O monitoramento da razão Z de duas variáveis através de gráfico de controle tem sido um tema recentemente explorado na literatura. Para analisar mais o assunto, o estudo avalia a eficiência e viabilidade de aplicação dessa ferramenta como suporte na tomada de decisão para gerenciamento de capacidade de mão de obra de retaguarda (doravante mencionado como Backoffice) de serviço de empresa do setor bancário. Tradicionalmente, gráficos de controle tem sido utilizados para monitorar o processo produtivo de manufaturas, mas recentemente tem sido adotado para monitoramento de alguns serviços. Apesar de ainda seguir muitos conceitos pioneiros na manufatura, a atividade do setor de serviços apresenta suas particularidades como, por exemplo, a impossibilidade de gerar estoque. Assim, a necessidade de adequar seus recursos à demanda torna-se essencial, sendo fundamental a gestão de controles e sua urgência para que possa reagir rapidamente em caso de variação de demanda e adequar sua capacidade. Em um cenário de restrição de recursos, planejar é crucial para evitar desperdícios e garantir eficiência. O objetivo deste estudo é apresentar o gráfico de controle como ferramenta para monitorar a razão de duas variáveis aleatórias: a demanda e a mão de obra em Backoffice de serviço em um banco. Nesse trabalho, gráfico de controle de Shewhart tradicional e gráfico de controle de Shewhart com regras suplementares são analisados e os resultados obtidos confirmam a possibilidade de utilização da ferramenta de gráficos de controle para o gerenciamento e adequação de mão de obra para atender a demanda. O monitoramento da razão (demanda/ mão de obra) ajudará o gestor a alocar adequadamente o time (mão de obra) de acordo com a demanda e a capacidade produtiva. Como contribuição, o estudo avalia o comportamento da razão Z = X/Y em situação de alta variabilidade da variável X e baixa variabilidade da variável Y . / The monitoring of the ratio Z of two variables through control chart has been recently explored in the literature. This study analyses the efficiency and viability of this tool as a support to the manager\'s decision in capacity management of a Backoffice service in a business banking service. Traditionally, control charts have been used to monitoring production process in manufacturing companies, but recently it has been adopted in monitoring some classes of services. Although many pioneering definitions developed for manufacturing are still applied in the service activities, the service industry has some particularities as the impossibility to generate stock, for example. Thus, the need to adapt the resources of manpower to attend the demand becomes essential mainly in a current financial global crisis, with resource constraints. The control management is fundamental and urgent to plan a fast reaction to adequate its capacity in case of a large demand variation. Thus, monitoring is crucial to avoid vast and ensure efficiency. The aim of this paper is to present a control chart to monitor the ratio of the two random quantities: the demand and the labor of a Backoffice service in a business banking service. In this paper, traditional Shewhart and Shewhart with supplementary rules control charts are considered and the results confirmed the possibility to apply the control charts to help the management to adequate the manpower in order to attend the demand. The monitoring of the ratio (demand/manpower) will help the manager to allocate adequately the team (the manpower) according to the demand and the production capacity. The contribution of this study is the analysis of the behavior of the ratio Z = X/Y in situation of large variability of the variable X and low variability of the variable Y .

