Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-01T16:28:42Z No. of bitstreams: 1 arquivototal.pdf: 706603 bytes, checksum: 4bcd99d1191e9b1e81f9c94952955989 (MD5) / Approved for entry into archive by Fernando Souza (fernandoafsou@gmail.com) on 2017-09-04T10:55:58Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 706603 bytes, checksum: 4bcd99d1191e9b1e81f9c94952955989 (MD5) / Made available in DSpace on 2017-09-04T10:55:58Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 706603 bytes, checksum: 4bcd99d1191e9b1e81f9c94952955989 (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we will study inequalities between real numbers. In special, we will study the inequalities between means, Bernoulli’s inequality, the Cauchy-Schwarz inequality and Chebishev’s inequality and some applications. / Neste trabalho estudaremos algumas desigualdades entre números reais. De maneira especial, estudaremos as desigualdades das médias, as desigualdades de Bernoulli, Cauchy-Schwarz e de Chebishev, assim como algunas aplicações.

We present a scalable information-optimal compressive imager optimized for the target classification task, discriminating between two target classes. Compressive projections are optimized using the Cauchy-Schwarz Mutual Information (CSMI) metric, which provides an upper-bound to the probability of error of target classification. The optimized measurements provide significant performance improvement relative to random and PCA secant projections. We validate the simulation performance of information-optimal compressive measurements with experimental data.

Au cours de ma thèse, je me suis intéressé à deux aspects de l'interaction charge-rayonnement dans des jonctions tunnel. Premièrement j'ai étudié la dynamique des transferts de charge à travers une jonction tunnel normale lorsque celle-ci est couplée à un environnement dont l'impédance est comparable au quantum d'impédance (RK= h/e^2). Nous avons montré que les uctuations de courant portent des signatures de processus à un, deux et trois photons. Deuxièmement j'ai caractérisé le rayonnement émis par une jonction Josephson lorsque celle-ci est couplée à deux résonateurs de fréquences différentes, nu_1 et nu_2, et soumise à une tension 2eV = h nu_1+h nu_2. Nous avons montré que les photons sont émis pas paires, ce qui constitue un rayonnement non-classique violant l'inégalité de Cauchy-Schwarz.Nos résultats montrent que le blocage de Coulomb dynamique constitue une ressource pour la production de micro-ondes quantiques. / In this thesis work, I have focused on two aspects of the charge-light interaction for tunnel junctions. On one hand, I have investigated the influence of the coupling to electromagnetic radiation on the dynamics of charge transfer through a normal tunnel junction when the impedance of its environment gets comparable to the resistance quantum (RK=h/e^2). We showed that the current fluctuations bear signature of the processes where one, two or three photons are emitted.On the other hand, we used a Josephson junction, embedded in a circuit made of two resonators at different frequencies, nu_1 and nu_2, and biased at the voltage 2eV=h nu_1+h nu_2. We showed that the Josephson junction emits photon pairs corresponding to a non classical state of radiation which violates the Cauchy-Schwarz inequality.Our results extend the toolbox for performing quantum optics experiments in the microwave domain.

Since most financial institutions use the Sharpe Ratio to evaluate the performance of mutual funds, the objective of most fund managers is to select the portfolio that can generate the highest Sharpe Ratio. Traditionally, they can revise the objective function of the Markowitz mean-variance portfolio model and resolve non-linear programming to obtain the maximum Sharpe Ratio portfolio. In the scenario with short sales allowed, this project will propose a closed-form solution for the optimal Sharpe Ratio portfolio by applying Cauchy-Schwarz maximization. This method without using a non-linear programming computer program is easier than traditional method to implement and can save computing time and costs. Furthermore, in the scenarios with short sales disallowed, we will use Kuhn-Tucker conditions to find the optimal Sharpe Ratio portfolio. On the other hand, an efficient frontier generated by Markowitz mean-variance portfolio model normally has higher risk higher return characteristic, which often causes dilemma for decision maker. This research applies generalized loss function to create a family of decision-aid performance measures called IRp which can well tradeoff return with risk. We compare IRp with Sharpe Ratio and utility functions to confirm that IRp measures are approapriate to evaluate portfolio performance on efficient frontier and to improve asset allocation decisions. In addition, empirical data of domestic and international investment instruments will be used to examine the feasibility and fitness of the new proposed method and IRp measures. This study applies the methods of Cauchy-Schwarz maximization in multivariate statistical analysis and loss function in quality engineering to portfolio decisions. We believe these new applications will complete portfolio model theory and will be meaningful for academic and business fields.

