Very fast automatic rejection algorithms were developed recently which allow to generate random variates from large classes of unimodal distributions. They require the choice of several design points which decompose the domain of the distribution into small sub-intervals. The optimal choice of these points is an important but unsolved problem. So we present an approach that allows to characterize optimal design points in the asymptotic case (when their number tends to infinity) under mild regularity conditions. We describe a short algorithm to calculate these asymptotically optimal points in practice. Numerical experiments indicate that they are very close to optimal even when only six or seven design points are calculated. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Non-invasive physical examination helps to make disease diagnosis with minimum injury to the body. Cardiology ultrasound is a non-invasive examination which can be used as a auxiliary tool for diagnose cardiac structure abnormalities. With more understanding of heart diseases, it has been recognized that heart failures are closely related to left ventricular systolic and diastolic function. Following Chen (2011) and Kao (2011), we study association of heart diseases with the change of gray-scale values in the cardiology ultrasound images of left ventricular systolic and diastolic. Since data obtained from ultrasound image is of matrix type with high dimensions, following the method proposed by Chen (2011) and Kao (2011), factor scores obtained from factor analysis are used as a basis for classification. We take the factor scores of normal subjects to establish the bench mark and calculate the Mahalanobis distance of each abnormal subject with the model established by the data from normal group. Later based on this distance to the normal group, cardiac function of the subject is distinguished as normal or not. In order to improve the accuracy of the classification, influential points which may cause inaccurate covariance matrix estimate on the subjects in normal group are identified. Based on concepts from optimal designs theory, some criteria are established for screening out the influential points.

The general public considers Fixed-Route Transit (FRT) to be inconvenient while Demand-Responsive Transit (DRT) provides much of the desired flexibility with a door-to-door type of service. However, FRT is typically more cost efficient than DRT to deploy. Therefore, there is an increased interest in flexible transit services including all types of hybrid services that combine FRT and pure DRT. The demand-responsive feeder transit, also known as Demand-Responsive Connector (DRC), is a flexible transit service because it operates in a demand-responsive fashion within a service area and moves customers to/from a transfer point that connects to a FRT network. In this research we develop analytical models, validated by simulation, to design the DRC system. Feeder transit services are generally operated with a DRC policy which might be converted to a traditional FRT policy for higher demand. By using continuous approximations, we provide an analytical modeling framework to help planners and operators in their choice of the two policies. We compare utility functions of the two policies to derive rigorous analytical and approximate closed-form expressions of critical demand densities. They represent the switching conditions, that are functions of the parameters of each considered scenario, such as the geometry of the service area, the vehicle speed and also the weights assigned to each term contributing to the utility function: walking time, waiting time and riding time. We address the problem faced by planners in determining the optimal number of zones for dividing a service area. We develop analytical models representing the total cost functions balancing customer service quality and vehicle operating cost. We obtain close-form expressions for the FRT and approximation formulas for the DRC to determine the optimal number of zones. Finally we develop a real-case application with collected customer demand data and road network data of El Cenizo, Texas. With our analytical formulas, we obtain the optimal number of zones, and the times for switching FRT and DRC policies during a day. Simulation results considering the road network of El Cenizo demonstrate that our analytical formulas provide good estimates for practical use.

The growth of embedded generation and portable electrical installations has led to an increased demand for low cost, flexible and reliable generator systems for military and commercial applications. An interior permanent magnet (IPM) machine has high power density due to its reluctance torque and magnetic torque components so it can produce a large constant power-speed range. However, an IPM machine needs demagnetizing current at high-speed during the flux-weakening region and thus develops an inverter shutdown problem in an uncontrolled generator mode operation. In order to overcome the disadvantages of the IPM machine, the permanent magnet assisted synchronous reluctance generator (PMa-SynRG) can be a good solution for low cost, high efficiency reliable generator systems. A PMa-SynRG can produce a high efficiency drive by utilizing the proper amount of magnet and reluctance torque. This work proposes a PMa-SynRG with two flux barriers and permanent magnets embedded in the second layer of the rotor. A neodymium magnet (NdFeB) was used as permanent magnets in the rotor to prevent demagnetization. Finding the minimum amount of magnet is one of the goals of the optimization process. The objectives of this work are to build an optimal design for the 3kW generator and an advanced power electronics converter for the PMa-SynRG drive system. In order to find the optimized 3kW machine, a Lumped Parameter Model (LPM) was used to achieve fast computation, and Differential Evolution Strategy (DES) was used to embed the LPM in an efficient numerical optimization routine to identify optimum designs. Finite Element Analysis (FEA) was used for test performance of optimum designs. On the basis of differences between LPM and FEA, model predictions were used to fine tune the LPM model. For new optimum design converges, numerical optimizations and iterations were performed to produce LPM and FEA predictions. For the drive system, the thyristor based, current-fed drive is much simpler and has lower power losses compared to the pulse width modulation (PWM) drive. Eliminating the requirement for self-controlled switches is a distinct advantage for lower cost. Another feature of the developed current-fed drive is its inherent capability to provide generating action by making the PMa-SynRG operates as a generator, rectifying the phase voltages by means of the three-phase rectifier and feeding the power into the load. These features make the current-fed drive a good candidate for driving any type of synchronous generators including the proposed PMa-SynRG.