Ultra Wideband (UWB) communication has recently drawn considerable attention from academia and industry. This is mainly owing to the ultra high speeds and cognitive features it could offer. The employability of UWB in numerous areas including but not limited to Wireless Personal Area Networks, WPAN's, Body Area Networks, BAN's, radar and medical imaging etc. has opened several avenues of research and development. However, still there is a disagreement on the standardization of UWB. Two contesting radios for UWB are Multiband Orthogonal Frequency Division Multiplexing (MB-OFDM) and DS-UWB (Direct Sequence Ultra Wideband). As nearly all of the reported research on UWB hasbeen about a very narrow/specific area of the communication system, this thesis looks at the end-to-end performance of an MB-OFDM approach. The overall aim of this project has been to first focus on three different aspects i.e. interference, antenna and propagation aspects of an MB-OFDM system individually and then present a holistic or an end-to-end system analysis finally. In the first phase of the project the author investigated the performance of MB-OFDM system under the effect of his proposed generic or technology non-specific interference. Avoiding the conventional Gaussian approximation, the author has employed an advanced stochastic method. A total of two approaches have been presented in this phase of the project. The first approach is an indirect one which involves the Moment Generating Functions (MGF's) of the Signal-to-Interference-plus-Noise-Ratio (SINR) and the Probability Density Function (pdf) of the SINR to calculate the Average Probabilities of Error of an MB-OFDM system under the influence of proposed generic interference. This approach assumed a specific two-dimensional Poisson spatial/geometric placement of interferers around the victim MB-OFDM receiver. The second approach is a direct approach and extends the first approach by employing a wider class of generic interference. In the second phase of the work the author designed, simulated, prototyped and tested novel compact monopole planar antennas for UWB application. In this phase of the research, compact antennas for the UWB application are presented. These designs employ low-loss Rogers duroid substrates and are fed by Copla-nar Waveguides. The antennas have a proposed feed-line to the main radiating element transition region. This transition region is formed by a special step-generating function-set called the "Inverse Parabolic Step Sequence" or IPSS. These IPSS-based antennas are simulated, prototyped and then tested in the ane-choic chamber. An empirical approach, aimed to further miniaturize IPSS-based antennas, was also derived in this phase of the project. The empirical approach has been applied to derive the design of a further miniaturized antenna. More-over, an electrical miniaturization limit has been concluded for the IPSS-based antennas. The third phase of the project has investigated the effect of the indoor furnishing on the distribution of the elevation Angle-of-Arrival (AOA) of the rays at the receiver. Previously, constant distributions for the AOA of the rays in the elevation direction had been reported. This phase of the research has proposed that the AOA distribution is not fixed. It is established by the author that the indoor elevation AOA distributions depend on the discrete levels of furnishing. A joint time-angle-furnishing channel model is presented in this research phase. In addition, this phase of the thesis proposes two vectorial or any direction AOA distributions for the UWB indoor environments. Finally, the last phase of this thesis is presented. As stated earlier, the overall aim of the project has been to look at three individual aspects of an MB-OFDM system, initially, and then look at the holistic system, finally. Therefore, this final phase of the research presents an end-to-end MB-OFDM system analysis. The interference analysis of the first phase of the project is revisited to re-calculate the probability of bit error with realistic/measured path loss exponents which have been reported in the existing literature. In this method, Gaussian Quadrature Rule based approximations are computed for the average probability of bit error. Last but not the least, an end-to-end or comprehensive system equation/impulse response is presented. The proposed system equation covers more aspects of an indoor UWB system than reported in the existing literature.

Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out. / Decision Sciences

Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden. Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden.:6. Grenzwertsätze für mittlere Abweichungen für verschieden verteilte Zufallsgrößen S. 1 7. Beweise zum Abschnitt 6 S. 2 8. Diskussion der Ergebnisse S. 6 Literatur S. 10 / The paper is divided in two parts: part 1 (cp. Informationen/07; 1976,05) and part 2 (cp. Informationen/07; 1976,06). Part 1 contains an introduction and limit theorems for iid random variables and the transfer of the considered limit theorems to the case of the existence of onesided moments. Part 2 contains limit theorems of moderate deviations for sums of series of non iid random variables and a discussion of all obtained results in part 1 and 2 and finally some references. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are iid random variables with mean 0 and variance 1 and with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_i are computed such that we have an error estimate in the nonuniform central limit theorem with the L_i, where i corresponds to the five cases considered: small x, moderate deviations for x, large deviations for x, small n , large n. Additional upper bounds for 1-F_n(x) are obtained if the one-sided moments of order m, m>2, are finite and if x>D_m*n^(1/2)*ln(n) and x>D_m*n^(1/2)*(ln(n))^(1/2) respectively improving results by S.V.NAGAEV (1965).:6. Grenzwertsätze für mittlere Abweichungen für verschieden verteilte Zufallsgrößen S. 1 7. Beweise zum Abschnitt 6 S. 2 8. Diskussion der Ergebnisse S. 6 Literatur S. 10

Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden.:1. Einführung S. 2 2. Grenzwertsätze für identisch verteilte Zufallsgrößen S. 3 3. Übertragung der formulierten Grenzwertsätze auf den Fall der Existenz einseitiger Momente S. 6 4. Beweis zum Abschnitt 2 S. 8 5. Beweise zum Abschnitt 3 S. 13 / The paper is divided in two parts: part 1 (cp. Informationen/07; 1976,05) and part 2 (cp. Informationen/07; 1976,06). Part 1 contains an introduction and limit theorems for iid random variables and the transfer of the considered limit theorems to the case of the existence of onesided moments. Part 2 contains limit theorems of moderate deviations for sums of series of non iid random variables and a discussion of all obtained results in part 1 and 2 and finally some references. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are iid random variables with mean 0 and variance 1 and with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_i are computed such that we have an error estimate in the nonuniform central limit theorem with the L_i, where i corresponds to the five cases considered: small x, moderate deviations for x, large deviations for x, small n , large n. Additional upper bounds for 1-F_n(x) are obtained if the one-sided moments of order m, m>2, are finite and if x>D_m*n^(1/2)*ln(n) and x>D_m*n^(1/2)*(ln(n))^(1/2) respectively improving results by S.V.NAGAEV (1965).:1. Einführung S. 2 2. Grenzwertsätze für identisch verteilte Zufallsgrößen S. 3 3. Übertragung der formulierten Grenzwertsätze auf den Fall der Existenz einseitiger Momente S. 6 4. Beweis zum Abschnitt 2 S. 8 5. Beweise zum Abschnitt 3 S. 13

