This paper studies the endogenous evolution of investment behaviour under the various macroeconomic circumstances, which might be relatively constructed by free-float, fixed and target zone regimes as the economic stability policy. It applies the issues of stock price target zone policy to a simultaneous stochastic differential equation system. We construct the stochastic macro model which utilized the basic conception of Dornbusch [1976] with the different price adjustment mechanism. In addition, we intend to apply the topological method which used by Miller and Weller [1991] to analyze the general economic property from the non-recursive model. The main purpose of this paper is to discuss how the public’s expectation affects the dynamic loci of commodity and stock price when the public agents have the perfect or imperfect credibility. We utilize this model to investigate whether stock price target zone regime will have honeymoon effect or not, when the government announce to execute the stock price target zone policy in the various situations. Moreover, we discuss whether stock price target zone can simultaneously stabilize other variables in the different situations.

1 Topological and Geometrical Combinatorics Martin Tancer Abstract The task of the thesis is to present several new results on topological methods in combinatorics. The results can be split into two main streams. The first stream regards intersection patterns of convex sets. It is shown in the thesis that finite projective planes cannot be intersection patterns of convex sets of fixed dimension which answers a question of Alon, Kalai, Matoušek and Meshulam. Another result shows that d-collapsibility (a necessary condition on properties of in- tersection patterns of convex sets in dimension d) is NP-complete for recognition if d ≥ 4. In addition it is shown that d-collapsibility is not a necessary condition on properties of intersection patterns of good covers, which disproves a conjecture of G. Wegner from 1975. The second stream considers algorithmic hardness of recognition of simplicial com- plexes embeddable into Rd . The following results are proved: It is algorithmically un- decidable whether a k-dimensional simplicial complex piecewise-linearly embeds into Rd for d ≥ 5 and k ∈ {d−1, d}; and this problem is NP-hard if d ≥ 4 and d ≥ k ≥ 2d−2 3 .

[pt] A visualização de campos vetoriais é uma componente essencial de numerosas aplicações, em particular na Visualização Científica. Porém, produzir representações de um fluxo nem sempre é uma tarefa simples, principalmente em se tratando de dados medidos, pois estes se apresentam corrompidos por ruídos. Esse trabalho apresenta uma técnica de visualização baseada em imagens auto-animadas, que expressa o movimento do fluxo à base de ilusões ópticas. A utilização de informações topológicas é proposta tanto como forma de melhorar o desempenho das técnicas existentes como na remoção de ruído, onde o conhecimento do usuário sobre o dado se torna peça fundamental no processo. / [en] Vector field visualization is an essential component of various applications, particularly in Scientific Visualization. However generating useful ow representation is not a simple task, especially when dealing with measured data which is corrupted by noise. This work presents a self-animating image visualization technique which conveys the ow movement based on optical illusions. The field s topological information is used to improve the performance of existing techniques and remove noise, where the user s knowledge of data is fundamental.

Ce mémoire est divisé en deux parties : Partie 1 : Nous obtenons des résultats d'existence pour des problèmes au limite mettant en jeu des opérateurs polyharmoniques conformément invariants. Nous nous plaçons indifféremment dans le cas d'une variété riemannienne avec ou sans bord. En particulier, nous montrons que la meilleure constante de Sobolev sur les variétés est exactement la constante euclidienne. En conséquence, nous montrons l'existence d'une solution d'énergie minimale lorsque la fonctionnelle descend en-dessous d'un seuil quantifié. Puis nous montrons l'existence de solutions de haute énergie en utilisant la méthode topologique de Coron. Nous généralisons la décomposition des suites de Palais-Smale comme somme de bulles sur une variété avec ou sans bord : il s'agit d'un résultat dans l'esprit du célèbre théorème de Struwe en 1984. Nous obtenons aussi une version du lemme de compacité-concentration de Pierre-Louis Lions sur les variétés. Partie 2 : Dans cette partie, nous effectuons une analyse de blow-up pour une équation de Hardy-Sobolev à croissance critique et à singularité évanescente au bord. En supposant que l'équation limite n'admet pas de solution minimisante, nous étudions le comportement asymptotique d’une suite de solutions de l'équation perturbée. Ici, la perturbation est la singularité à l'origine. Dans un premier temps, nous obtenons un contrôle ponctuel optimal de la suite de solutions. Dans un second temps, nous obtenons des informations précises sur le point d'explosion en utilisant une identité de Pohozaev / This memoir can be divided into two parts: Part 1: In this part we obtain some existence results for conformally invariant polyharmonic boundary value problems on a compact Riemannian manifold with or without boundary. In particular we show that the best constant of the Sobolev embedding on manifolds is same as the euclidean one, and as a consequence prove the existence of minimum energy solutions when the energy functionnal goes below a quantified threshold. Next we show the existence of high energy solution using the topological method of Coron. We generalize the decomposition of Palais Smale sequences as a sum of bubble on manifolds with or without boundary, a result in the spirit of Struwe's celebrated 1984 result and also an extension of PL Lions concentration compactness result on manifolds. Part2: In this part we do a blow-up analysis of the nonlinear elliptic Hardy-Sobolev equation with critical growth and vanishing boundary singularity. We assume that our equation does not admit minimising solutions, and study the asymptotic behaviour of a sequence of solution to the perturbed equation. Here the perturbation is the singularity at the origin. First we obtain optimal pointwise controlon the sequence and then obtain more precise informations on the localization of the blow-up point using the Pohozaev identity

The thesis deals with qualitative properties of solutions of singular initial value problems for ordinary differential and integrodifferential equations which occur in the theory of linear and nonlinear electrical circuits and the theory of therminionic currents. The research is concentrated especially on questions of existence and uniqueness of solutions, asymptotic estimates of solutions and modications of Adomian decomposition method for singular initial problems. Solution algoritms are derived for scalar differential equations of Lane-Emden type using Taylor series and modication of the Adomian decomposition method. For certain classes of nonlinear of integrodifferential equations asymptotic expansions of solutions are constructed in a neighbourhood of a singular point. By means of the combination of Wazewski's topological method and Schauder xed-point theorem there are proved asymptotic estimates of solutions in a region which is homeomorphic to a cone having vertex coinciding with the initial point. Using Banach xed-point theorem the uniqueness of a solution of the singular initial value problem is proved for systems of integrodifferential equations of Volterra and Fredholm type including implicit systems. Moreover, conditions of continuous dependence of a solution on a parameter are determined. Obtained results are presented in illustrative examples.