In this study two nonlinear analysis methods are proposed for investigation of nonlinear effects of high temperature superconductive(HTSC) thin film planar microwave circuits. The MoM-HB combination method is based on the combination formulation of the moment method(MoM) and the harmonic balance(HB) technique. It consists of linear and nonlinear solvers. The power series method treats the voltages at higher order frequencies as the excitations at the corresponding frequencies, and the higher order current distributions are then obtained by using the moment method again. The power series method is simple and fast for finding the output power at higher order frequencies. The MoM-HB combination method is suitable for strong nonlinearity, and it can be also used to find the fundamental current redistribution, conductor loss, and the scattering parameters variation at the fundamental frequency. These two proposed methods are efficient, accurate, and suitable for distributed-type HTSC nonlinearity. They can be easily incorporated into commercial EM CAD softwares to expand their capabilities. These two nonlinear analysis method are validated by analyzing a HTSC stripline filter and HTSC antenna dipole circuits. HTSC microstrip lines are then investigated for the nonlinear effects of HTSC material on the current density distribution over the cross section and the conductor loss as a function of the applied power. The HTSC microstrip patch filters are then studied to show that the HTSCinterconnecting line could dominate the behaviors of the circuits at high power. The variation of the transmission and reflection coefficients with the applied power and the third output power are calculated. The HTSC microstrip line structure with gilded edges is proposed for improving the power handling capability of HTSC thin film circuit based on a specified limit of harmonic generation and conductor loss. A general analysis approach suitable for any thickness of gilding layer is developed by integrating the multi-port network theory into aforementioned proposed nonlinear analysis methods. The conductor loss and harmonic generation of the gilded HTSC microstrip line are investigated.

We present results on smooth and nonsmooth variational properties of {it symmetric} functions of the eigenvalues of a real symmetric matrix argument, as well as {it absolutely symmetric} functions of the singular values of a real rectangular matrix. Such results underpin the theory of optimization problems involving such functions. We answer the question of when a symmetric function of the eigenvalues allows a quadratic expansion around a matrix, and then the stronger question of when it is twice differentiable. We develop simple formulae for the most important nonsmooth subdifferentials of functions depending on the singular values of a real rectangular matrix argument and give several examples. The analysis of the above two classes of functions may be generalized in various larger abstract frameworks. In particular, we investigate how functions depending on the eigenvalues or the singular values of a matrix argument may be viewed as the composition of symmetric functions with the roots of {it hyperbolic polynomials}. We extend the relationship between hyperbolic polynomials and {it self-concordant barriers} (an extremely important class of functions in contemporary interior point methods for convex optimization) by exhibiting a new class of self-concordant barriers obtainable from hyperbolic polynomials.

<p>In this dissertation, I discuss two important factors in individuals' decision-making processes: subjective expectation bias and time-inconsistent preferences. In Chapter I, I look at how individuals' own subjective expectations about certain future events are different from what actually happens in the future, even after controlling for individuals' private information. This difference, which is defined as the expectation bias in this paper, is found to have important influence on individuals' choices. Specifically, I look into the relationship between US elderly's subjective longevity expectation biases and their smoking choices. I find that US elderly tend to over-emphasize the importance of their genetic makeup but underestimate the influence of their health-related choices, such as smoking, on their longevity. This finding can partially explain why even though US elderly are found to be more concerned with their health and more forward-looking than we would have concluded using a model which does not allow for subjective expectation bias, we still observe many smokers. The policy simulation further confirms that if certain public policies can be designed to correct individuals' expectation biases about the effects of their genes and health-related choices on their longevity, then the average smoking rate for the age group analyzed in this paper will go down by about 4%.</p><p>In Chapter II, my co-author, Hanming Fang, and I look at one possible explanation to the under-utilization of preventive health care in the United States: procrastination. Procrastination, the phenomenon that individuals postpone certain decisions which incur instantaneous costs but bring long-term benefits, is captured in economics by hyperbolic discount factors and the corresponding time-inconsistent preferences. This chapter extends the semi-parametric identification and estimation method for dynamic discrete choice models using Hotz and Miller's (1993) conditional choice probability approach to the setting where individuals may have hyperbolic discounting time preferences and may be naive about their time inconsistency. We implement the proposed estimation method to US adult women's decisions of undertaking mammography tests to evaluate the importance of present bias and naivety in the under-utilization of mammography, controlling for other potentially important explanatory factors such as age, race, household income, and marital status. Preliminary results show evidence for both present bias and naivety in adult women's decisions of undertaking mammography tests. Using the parameters estimated, we further conduct some policy simulations to quantify the effects of the present bias and naivety on the utilization of preventive health care in the US.</p> / Dissertation

