes symplectiques de par leur construction et leurs propriétés. Dans ce travail, j'étudie leur cohomologie classique et quantique. Pour les grassmanniennes symplectiques impaires de droites, j'obtiens une règle de Pieri quantique ainsi qu'une présentation de l'anneau de cohomologie quantique. J'en déduis la semi-simplicité de cet anneau et je détermine une collection exceptionnelle complète pour la catégorie dérivée, ce qui me permet de vérifier pour cet exemple une conjecture de Dubrovin. Dans le cas général, je démontre un principe quantique-classique pour certains invariants de Gromov-Witten de degré un. Sous réserve de l'énumérativité des invariants de degré supérieur, je prouve que la règle de Pieri quantique est entièrement déterminée par le calcul des invariants de degré un. / Odd symplectic Grassmannians are a family of quasi-homogeneous spaces that are closely related to symplectic Grassmannians by their construction and properties. The goal of this work is to study their classical and quantum cohomology. For odd symplectic Grassmannians of lines, I obtain a quantum Pieri rule and a presentation of the quantum cohomology ring. I prove the semisimplicity of this ring and determine a full exceptional collection for the derived category, which enables me to check a conjecture of Dubrovin in this example. In the general case, I prove a quantum-to-classical principle for some degree one Gromov-Witten invariants. Assuming higher-dimensional Gromov-Witten invariants are enumerative, I conclude that the quantum Pieri rule is entirely determined by the knowledge of degree one invariants.

This work is devoted to investigating the algebraic and analytic integrability of first order polynomial partial differential equations via an understanding of the well-developed area of local and global integrability of polynomial vector fields. In the view of characteristics method, the search of first integrals of the first order partial differential equations P(x,y,z)∂z(x,y) ∂x +Q(x,y,z)∂z(x,y) ∂y = R(x,y,z), (1) is equivalent to the search of first integrals of the system of the ordinary differential equations dx/dt= P(x,y,z), dy/dt= Q(x,y,z), dz/dt= R(x,y,z). (2) The trajectories of (2) will be found by representing these trajectories as the intersection of level surfaces of first integrals of (1). We would like to investigate the integrability of the partial differential equation (1) around a singularity. This is a case where understanding of ordinary differential equations will help understanding of partial differential equations. Clearly, first integrals of the partial differential equation (1), are first integrals of the ordinary differential equations (2). So, if (2) has two first integrals φ1(x,y,z) =C1and φ2(x,y,z) =C2, where C1and C2 are constants, then the general solution of (1) is F(φ1,φ2) = 0, where F is an arbitrary function of φ1and φ2. We choose for our investigation a system with quadratic nonlinearities and such that the axes planes are invariant for the characteristics: this gives three dimensional Lotka– Volterra systems x' =dx/dt= P = x(λ +ax+by+cz), y' =dy/dt= Q = y(µ +dx+ey+ fz), z' =dz/dt= R = z(ν +gx+hy+kz), where λ,µ,ν 6= 0. v Several problems have been investigated in this work such as the study of local integrability and linearizability of three dimensional Lotka–Volterra equations with (λ:µ:ν)–resonance. More precisely, we give a complete set of necessary and sufficient conditions for both integrability and linearizability for three dimensional Lotka-Volterra systems for (1:−1:1), (2:−1:1) and (1:−2:1)–resonance. To prove their sufficiency, we mainly use the method of Darboux with the existence of inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable. Also, more general three dimensional system have been investigated and necessary and sufficient conditions are obtained. In another approach, we also consider the applicability of an entirely different method which based on the monodromy method to prove the sufficiency of integrability of these systems. These investigations, in fact, mean that we generalized the classical centre-focus problem in two dimensional vector fields to three dimensional vector fields. In three dimensions, the possible mechanisms underling integrability are more difficult and computationally much harder. We also give a generalization of Singer’s theorem about the existence of Liouvillian first integrals in codimension 1 foliations in Cnas well as to three dimensional vector fields. Finally, we characterize the centres of the quasi-homogeneous planar polynomial differential systems of degree three. We show that at most one limit cycle can bifurcate from the periodic orbits of a centre of a cubic homogeneous polynomial system using the averaging theory of first order.

Ce travail a pour but d'étudier la tolérance à l'impact de 3 stratifiés carbone/époxy soumis simultanément à différents types de chargements hygrothermiques et mécaniques. Ces stratifications présentant des caractéristiques mécaniques globales particulières d'isotropie, il s'agit ici de déterminer l'influence de la séquence d'empilement sur le développement de l'endommagement lors d'un impact. Dans un premier temps, la cinétique de vieillissement hygrothermique des trois stratifications est étudiée et analysée. Ensuite, leur tolérance à un unique impact ainsi qu'à des impacts répétés est évaluée. L'endommagement résultant de ces impacts est analysé par contrôle ultrasonore. La morphologie générale et l'amplitude de l'endommagement dans la profondeur des matériaux sont mises en relation avec les propriétés mécaniques et la séquence d'empilement spécifique à chaque stratifié. Dans un deuxième temps, l'influence combinée de plusieurs sollicitations est étudiée. Différents scénarii associant un vieillissement hygrothermique ainsi qu'un ou deux impacts sont mis en oeuvre. L'endommagement résultant est mis en rapport avec les temps relatifs de vieillissement et la position des impact durant le cycle de vieillissement. Ensuite, l'influence d'une précharge de traction sur la tolérance à l'impact est mise en évidence. Un montage spécifique a été conçu et fabriqué pour réaliser ces tests. Enfin, l'association d'un vieilllissement hygrothermique et d'une précharge de traction est abordée afin d'identifier la sollicitation la plus pénalisant en terme de tolérance et d'impact / This study examines impact damage processes in three types of CFRP composite materials simultaneously subjected to different hygrothermal and mechanical loading conditions. The composite structures tested are chosen for having particular global isotropic responses when loaded, the aim being to ascertain the exact influence of lay-up sequence on impact damage propagation. The work is presented in four main sections. Firstly by establishing hygrothermal ageing dynamics for the three composite structure types and their behaviour when impacted once or several times ; impact damage is measured and analysed using ultrasonic method. The extent and general morphology of the damage through the material thickness is correlated with mechanical properties and lay-up sequence specific to each material. Secondly the influence of simultaneous load combinations is examined. These include different durations of hygrothermal ageing associated with single or double impacts.The resulting damage incurred is analysed with respect to overall ageing time and time during the ageing cycle when the impact was applied. Thirdly the effect of tensile loading during impact on damage within the material was studied. This was achieved using a specially designed test apparatus that allows loading and impacting conditions to be independently modified. By associating a high-speed digital camera to film specimen impacts it is possible to evaluate a relationship between overall composite specimen stiffness and the impact damage. Finally, in order to identify the most unfavourable situation with regard to impact damage resistance an association between hygrothermal ageing and an applied tensile load is examined