Dans cette thèse, on a d’abord considéré une équation d'onde. On a premièrement montré que l’équation est bien-posée presque sûre par la méthode de décomposition de fréquence de Bourgain sous l’hypothèse de régularité que s > 2(p−3)/(p-1). Ensuite, nous avons réduit de cette exigence de régulation à (p-3)/(p−1) en appelant une estimation probabiliste a priori. Nous considérons également l’approximation des solutions obtenues ci-dessus par des solutions lisses et la stabilité de cette procédure d’approximation. Et nous avons conclu que l’équation est partout mal-posée dans le régime de super-critique. Nous avons considéré ensuite l’équation du faisceau quintique sur le tore 3D. Et nous avons montré que cette équation est presque sûr bien-posée globalement dans certain régimes de super-critique. Enfin, nous avons prouvé que la mesure de l’image de la mesure gaussienne sous l’application de flot de l’équation BBM généralisé satisfait une inégalité de type log-Sobolev avec une petit peu de perte de l’intégrabilité. / In this thesis, we consider a wave equation. We first showed that the equation is almost sure global well-posed via Bourgain’s high-low frequency decomposition under the regularity assumption s > 2(p−3)/(p−1). Then we lowered down this regularity requirement to be (p−3)/(p−1) by invoking a probabilistic a priori estimate. We also consider approximation of the above achieved solutions by smooth solutions and the stability of this approximating procedure. And we concluded that this equation is everywhere ill-posed in the super-critical regime. Next, we considered the quintic beam equation on 3D torus. And we showed that this equation is almost sure global well-posed in certain super-critical regime. Lastly, we proved that the image measure of the Gaussian measure under the generalized BBM flow map satisfies a log-Sobolev type inequality with a little bit loss of integrability.

[pt] Há alguns anos temos visto um grande progresso na resolução de problemas antigos na teoria das superfícies mínimas. Dentre esse problemas estão as conjecturas de Calabi-Yau, que datam dos anos 60 do século passado. A primeira delas afirmava que não existiam superfícies mínimas completas contidas em uma bola de R3, e a segunda que todas as superfícies mínimas completas tinham uma projeção ilimitada em cada eixo. Neste trabalho pretendemos revisar dois exemplos que mostram a falsidade da segunda conjectura. O primeiro foi dado por L. P. Jorge e F. Xavier (1980), e o segundo por H. Rosenberg e E. Toubiana (1987). A primeira conjectura também é falsa. O primeiro contraexemplo foi dado por N. Nadirashvili (1996) e também constitui um contraexemplo da conjectura de Hadamard, que afirmava que não existiam superfícies completas limitadas com curvatura Gaussiana negativa. O desenvolvimento do artigo de Nadirashvili é o principal objetivo desta dissertação. A técnica usada nestes três trabalhos é o uso da Representação de Enneper-Weierstrass, combinada com aplicações adequadas do Teorema de Runge. / [en] During some years we have seen great progress in solving old problems in minimal surfaces theory. Among these problems are the Calabi-Yau s conjectures, dating from the 60s of last century. The first one stated that there were no complete minimal surfaces contained in a ball of R3, and the second one that all complete minimal surface should have an unbounded projection in each axes. In this work we pretend to review two examples that proof the falsity of the second conjecture. The first one was given by L. P. Jorge e F. Xavier (1980) and the second one by H. Rosenberg e E. Toubiana (1987). The first conjecture is also false. The first counterexample was given by N. Nadirashvili (1996) and it is also a counterexample to the conjecture of Hadamard, which stated that there were no complete bounded surfaces with negative Gaussian curvature. Development of Nadirashvilli s article is the main objective of this dissertation. The technique used in these three works is the use of the Enneper-Weierstrass Representation, combined with appropriate applications of Runge s theorem.

No description available.

Um resultado clássico em Geometria Diferencial, conhecido como teorema de Hadamard, e demonstrado pelo mesmo ([Ha]), estabelece que uma superfície conexa compacta no espaço Euclidiano cujas curvaturas principais são todas positivas é o bordo de um corpo convexo. Em part icular, a superfície é difeomorfa a uma esfera. Neste trabalho apresentamos extensões parciais deste teorema para imersões de codimensão arbitrária e para outros espaços ambientes que o E uclidiano conforme feito em [R]. / A classical result in differential geometry, known as Hadamard's theorem and proved by himself ([Ha]). establishes that a compact connected surface in the Euclidean space whose principal curvatures are everywhere positive is the boundary of a convex body. In particular, the surface is diffeomorphic to a sphere. In this work we present IJartial extensions of this theorem to immersions of arbitrary codimension and to other spaces than the Euclidean one, as clone in [R].

