Electromagnetic scattering by 3-D arbitrarily shaped homogeneous dielectric objects is characterized. In the analysis, the method of moments is first employed to solve the combined field integral equation for scattering properties of these three-dimensional homogeneous dielectric objects of arbitrary shape. The fast multipole method, and the multi-level fast multipole algorithm are implemented into our codes for matrix-vector manipulations. Specifically, four proposals are made and discussed to increase convergence and accuracy of iterative procedures (conjugate gradient method). Numerical results are obtained using various methods and compared to each other. / Singapore-MIT Alliance (SMA)

Dielectric resonator antennas(DRAs) offer some attractive characteristics over conventional microstrip antennas, such as small size, low profile, light weight, ease of excitation, and high radiation efficiency at higher frequency bands. Since DRAs attract more and more attention, theoretical analysis have been insufficient to simulate various configurations of dielectric resonator antennas. Therefore some researchers introduce numerical methods to analyze DRAs, such as Finite Difference Time Domain (FDTD) method, Method of Moment (MoM), Finite Element Method (FEM). In this author, we apply two kinds of methods, including FDTD and MoM, to analysis DRA and compare the results applied these two methods. Then we simulate various configurations of dielectric resonator antennas using FDTD method. About designing the DRA construction, in this author we applied an equivalent approach to solve approximate dimensions of DRAs, and then we obtain accurate dimensions using FDTD method. In this author¡Aa DRA work at 5.8GHz have been proposed, then we using a L-shaped patch to increase impedance bandwidth. Above all, we hope to built a fast and accurate procedure to solve the resonant frequency, bandwidth, and far field pattern of DRAs. And to supply the engineer to reduce time consume in design DRAs.

<p>Constant technology advances have caused data explosion in recent years. Accord- ingly modern statistical and machine learning methods must be adapted to deal with complex and heterogeneous data types. This phenomenon is particularly true for an- alyzing biological data. For example DNA sequence data can be viewed as categorical variables with each nucleotide taking four different categories. The gene expression data, depending on the quantitative technology, could be continuous numbers or counts. With the advancement of high-throughput technology, the abundance of such data becomes unprecedentedly rich. Therefore efficient statistical approaches are crucial in this big data era.</p><p>Previous statistical methods for big data often aim to find low dimensional struc- tures in the observed data. For example in a factor analysis model a latent Gaussian distributed multivariate vector is assumed. With this assumption a factor model produces a low rank estimation of the covariance of the observed variables. Another example is the latent Dirichlet allocation model for documents. The mixture pro- portions of topics, represented by a Dirichlet distributed variable, is assumed. This dissertation proposes several novel extensions to the previous statistical methods that are developed to address challenges in big data. Those novel methods are applied in multiple real world applications including construction of condition specific gene co-expression networks, estimating shared topics among newsgroups, analysis of pro- moter sequences, analysis of political-economics risk data and estimating population structure from genotype data.</p> / Dissertation

The Method of Moments (MoM) has been widely used for the full-wave electromagnetic analysis of planar multilayered media. However, the MoM is a computationally intensive process and requires considerable computer resources to perform the analysis. Thus, several efficient numerical techniques both in the spectral domain and spatial domain are investigated and further developed in this research. Two fitting procedures, i.e., the Rational Function Fitting Method (RFFM) and the Discrete Complex Image Method (DCIM), are investigated and developed in order to obtain closed-form spatial-domain Green's functions (GFs). Because the subtraction of the surface-wave pole contribution plays an important role for the accurate estimation of the spatial-domain GFs via DCIM, an efficient and accurate surface-wave pole location method is developed to find all the surface-wave poles for general multilayered media. The RFFM can be realized through either the Total Least Square Algorithm (TLSA) or the Vector Fitting (VECTFIT) method. Both the RFFM using VECTFIT and DCIM are detailed in step by step procedures. An efficient and low cost algorithm combining the advantages of DCIM and TLSA is also developed to evaluate the closed-form Green's functions for general multilayered media. A prototype version of the Full-Wave Layered-Interconnect Simulator (UA-FWLIS) was developed by analytically calculating the MoM reaction elements via Cauchy's residue theorem and the Complementary Incomplete Lipschitz-Hankel Integrals in stripline structures. After applying RFFM via VECTFIT to the G-functions, which are directly related to the spectral-domain GFs for microstrip structures, a procedure that is similar to the one used in the previously developed UA-FWLIS for stripline structures can be applied to calculate the MoM reaction elements analytically when the two reaction cells are close (< 0.1λ₀) in the spectral domain via the Electrical Field Integral Equation (EFIE). When the two reaction cells are far enough away (> 0.10.1λ₀), a simple expression for the reaction element can be obtained in the spatial domain via the Mixed Potential Integral Equation (MPIE) by a summation of a few complex image terms for the evaluation of the vector and scalar GFs. An efficient hybrid spectral-spatial method is thus developed to extend UA-FWLIS to microstrip structures. The method is validated by several numerical examples.

