The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary solutions as well as with their representations and the computation of their moment functions. Assuming small perturbations of the system matrix we apply perturbation techniques to find series representations of the stationary solutions and give asymptotic expansions for their first- and second-order moment functions. We illustrate the findings with a numerical example of a scalar ODE, for which the moment functions of the stationary solution still can be computed explicitly. This allows the assessment of the goodness of the approximations found from the derived asymptotic expansions.

The thesis is created in order to conduct a comparative analysis of organizational structure of the company. The parameters for comparison are determined. The first one is the comparative analysis of the Amoeba Management System with a Divisional Structure. The second one is the comparative analysis of Fractal and Matrix Organizational Structure. The conslusions of these analyzes determine the key parameters for management on the basis of the suggested organizational structure for effective management.

The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary solutions as well as with their representations and the computation of their moment functions. Assuming small perturbations of the system matrix we apply perturbation techniques to find series representations of the stationary solutions and give asymptotic expansions for their first- and second-order moment functions. We illustrate the findings with a numerical example of a scalar ODE, for which the moment functions of the stationary solution still can be computed explicitly. This allows the assessment of the goodness of the approximations found from the derived asymptotic expansions.

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Le développement de plusieurs méthodes de reconstruction quantitatives dédiées à la Tomographie par Emission Mono Photonique du petit animal a été au cœur de cette thèse. Dans cette optique, une modélisation rigoureuse par simulation Monte Carlo du processus d’acquisition du système disponible, a été mise en place et validée. La modélisation matricielle combinée à l’algorithme de reconstruction itératif OS-EM, a permis la caractérisation des performances du système. Les valeurs de sensibilité et de résolution spatiale tomographique sont respectivement de 0,027% au centre du champ de vue et de 0,87 mm. Les limitations majeures des méthodes Monte Carlo nous ont conduit à développer une génération matricielle efficace et simplifiée des effets physiques occurrents dans le sujet. Mon approche, basée sur une décomposition de la matrice système, associée à une base de données pré-calculées, a démontré un temps acceptable pour un suivi quotidien (1h), conduisant à une reconstruction d’images personnalisée. Les approximations inhérentes à l’approche mise en place ont un impact modéré sur les valeurs des coefficients de recouvrement, une correction d’environ 10% ayant été obtenue. / My thesis focuses on the development of several quantitative reconstruction methods dedicated to small animal Single Photon Emission Computed Tomography. The latter is based on modeling the acquisition process of a 4-heads pinhole SPECT system using Monte Carlo simulations.The system matrix approach, combined with the OS-EM iterative reconstruction algorithm, enabled to characterize the system performances and to compare it to the state of the art. Sensitivity of about 0,027% in the center of the field of view combined with a tomographic spatial resolution of 0,87 mm were obtained.The major drawbacks of Monte Carlo methods led us to develop an efficient and simplified modeling of the physical effects occurring in the subject. My approach based on a system matrix decomposition, associated to a scatter pre-calculated database method, demonstrated an acceptable time for a daily imaging subject follow-up (1h), leading to a personalized imaging approach. The inherent approximations of the scatter pre-calculated approach have a moderate impact on the recovery coefficients results, nevertheless a correction of about 10% was achieved.

This work deals with properties of electro insulating varnishes and composite materials. The general aim is to study the influence of nanoparticles on dielectric properties of electro insulating varnishes.

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