<p>This dissertation concerns methods to test whether or not self-control</p><p>is costly, the form of temptation, and the affects different assumptions</p><p>about costly self-control and temptation have on optimal borrowing</p><p>and saving mechanisms. The second chapter shows that costly self-control</p><p>and temptation can be differentiated from changing impatience in a</p><p>stochastic income consumption-savings environment. The third chapter</p><p>describes an experiment to test whether subjects have time inconsistent</p><p>preferences, whether self-control is costly, and if so, whether the</p><p>cost of self-control is time dependent. The fourth chapter describes</p><p>the affects on the optimal borrowing and savings mechanisms that assumptions</p><p>about the myopia of temptation and the strength of costly self-control</p><p>have.</p> / Dissertation

D. Tech. Mathematical Technology. / Investigates hyperbolic and pseudohyperbolic equations and the results are applied to higher-order rod approximations for the propagation of the longitudinal stress waves in elastic rods. The main objectives of this thesis are: 1. Provide a unified approach to the derivation of the families of one-dimensional hyperbolic differential equations simultaneously with the associated natural and essential boundary conditions describing longitudinal vibration of finite length rods. 2. Establish a new theoremto shorten the derivation of equations of motion and the corresponding boundary conditions, modelling longitudinal wave propagation in the rod. 3. Prove that, when deriving the higher-order rod equations, the lower-order are still included, thus increasing the number of deformations in the rod or the accuracy of the model. 4. Provide mathematical tools for the classification of the obtained equations. 5. Compare the accuracy of the above-mentioned vibration theories in elastic rods based on the investigation of their frequency spectrums which are not available in the literature. 6. Show how two of the above vibration theories, the Rayleigh-Bishop and Mindlin-Herrmann theories, can be applied to predict wave propagation in a piezoelectric circular cylinder and isotropic conical rod. In both cases a numerical example is given as a simulation of the solution.7. Find general methods for solving problems of longitudinal vibration of finite length rods for all of the above-mentioned theories.

Τα δυναμικά βαρυτικών συστημάτων μπορούν να περιγραφούν ασυμπτωτικά στη γειτονιά μιας χωρικής ανωμαλίας σαν μια κίνηση μπιλιάρδου στον υπερβολικό χώρο.Η περιγραφή αυτή μπορεί να πραγματοποιηθεί με άλγεβρες Kac-Moody λαμβάνοντας σαν σύστημα ένα σ-μοντέλο. / The dynamics of some models in Gravity can be described as a billiard motion in the vicinity of a spacelike singularity in hyperbolic space. This description is equivalent in terms of a sigma model and can be described by some hyperbolic Kac-Moody algebras

We study the hyperbolic dynamical systems known as Smale spaces. More specifically we investigate the C*-algebras constructed from these systems. The K group of one of these algebras has a natural ring structure arising from an asymptotically abelian property. The K groups of the other algebras are then modules over this ring. In the case of a shift of finite type we compute these structures explicitly and show that the stable and unstable algebras exhibit a certain type of duality as modules. We also investigate the Bowen measure and its stable and unstable components with respect to resolving factor maps, and prove several results about the traces that arise as integration against these measures. Specifically we show that the trace is a ring/module homomorphism into R and prove a result relating these integration traces to an asymptotic of the usual trace of an operator on a Hilbert space.

We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domains of attractions in case of inward pointing vector fields in the limit of ε-> 0 has been investigated by the authors. We extend these results to domains with characteristic boundaries and show that the perturbed system exhibits a metastable behavior in the sense that there exits a unique ε-dependent time scale on which the random system converges to a continuous time Markov chain switching between the invariant measures. As examples we consider α-stable perturbations of the Duffing equation and a chemical system exhibiting a birhythmic behavior.

Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to tenth-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes, and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes

One-way and two-way classification models in experimental design for both balanced and unbalanced cases are considered when the errors have Generalized Secant Hyperbolic distribution. Efficient and robust estimators for main and interaction effects are obtained by using the modified maximum likelihood estimation (MML) technique. The test statistics analogous to the normal-theory F statistics are defined to test main and interaction effects and a test statistic for testing linear contrasts is defined. It is shown that test statistics based on MML estimators are efficient and robust. The methodogy obtained is also generalized to situations where the error distributions from block to block are non-identical.