Mobile communication has become an essential part of our daily life. We love the flexibility of wireless cell phones and even accept their lower quality of service when compared to wired links. Similarly, we are looking forward to the day that we can continue watching our favorite TV programs while travelling anywhere and everywhere. Mobility, flexibility, and portability are the themes of the next generation communication. Motivated and fascinated by such technology breakthroughs, this effort is geared towards enhancing the quality of wireless services and bringing mobile satellite reception one step closer to the market. Meanwhile, phased array antennas are vital components for RADAR applications where the antenna is required to have certain scan capabilities. One of the main concerns in that perspective is how to avoid the potential of scan blindness in the required scan range. Targeting to achieve wide-band wide-scan angle phased arrays free from any scan blindness our efforts is also geared. Conventionally, the key to lower the profile of the antenna is to use planar structures. In that perspective microstrip patch antennas have drawn the attention of antenna engineers since the 1970s due to their attractive features of being low profile, compact size, light weight, and amenable to low-cost PCB fabrication processes. However, patch elements are basically resonating at a single frequency, typically have <2% bandwidth, which is a major deficit that impedes their usage in relatively wide-band applications. There are various approaches to enhance the patch antennas bandwidth including suspended substrates, multi-stack patches, and metalized cavities backing these patches. Metalized cavity-backed patch structures have been demonstrated to give the best performance, however, they are very expensive to manufacture. In this dissertation, we develop an alternative low-cost bandwidth enhancement topology. The proposed topology is based on substrate-integrated waveguides. The great potential of the proposed structure lies in being amenable to the conventional PCB fabrication. Moreover, substrate-integrated cavity-backed structures facilitate the design of sophisticated arrays that are very expensive to develop using the conventional metalized cavity-backed topology, which includes the common broadside arrays used in fixed-beam applications and the scanned phased arrays used in RADAR applications.

In the first part of the thesis, the 2-D structures in stratified media are analyzed using an efficient MoM technique. The method is used to optimize transmitted or reflected electric fields from the 2-D structures. The genetic algorithm is used in the optimization process. In the second part a 3-D MoM technique is implemented to analyze multilayered structures with periodically implanted material blocks. Using the method, the dispersion and reflection characteristics of the structure are calculated for different configurations. The results are compared with the results found in the literature and it is seen that they are in good agreement. Asymptotic Waveform Evaluation (AWE) technique is utilized to obtain the Pade approximation of the solution in terms of frequency. The high order derivatives that are required by the AWE technique are calculated through Automatic Differentiation technique. Using the AWE method, the dispersion diagram and reflection characteristics of the periodic structures are obtained in a shorter time. The results are compared with the ones obtained through direct calculation and it is seen that they are in perfect agreement. The reflection coefficients that are obtained from the 3-D MoM procedure are used to calculate Green&rsquo / s functions that approximate electric field of an infinitesimal dipole on the periodically implanted substrate. Using the calculated Green&rsquo / s functions and the spectral domain MoM procedure, dispersion characteristics of a microstrip line on the periodically implanted substrate are obtained.

In this dissertation, we develop several new inference procedures that are based on randomized nomination sampling (RNS). The first problem we consider is that of constructing distribution-free confidence intervals for quantiles for finite populations. The required algorithms for computing coverage probabilities of the proposed confidence intervals are presented. The second problem we address is that of constructing nonparametric confidence intervals for infinite populations. We describe the procedures for constructing confidence intervals and compare the constructed confidence intervals in the RNS setting, both in perfect and imperfect ranking scenario, with their simple random sampling (SRS) counterparts. Recommendations for choosing the design parameters are made to achieve shorter confidence intervals than their SRS counterparts. The third problem we investigate is the construction of tolerance intervals using the RNS technique. We describe the procedures of constructing one- and two-sided RNS tolerance intervals and investigate the sample sizes required to achieve tolerance intervals which contain the determined proportions of the underlying population. We also investigate the efficiency of RNS-based tolerance intervals compared with their corresponding intervals based on SRS. A new method for estimating ranking error probabilities is proposed. The final problem we consider is that of parametric inference based on RNS. We introduce different data types associated with different situation that one might encounter using the RNS design and provide the maximum likelihood (ML) and the method of moments (MM) estimators of the parameters in two classes of distributions; proportional hazard rate (PHR) and proportional reverse hazard rate (PRHR) models.