Nous nous intéressons dans cette thèse à certains modèles mathématiques permettant une description de systèmes ouverts classiques et quantiques. Dans l'étude de ces systèmes en interaction avec un environnement, nous montrons que la dynamique induite par l'environnement sur le système donne lieu à l'apparition de bruits. Dans une première partie de la thèse, dédiée aux systèmes classiques, le modèle décrit est le schéma d'interactions répétées. Etant à la fois hamiltonien et markovien, ce modèle en temps discret permet d'implémenter facilement la dissipation dans des systèmes physiques. Nous expliquons comment le mettre en place pour des systèmes physiques avant d'en étudier la limite en temps continu. Nous montrons la convergence Lp et presque sûre de l'évolution de certains systèmes vers la solution d'une équation différentielle stochastique, à travers l'étude de la limite de la perturbation d'un schéma d'Euler stochastique. Dans une seconde partie de la thèse sur les systèmes quantiques, nous nous intéressons dans un premier temps aux actions d'environnements quantiques sur des systèmes quantiques aboutissant à des bruits classiques. A cette fin, nous introduisons certains opérateurs unitaires appelés « classiques », que nous caractérisons à l'aide de variables aléatoires dites obtuses. Nous mettons en valeur comment ces variables classiques apparaissent naturellement dans ce cadre quantique à travers des 3-tenseurs possédant des symétries particulières. Nous prouvons notamment que ces 3-tenseurs sont exactement ceux diagonalisables dans une base orthonormée. Dans un second temps, nous étudions la limite en temps continu d'une variante des interactions répétées quantiques dans le cas particulier d'un système biparti, c'est-à-dire composé de deux systèmes isolés sans interaction entre eux. Nous montrons qu'à la limite du temps continu, une interaction entre ces sous-systèmes apparaît explicitement sous forme d'un hamiltonien d'interaction; cette interaction résulte de l'action de l'environnement et de l'intrication qu'il crée / This dissertation is dedicated to some mathematical models describing classical and quantum open systems. In the study of these systems interacting with an environment, we particularly show that the dynamics induced by the environment leads to the appearance of noises. In a first part of this thesis, devoted to classical open systems, the repeated interaction scheme is developed. This discrete-time model, being Hamiltonian and Markovian at the same time, has the advantage to easily implement the dissipation in physical systems. We explain how to set this scheme up in some physical examples. Then, we investigate the continuous-time limit of these repeated interactions. We show the Lp and almost sure convergences of the evolution of the system to the solution of a stochastic differential equation, by studying the limit of a perturbed Stochastic Euler Scheme. In a second part of this dissertation on quantum systems, we characterize in a first work classical actions of a quantum environment on a quantum system. In this study, we introduce some “classical” unitary operators representing these actions and we highlight a strong link between them and some random variables, called obtuse random variables. We explain how these random variables are naturally connected to some 3-tensors having some particular symmetries. We particularly show that these 3 tensors are exactly the ones that are diagonalizable in some orthonormal basis. In a second work of this part, we study the continuous-time limit of a variant of the repeated interaction scheme in a case of a bipartite system, that is, a system made of two isolated systems not interaction together. We prove that an explicit Hamiltonian interaction between them appears at the limit. This interaction is due to the action of the environment and the entanglement between the two systems that it creates

Indiana University-Purdue University Indianapolis (IUPUI) / In medical research, data analysis often requires complex statistical methods where no closed-form solutions are available. Under such circumstances, Monte Carlo (MC) methods have found many applications. In this dissertation, we proposed several novel statistical models where MC methods are utilized. For the first part, we focused on semicompeting risks data in which a non-terminal event was subject to dependent censoring by a terminal event. Based on an illness-death multistate survival model, we proposed flexible random effects models. Further, we extended our model to the setting of joint modeling where both semicompeting risks data and repeated marker data are simultaneously analyzed. Since the proposed methods involve high-dimensional integrations, Bayesian Monte Carlo Markov Chain (MCMC) methods were utilized for estimation. The use of Bayesian methods also facilitates the prediction of individual patient outcomes. The proposed methods were demonstrated in both simulation and case studies. For the second part, we focused on re-randomization test, which is a nonparametric method that makes inferences solely based on the randomization procedure used in clinical trials. With this type of inference, Monte Carlo method is often used for generating null distributions on the treatment difference. However, an issue was recently discovered when subjects in a clinical trial were randomized with unbalanced treatment allocation to two treatments according to the minimization algorithm, a randomization procedure frequently used in practice. The null distribution of the re-randomization test statistics was found not to be centered at zero, which comprised power of the test. In this dissertation, we investigated the property of the re-randomization test and proposed a weighted re-randomization method to overcome this issue. The proposed method was demonstrated through extensive simulation studies.