Submitted by Danielle Karla Martins Silva (danielle.martins@ufpe.br) on 2015-03-12T15:00:27Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE Milrian da Silva Mendes.pdf: 9715367 bytes, checksum: d2f422f9ea59e0b5381776bcfc1de025 (MD5) / Made available in DSpace on 2015-03-12T15:00:27Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE Milrian da Silva Mendes.pdf: 9715367 bytes, checksum: d2f422f9ea59e0b5381776bcfc1de025 (MD5) Previous issue date: 2013 / Nesta tese estudamos o mecanismo de extração da informação armazenada em uma memória quântica constituída de um ensemble de átomos de césio aprisionados e resfriados em uma armadilha magneto-ótica. Consideramos memórias contendo uma única excitação de um estado atômico coletivo, mapeada em um único fóton durante o processo de leitura. Os processos de geração, deteção, e caracterização dos fótons no sistema experimental são detalhados. Observamos correlações não clássicas entre os campos óticos gerados no sistema. Resultados são obtidos na presença e na ausência dos campos magnéticos da armadilha. Além disso, apresentamos uma teoria para o pacote de onda do fóton extraído, conduzindo a uma expressão analítica que depende dos parâmetros principais do problema. Comparamos a teoria com uma série de situações experimentais e um acordo quantitativo satisfatório é obtido. Desta forma, estudamos sistematicamente a saturação e o espectro do processo de leitura, elucidando ainda o papel da superradiância no sistema. Utilizando uma alta profundidade ótica, observamos a formação da condição de transparência eletromagneticamente induzida no meio através do desaparecimento de uma estrutura característica no espectro de leitura. Tal estrutura é representada pela diminuição da probabilidade de extração do fóton em torno da ressonância, desaparecendo para altas potências de leitura. Estudamos ainda o comportamento da probabilidade condicional de geração de um par de fótons variando a profundidade ótica do meio e, consequentemente, a própria condição de superradiância.

The constant gamma in the strengthened Cauchy-Bunyakowskii-Schwarz inequality is a basic tool for constructing of two-level and multilevel preconditioning matrices. Therefore many authors consider estimates or computations of this quantity. In this paper the bilinear form arising from 3D linear elasticity problems is considered on a polyhedron. The cosine of the abstract angle between multilevel finite element subspaces is computed by a spectral analysis of a general eigenvalue problem. Octasection and bisection approaches are used for refining the triangulations. Tetrahedron, pentahedron and hexahedron meshes are considered. The dependence of the constant $\gamma$ on the Poisson ratio is presented graphically.

We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.

The constant gamma in the strengthened Cauchy-Bunyakowskii-Schwarz inequality is a basic tool for constructing of two-level and multilevel preconditioning matrices. Therefore many authors consider estimates or computations of this quantity. In this paper the bilinear form arising from 3D linear elasticity problems is considered on a polyhedron. The cosine of the abstract angle between multilevel finite element subspaces is computed by a spectral analysis of a general eigenvalue problem. Octasection and bisection approaches are used for refining the triangulations. Tetrahedron, pentahedron and hexahedron meshes are considered. The dependence of the constant $\gamma$ on the Poisson ratio is presented graphically.

No / This paper presents a novel concept to describe the couplings among the outputs of the stochastic systems which are represented by NARMA models. Compared with the traditional coupling description, the presented concept can be considered as an extension using statistical independence theory. Based on this concept, the decoupling control in statistical sense is established with the necessary and sufficient conditions for complete decoupling. Since the complete decoupling is difficult to achieve, a control algorithm has been developed using the Cauchy-Schwarz mutual information criterion. Without modifying the existing control loop, this algorithm supplies a compensative controller to minimise the statistical couplings of the system outputs and the local stability has been analysed. In addition, a further discussion illustrates the combination of the presented control algorithm and data-based mutual information estimation. Finally, a numerical example is given to show the feasibility and efficiency of the proposed algorithm.