We propose an algebraic construction of $(d+1)$-point $D$-optimal designs for $d$th degree polynomial regression with weight function $omega(x)ge 0$ on the interval $[a,b]$. Suppose that $omega'(x)/omega(x)$ is a rational function and the information of whether the optimal support contains the boundary points $a$ and $b$ is available. Then the problem of constructing $(d+1)$-point $D$-optimal designs can be transformed into a differential equation problem leading us to a certain matrix including a finite number of auxiliary unknown constants, which can be solved from a system of polynomial equations in those constants. Moreover, the $(d+1)$-point $D$-optimal interior support points are the zeros of a certain polynomial which the coefficients can be computed from a linear system. In most cases the $(d+1)$-point $D$-optimal designs are also the approximate $D$-optimal designs.

The exact D-optimal design problems for regression models has been in-vestigated in many literatures. Huang (1987) and Gaffke (1987) provided a sufficient condition for the minimum sample size for an certain set of candidate designs to be exact D-optimal for polynomial regression models on a compact interval. In this work we consider a mixture experiment with q nonnegative components, where the proportions of components are sub- ject to the simplex restriction $sum_{i=1}^q x_i =1$, $x_i ¡Ù 0$. The exact D-optimal designs for mixture experiments for Scheffe¡¦s quadratic models are investigated. Based on results in Kiefer (1961) results about the exact D-optimal designs for mixture models with two or three ingredients are provided and numerical verifications for models with ingredients between four and nine are presented.

Weighted polynomial regression of degree d with weight function Exp(£\ x) on an interval is considered. The D-optimal designs £i_d^* are completely characterized via three differential equations. Some invariant properties of £i_d^* under affine transformation are derived. The design £i_d^* as d goes to 1, is shown to converge weakly to the arcsin distribution. Comparisons of £i_d^* with the arcsin distribution are also made.

The aim of this thesis is to develop a Computer-aided Design software for high speed angular contact ball bearing system. First, to analyze the interaction of among the characteristics and parameters of a high-speed spindle system with angular contact ball bearing. These analyses were based on the kinematics of bearing systems and rotor dynamics. According to these analyses, several design charts for bearing system will be established by computer simulations. Secondly, an optimum design for high speed spindle system will also be proposed. After these analyses, an Computer-Aided Design software for high speed bearing system will be established. From the study, preliminary design trends about high speed spindle system will be proposed.

Radio wave absorbing materials (RAM) are commonly found amongst high-tech products such as LCD electronic devices, laptop and desktop computers. Electromagnetic wave absorbing materials are composed of dielectric materials mixed with ferrite, a magnetic material, with varying shapes and sizes. It should be capable of absorbing electromagnetic energy at normal and large incident angles over a wide range of frequencies. This requires the material to possess a large relative complex dielectric constant (permitivity £`r), as well as a large relative complex magnetic permeability constant (£gr). Due to the nature of the complexity of the RAM, which surpasses standard analysis techniques, we have derived, for this thesis, frequency-domain two-dimensional finite-difference formulas for modeling the electromagnetic behavior of RAM. This involves using a material that has a given £`r(1:10 range) and £gr(1:1000 range) which covers a vast range of indices of refraction. To reduce the computational domain, we took care of implementing the numerical absorbing boundary conditions, while also implementing material averaging schemes for the finite-difference coefficients that cover the region where sample medium changes. Simple numerical examples are included to verify our mathematical model. We also implemented an optimal one-dimensional multi-layered RAM design, designed by using a constrained optimization searching technique. Included in the thesis are two complete, practical, optimal designs considering available material parameters (finite loss tangent) as well as their actual manufacturing limitations (layer thickness).

A multi-layered periodic structure is investigated for optimal shape design in diffraction gratings. A periodic dielectric material is used as the scattering profile for a planar incident wave. Designing optimal profiles for scattering is a type of inverse problem. The ability to fabricate such materials on the order of the wavelength of the incoming light is key for design strategies. We compute a finite element approximation on a variational setup of the forward problem. On the inverse and optimal design problem, we discuss the stability of the designs and develop computational strategies based on a level-set evolutionary approach.