In this dissertation three different economic issues have been analyzed. The first issue is whether monetary policy rules can improve forecasting accuracy of inflation. The second is whether the preference of a central bank is symmetry or not. The last issue is whether the behavior of aggregate dividends is asymmetry. Each issue is considered in Chapter II, III and IV, respectively. The linkage between monetary policy rules and the prediction of inflation is explored in Chapter II. Our analysis finds that the prediction performance of the term structure model hinges on monetary policy rules, which involve the manipulation of the federal funds rate in response to the change in the price level. As the Fed's reaction to inflation becomes stronger, the predictive information contained in the term structure becomes weaker. Using the long-run Taylor rule, a new assessment of the prediction performance regarding future change in inflation is provided. The empirical results indicate that the long-run Taylor rule improves forecasting accuracy. In chapter III, the asymmetric preferences of the central bank of Korea are examined under New Keynesian sticky prices forward-looking economy framework. To this end, this chapter adopts the central bank's objective functional form as a linear-exponential function instead of the standard quadratic function. The monetary policy reaction function is derived and then asymmetric preference parameters are estimated during the inflation targeting period: 1998:9-2005:12. The empirical evidence supports that while the objective of output stability is symmetry, but the objective of price stability is not symmetry. Specifically, it appears that the central bank of Korea aggressively responds to positive inflation gaps compared to negative inflation gaps. Chapter IV examines the nonlinear dividend behavior of the aggregate stock market. We propose a nonlinear dividend model that assumes managers minimize the regime dependent adjustment costs associated with being away from their target dividend payout. By using the threshold vector error correction model, we find significant evidence of a threshold effect in aggregate dividends of S&P 500 Index in quarterly data when real stock prices are used for the target. We also find that when dividends are relatively higher than target, the adjustment cost of dividends is much smaller than that when they are lower.

Beam problem is very important for engineering theoretically and practically. In this thesis we study such kind of nonlinear 4-th order ordiniary differential equations with nonlinear boundary conditions. The well-posedness of these boundary value problems will be discussed. Moreover, we will design different schemes to solve them, through differential equation, integral equation or minimization. Each type can further be discretized by finite difference, finite element or spectral method, etc. In the end we will compare all methods and find the best one.

Abstract¡G For the fractional-N frequency synthesizers using delta-sigma modulation techniques, the noise source dominant to degrade the spectral purity comes from phase intermodulation of quantization noise due to the PLL nonlinearity. To study and improve the PLL nonlinearity effect, this thesis applies the theory of white quantization noise and nonlinear analysis method to simulate the frequency responses of quantization noises in delta-sigma modulators (DSM) with different order and in various architecture. With the help of Agilent EEsof¡¦s ADS tool, the phase noise performance of the studied fractional-N frequency synthesizers can be well predicted. For demonstration, this thesis work implements a 2.4 GHz fractional-N frequency synthesizer hybrid module, and measures the phase noise under considering various combinations of DSM order and architecture, PLL bandwidth and reference frequency. Another demonstration of this thesis is to implement a PLL IC using 0.18 £gm CMOS process. The implemented PLL IC operates in the frequency range from 2120 to 2380 MHz with a supply voltage of 1.8 V and a current consumption of 27 mA. Under the test condition of reference frequency and PLL bandwidth equal to 20 MHz and 50 kHz, respectively, the measured phase noise is 90 dBc/Hz at an offset frequency of 100 kHz and the measured stable time is about 40 £gs for a frequency jump of 80MHz.

In this thesis we obtain several interesting algebraic properties of the operations used in the block cipher IDEA which are important for cryptographic analyzes. We view each of these operations as a function from $mathbb Z_{2}^n times mathbb Z_{2}^n to mathbb Z_{2}^n$. By fixing one of variables $v(z)=mathbf Z$ in $mathbb Z_{2}^n times mathbb Z_{2}^n$, we define functions $mathbf {f}_z$ and $mathbf {g}_z$ from $mathbb Z_{2}^n$ to $mathbb Z_{2}^n$ for the addition $BIGboxplus$ and the multiplication $BIGodot$ operations, respectively. We first show that the nonlinearity of $mathbf {g}_z$ remains the same under some transformations of $z$. We give an upper bound for the nonlinearity of $mathbf {g}_{2^k}$, where $2leq k &lt / n-1$. We list all linear relations which make the nonlinearity of $mathbf {f}_z$ and $mathbf {g}_z$ zero and furthermore, we present all linear relations for $mathbf {g}_z$ having a high probability. We use these linear relations to derive many more linear relations for 1-round IDEA. We also devise also a new algorithm to find a set of new linear relations for 1-round IDEA based on known linear relations. Moreover, we extend the largest known linear class of weak keys with cardinality $2^{23}$ to two classes with cardinality $2^{24}$ and $2^{27}$. Finally, we obtain several interesting properties of the set $ { ({mathbf X},{mathbf X} BIGoplus {mathbf A}) in mathbb Z_2^n times mathbb Z_2^n ,|, (mathbf {X}BJoin {mathbf Z})BIGoplus( ({mathbf X} BIGoplus {mathbf A} ) BJoin mathbf {Z} ) = {mathbf B} }$ for varying ${mathbf A}, {mathbf B}$ and ${mathbf Z}$ in $mathbb Z_2^n$, where $BJoin in { BIGodot,BIGboxplus }$. By using some of these properties, we present impossible differentials for 1-round IDEA and Pseudo-Hadamard Transform.