Oblivious Transfer (OT) is one of the most fundamental cryptographic primitives with wide-spread application in general secure multi-party computation (MPC) as well as in a number of tailored and special-purpose problems of interest such as private set intersection (PSI), private information retrieval (PIR), contract signing to name a few. Often the instantiations of OT require prohibitive communication and computation complexity. OT extension protocols are introduced to compute a very large number of OTs referred as extended OTs at the cost of a small number of OTs referred as seed OTs. We present a fast OT extension protocol for small secrets in active setting. Our protocol when used to produce 1-out-of-n OTs outperforms all the known actively secure OT extensions. Our protocol is built on the semi-honest secure extension protocol of Kolesnikov and Kumaresan of CRYPTO'13 (referred as KK13 protocol henceforth) which is the best known OT extension for short secrets. At the heart of our protocol lies an efficient consistency checking mechanism that relies on the linearity of Walsh-Hadamard (WH) codes. Asymptotically, our protocol adds a communication overhead of O( log ) bits over KK13 protocol irrespective of the number of extended OTs, where and refer to computational and statistical security parameter respectively. Concretely, our protocol when used to generate a large enough number of OTs adds only 0:011-0:028% communication overhead and 4-6% runtime overhead both in LAN and WAN over KK13 extension. The runtime overheads drop below 2% when in addition the number of inputs of the sender in the extended OTs is large enough. As an application of our proposed extension protocol, we show that it can be used to obtain the most efficient PSI protocol secure against a malicious receiver and a semi-honest sender.

Um resultado clássico em Geometria Diferencial, conhecido como teorema de Hadamard, e demonstrado pelo mesmo ([Ha]), estabelece que uma superfície conexa compacta no espaço Euclidiano cujas curvaturas principais são todas positivas é o bordo de um corpo convexo. Em part icular, a superfície é difeomorfa a uma esfera. Neste trabalho apresentamos extensões parciais deste teorema para imersões de codimensão arbitrária e para outros espaços ambientes que o E uclidiano conforme feito em [R]. / A classical result in differential geometry, known as Hadamard's theorem and proved by himself ([Ha]). establishes that a compact connected surface in the Euclidean space whose principal curvatures are everywhere positive is the boundary of a convex body. In particular, the surface is diffeomorphic to a sphere. In this work we present IJartial extensions of this theorem to immersions of arbitrary codimension and to other spaces than the Euclidean one, as clone in [R].

Um resultado clássico em Geometria Diferencial, conhecido como teorema de Hadamard, e demonstrado pelo mesmo ([Ha]), estabelece que uma superfície conexa compacta no espaço Euclidiano cujas curvaturas principais são todas positivas é o bordo de um corpo convexo. Em part icular, a superfície é difeomorfa a uma esfera. Neste trabalho apresentamos extensões parciais deste teorema para imersões de codimensão arbitrária e para outros espaços ambientes que o E uclidiano conforme feito em [R]. / A classical result in differential geometry, known as Hadamard's theorem and proved by himself ([Ha]). establishes that a compact connected surface in the Euclidean space whose principal curvatures are everywhere positive is the boundary of a convex body. In particular, the surface is diffeomorphic to a sphere. In this work we present IJartial extensions of this theorem to immersions of arbitrary codimension and to other spaces than the Euclidean one, as clone in [R].

Orientadores: Max Henrique Machado Costa, Leonardo de Souza Mendes / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-08T14:35:04Z (GMT). No. of bitstreams: 1 Testoni_Vanessa_M.pdf: 4002014 bytes, checksum: 340fce287ea15c5d681c3f317544e1ab (MD5) Previous issue date: 2007 / Resumo: As pesquisas na área de codificação de vídeo buscam técnicas que alcancem taxas de compressão cada vez mais altas. O aumento da compressão é obtido ao custo do aumento da complexidade dos algoritmos de codificação, que é suportado pelo também constante aumento da capacidade dos processadores. Entretanto, em alguns cenários de codificação e transmissão de vídeo, a utilização destes processadores de alta capacidade não é possível ou desejada. Isso exige o desenvolvimento de codificadores de vídeo focados na obtenção de tempos de processamento reduzido e na utilização de poucos recursos computacionais, tais como o sistema de codificação apresentado neste trabalho. Para o desenvolvimento deste sistema foi utilizada a transformada de Hadamard tridimensional implementada de forma otimizada e um codificador adaptativo de Golomb por planos de bits que acrescenta ao sistema a desejável característica de ser progressivo. A implementação do sistema é adaptada para realizar somente operações matemáticas rápidas e alocar pouca memória computacional. Mesmo com a utilização destas técnicas focadas em rapidez, foram obtidos bons resultados experimentais em termos da razão de sinal de pico por ruído em função da taxa de bits por pixel / Abstract: The research on video coding systems has always been looking for techniques that can reach the highest possible compression rate. This compression rate increase is generally achieved by means of increased coding complexity, which is supported by the continuous increase verified in computational power. However, in some video coding and transmission situations, the use of high capacity processors is not possible or desirable. These situations require the development of video coders focused on the achievement of reduced execution times and on the requirement of few computational resources, just as the video coding system proposed in this dissertation. The proposed system uses three dimensional Hadamard transforms, implemented in an efficient way, and adaptive entropy coding with Golomb codes applied to bit planes, whichs adds to the system the desirable characteristic of being progressive. The computational system implementation is designed to perform only fast mathematical operations and to require small computational memory. Even with the use of these constrained techniques, good experimental results, in terms of peak signal to noise ratio (PSNR) versus pixel bit-rate were achieved. / Mestrado / Telecomunicações e Telemática / Mestre em Engenharia Elétrica