Η παρούσα μεταπτυχιακή διατριβή εντάσσεται ερευνητικά στην περιοχή της Στατιστικής θεωρίας Αποφάσεων και ειδικότερα στη μελέτη της αρνητικής διωνυμικής κατανομής καθώς επίσης και στην εκτίμηση των παραμέτρων της. Στο Κεφάλαιο 1 παρουσιάζονται κάποιοι χρήσιμοι, για την πορεία της μελέτης μας, ορισμοί και θεωρήματα. Στο Κεφάλαιο 2 μελετάται το μοντέλο της αρνητικής διωνυμικής κατανομής, δίνονται τα χαρακτηριστικά μεγέθη αυτής και παρουσιάζονται οι διαφορετικές παραμετρικοποιήσεις της. Στο Κεφάλαιο 3, εξετάζεται το πρόβλημα εκτίμησης των παραμέτρων της αρνητικής διωνυμικής κατανομής και πιο ειδικά η εκτίμηση για τις διάφορες παραμετρικοποιήσης της. Για περισσότερη ανάλυση χρησιμοποιούνται η εκτίμηση μέγιστης πιθανοφάνειας, η εκτίμηση με τη μέθοδο των ροπών και πιο εξειδικευμένες υπολογιστικές μέθοδοι εκτίμησης. Στο Κεφάλαιο 4, και για το ίδιο πρόβλημα εκτίμησης που πραγματεύεται το προηγούμενο κεφάλαιο, επιλέγεται ο βέλτιστος εκτιμητής των παραμέτρων της αρνητικής διωνυμικής κατανομής και παρουσιάζεται ένα παράδειγμα για την κατανόηση των μεθόδων εκτίμησης. / The master thesis we are going to introduce takes place in the region of Statistical Decision Theory and particularly in studying the Negative Binomial Distribution and the estimation of its parameters. In Chapter 1 some useful definitions and theorems are presented. In Chapter 2 the model of negative binomial distribution is studied and its different parameterizations are discussed. In Chapter 3 we examine the problem of estimating the parameters of our model and for its parameterizations. In particular we give the method of Maximum Likelihood Estimation, the Method of Moments and more specified Estimation Methods. In Chapter 4 and for the same estimation problem, as in previous chapter, it’s been chosen the best estimator of the parameters in our model and it’s been derived an example for the better understanding of the above methods.

<p dir="ltr">There is a growing demand for lower-cost, lighter-weight, and more compact electric ma-<br>chines used for vehicle propulsion. In this research, a dual-rotor inert-core machine (ICM) is<br>considered to meet this demand. In the ICM, permanent-magnet-based Halbach arrays are<br>placed on inner and outer rotating structures. This enables one to eliminate magnetic steels<br>used in the stator and rotor of traditional electric machinery. In addition, a stator structure<br>that leverages a thermal plastic is proposed that facilitates straightforward active cooling<br>of phase windings, which greatly increases current density. To support the multi-objective<br>design of the ICM, a multi-physics toolbox has been developed. Within the toolbox, electro-<br>magnetic performance is predicted using a method-of-moments-based field solver. Thermal<br>performance is assessed using a thermal equivalent circuit that includes conductive heat<br>transfer from stator windings to the surrounding environment as well as convective heat<br>transfer to moving fluids. The structural integrity of the stator is assessed using analytical<br>expressions to predict stress from material properties, geometry, and applied external forces.<br>Calculated loss of proposed designs includes those of the stator windings as well as those<br>required for active cooling. Several optimization studies have been conducted to evaluate the<br>performance of the ICM under an expected electric vehicle driving cycle. From the studies,<br>Pareto-optimal fronts are obtained and used to explore the impact of alternative cooling<br>strategies on volumetric power density.</p>

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