In this work, a new method is suggested for the modal identification of nonlinear structures and for the use of the modal data in calculating response of the nonlinear system to harmonic excitation. Nonlinearity in mechanical structures is usually encountered in connection regions. In this study, the nonlinear part of such a structure is modeled as a single nonlinear element and modal parameters of the structure are obtained as a function of displacement amplitude. Identification and modeling of nonlinear elements can be done through modal tests conducted at different response levels. Response level dependent modal parameters are used in calculating the response of the system to harmonic excitation at any forcing level. Furthermore, the modal model of a nonlinear substructure can be used in structural coupling of the nonlinear system with a linear one, and in structural modification problems where a nonlinear structure is modified with linear elements. Validation of the modal model proposed, and the use of this model in harmonic response computation, structural coupling and structural modification problems are demonstrated with several case studies.

My dissertation focuses primarily on the following three aspects associated with passing seismic waves in the field of earthquake seismology: temporal changes of fault zone properties, nonlinear site response, and dynamic triggering. Quantifying the temporal changes of material properties within and around active fault zones (FZ) is important for better understanding of rock rheology and estimating the strong ground motion that can be generated by large earthquakes. As high-amplitude seismic waves propagate through damaged FZ rocks and/or shallow surface layers, they may produce additional damage leading to nonlinear wave propagation effects and temporal changes of material properties (e.g., seismic velocity, attenuation). Previous studies have found several types of temporal changes in material properties with time scales of tens of seconds to several years. Here I systematically analyze temporal changes of fault zone (FZ) site response along the Karadere-Düzce branch of the North Anatolian fault that ruptured during the 1999 İzmit and Düzce earthquake sequences. The coseismic changes are on the order of 20-40%, and are followed by a logarithmic recovery over an apparent time scale of ~1 day. These results provide a bridge between the large-amplitude near-instantaneous changes and the lower-amplitude longer-duration variations observed in previous studies. The temporal changes measured from this high-resolution spectral ratio analysis also provide a refinement for the beginning of the longer more gradual process typically observed by analyzing repeating earthquakes. An improved knowledge on nonlinear site response is critical for better understanding strong ground motions and predicting shaking induced damages. I use the same sliding-window spectral ratio technique to analyze temporal changes in site response associated with the strong ground motion of the Mw6.6 2004 Mid-Niigata earthquake sequence recorded by the borehole stations in Japanese Digital Strong-Motion Seismograph Network (KiK-Net). The coseismic peak frequency drop, peak spectral ratio drop, and the postseismic recovery time roughly scale with the input ground motions when the peak ground velocity (PGV) is larger than ~5 cm/s, or the peak ground acceleration (PGA) is larger than ~100 Gal. The results suggest that at a given site the input ground motion plays an important role in controlling both the coseismic change and postseismic recovery in site response. In a follow-up study, I apply the same sliding-window spectral ratio technique to surface and borehole strong motion records at 6 KiK-Net sites, and stack results associated with different earthquakes that produce similar PGAs. In some cases I observe a weak coseismic drop in the peak frequency when the PGA is as small as ~20-30 Gal, and near instantaneous recovery after the passage of the direct S waves. The percentage of drop in the peak frequency starts to increase with increasing PGA values. A coseismic drop in the peak spectral ratio is also observed at 2 sites. When the PGA is larger than ~60 Gal to more than 100 Gal, considerably stronger coseismic drops of the peak frequencies are observed, followed by a logarithmic recovery with time. The observed weak reductions of peak frequencies with near instantaneous recovery likely reflect nonlinear response with essentially fixed level of damage, while the larger drops followed by logarithmic recovery reflect the generation (and then recovery) of additional rock damage. The results indicate clearly that nonlinear site response may occur during medium-size earthquakes, and that the PGA threshold for in situ nonlinear site response is lower than the previously thought value of ~100-200 Gal. The recent Mw9.0 off the Pacific coast of Tohoku earthquake and its aftershocks generated widespread strong shakings as large as ~3000 Gal along the east coast of Japan. I systematically analyze temporal changes of material properties and nonlinear site response in the shallow crust associated with the Tohoku main shock, using seismic data recorded by the Japanese Strong Motion Network KIK-Net. I compute the spectral ratios of windowed records from a pair of surface and borehole stations, and then use the sliding-window spectral ratios to track the temporal changes in the site response of various sites at different levels of PGA The preliminary results show clear drop of resonant frequency of up to 70% during the Tohoku main shock at 6 sites with PGA from 600 to 1300 Gal. In the site MYGH04 where two distinct groups of strong ground motions were recorded, the resonant frequency briefly recovers in between, and then followed by an apparent logarithmic recovery. I investigate the percentage drop of peak frequency and peak spectral ratio during the Tohoku main shock at different PGA levels, and find that at most sites they are correlated. The third part of my thesis mostly focuses on how seismic waves trigger additional earthquakes at long-range distance, also known as dynamic triggering. Previous studies have shown that dynamic triggering in intraplate regions is typically not as common as at plate-boundary regions. Here I perform a comprehensive analysis of dynamic triggering around the Babaoshan and Huangzhuang-Gaoliying faults southwest of Beijing, China. The triggered earthquakes are identified as impulsive seismic arrivals with clear P- and S-waves in 5 Hz high-pass-filtered three-component velocity seismograms during the passage of large amplitude body and surface waves of large teleseismic earthquakes. I find that this region was repeatedly triggered by at least four earthquakes in East Asia, including the 2001 Mw7.8 Kunlun, 2003 Mw8.3 Tokachi-oki, 2004 Mw9.2 Sumatra, and 2008 Mw7.9 Wenchuan earthquakes. In most instances, the microearthquakes coincide with the first few cycles of the Love waves, and more are triggered during the large-amplitude Rayleigh waves. Such an instantaneous triggering by both the Love and Rayleigh waves is similar to recent observations of remotely triggered 'non-volcanic' tremor along major plate-boundary faults, and can be explained by a simple Coulomb failure criterion. Five earthquakes triggered by the Kunlun and Tokachi-oki earthquakes were recorded by multiple stations and could be located. These events occurred at shallow depth (< 5 km) above the background seismicity near the boundary between NW-striking Babaoshan and Huangzhuang-Gaoliying faults and the Fangshan Pluton. These results suggest that triggered earthquakes in this region likely occur near the transition between the velocity strengthening and weakening zones in the top few kms of the crust, and are likely driven by relatively large dynamic stresses on the order of few tens of KPa.