Radio frequency interference is an ever growing problem in the wireless community. This dissertation presents methods to reduce interference for vehicular multi-antenna devices. This document is organized into two parts: the main chapters and the appendices. The main chapters present research conducted primarily by the author. These deserve the reader's primary attention. The appendices showcase contributions made by the author serving in a supporting role to projects led by others and/or do not fit the vehicular theme. These should receive secondary attention. The main chapter contributions are summarized as follows. A device was created that provides over 105 dB of transmit to receive isolation in a full duplex printed circuit board radio. This technology can improve the effective range of vehicular radar systems and increase the bandwidth of full duplex communication schemes for vehicles. The technologies involved are compatible with existing circuit board topologies and are mindful of the size and weight requirements for vehicular use. This isolation performance pushes the state of the art for printed circuit board designs and provides greater capability for these kinds of devices. Recent system on chip computing architectures are opening new pathways for integrating phased array technologies into a single chip. The computer engineering required to configure these devices is beyond the capabilities of many vehicle systems engineers, inviting the author to use one to implement a 16 antenna adaptive beamformer for GPS. The adaptive beamformer can combat multipath bounces and malicious spoofing from ground sources. The high rate analog conversion architecture eliminates the local oscillator distribution to simplify the analog front end to an active antenna. This allows vehicular phased arrays to use smaller footprints and suggests that multi-antenna beamforming devices may be easier to deploy on small to midsized vehicles. Bench tests of the beamformer indicate it can adapt to the environment and increase the received signal strength suggesting it can improve GPS quality for active deployments. The bank of subspace projection beamformers is a popular choice for mitigating interference in digital phased array receivers. A method was discovered that maps that matrix operator into a circuit topology that is simple to implement in an analog circuit and cancels across the entire bandwidth simultaneously. This can offload computational interference mitigation from the signal processor while still allowing secondary multi-pixel digital beamforming downstream. This beamformer was analytically connected to the body of phased array literature and studied to estimate practical error bounds and design methods of calibration.

This dissertation deals with some crucial building blocks of cryptosystems in symmetric cryptography / namely the Boolean functions that produce a single-bit result for each possible value of the m-bit input vector, where m&gt / 1. Objectives in this study are two-fold / the first objective is to develop relations between cryptographic properties of Boolean functions, and the second one is to form new concepts that associate coding theory with cryptology. For the first objective, we concentrate on the cryptographic properties of Boolean functions such as balancedness, correlation immunity, nonlinearity, resiliency and propagation characteristics / many of which are depending on the Walsh spectrum that gives components of the Boolean function along the direction of linear functions. Another efficient tool to study Boolean functions is the subject of covering sequences introduced by Carlet and Tarannikov in 2000. Covering sequences are defined in terms of the derivatives of the Boolean function. Carlet and Tarannikov relate the correlation immunity and balancedness properties of the Boolean function to its covering sequences. We find further relations between the covering sequence and the Walsh spectrum, and present two theorems for the calculation of covering sequences associated with each null frequency of the Walsh spectrum. As for the second objective of this thesis, we have studied linear codes over the rings Z4 and Z8 and their binary images in the Galois field GF(2). We have investigated the best-known examples of nonlinear binary error-correcting codes such as Kerdock, Preperata and Nordstrom-Robinson, which are -linear codes. We have then reviewed Tokareva&rsquo / s studies on Z4-linear codes and extended them to Z8-linear codes. We have defined a new classes of bent functions. Next, we have shown that the newly defined classes of bent, namely Tokareva&rsquo / s k-bent and our t,k-bent functions are affine equivalent to the well-known Maiorana McFarland class of bent functions. As a cryptological application, we have described the method of cubic cryptanalysis, as a generalization of the linear cryptanalysis given by Matsui in 1993. We conjecture that the newly introduced t,k-bent functions are also strong against cubic cryptanalysis, because they are as far as possible to t,k-bent functions.