The construction of a substitution box (S-box) with high nonlinearity and high resiliency is an important research area in cryptography. In this thesis, t-resilient nxm S-box construction methods depending on linear block codes presented in &quot / A Construction of Resilient Functions with High Nonlinearity&quot / by T. Johansson and E. Pasalic in 2000, and two years later in &quot / Linear Codes in Generalized Construction of Resilient Functions with Very High Nonlinearity&quot / by E. Pasalic and S. Maitra are compared and the former one is observed to be more promising in terms of nonlinearity. The first construction method uses a set of nonintersecting [n-d,m,t+1] linear block codes in deriving t-resilient S-boxes of nonlinearity 2^(n-1)-2^(n-d-1),where d is a parameter to be maximized for high nonlinearity. For some cases, we have found better results than the results of Johansson and Pasalic, using their construction. As a distinguished reference for nxn S-box construction methods, we study the paper &quot / Differentially Uniform Mappings for Cryptography&quot / presented by K.Nyberg in Eurocrypt 1993. One of the two constructions of this paper, i.e., the inversion mapping described by Nyberg but first noticed in 1957 by L. Carlitz and S. Uchiyama, is used in the S-box of Rijndael, which is chosen as the Advanced Encryption Standard. We complete the details of some theorem and proposition proofs given by Nyberg.

In this thesis, one finalist cipher of the Advanced Encryption Standard (AES) block cipher contest, Twofish proposed by Schneier et al, is studied in order to observe the validity of the statement made by Arikan about the randomness of the cipher, which contradicts National Institute of Standards and Technology (NIST)&rsquo / s results. The strength of the cipher to cryptanalytic attacks is investigated by measuring its randomness according to the avalanche criterion. The avalanche criterion results are compared with those of the Statistical Test Suite of the NIST and discrepancies in the second and third rounds are explained theoretically.

This study concentrates on the performance evaluation of a specific modulation scheme under nonlinear operation. This modulation scheme is the phase shift keying (PSK) modulation, exemplified by the special cases of BPSK, QPSK, OQPSK, &amp / #960 / /4-QPSK. The specific nonlinear block is chosen to be the solid state power amplifier (SSPA) structure whose simulation model is the Rapp model. Varying transmitter filter characteristic and one of the power amplifier parameters constitute the main methodology of simulations. Bit error rate (BER), error vector magnitude (EVM), and Space Frequency Coordination Group (SFCG) spectral mask constraint are the evaluation parameters taken into account throughout this study. Simulation results support the initial literature survey, which reveals additional features showing how each modulation scheme is affected by various SSPA nonlinearity characteristics.

This thesis consists of two major parts. In the first part, I monitor the temporal change of S-wave velocity in shallow soil layers using seismic data collected in an experiment at Panola Mt. Atlanta, GA, 2006. I use the cross correlation function to find the arrival time differences for different water levels, and then calculate the change of Rayleigh wave phase velocity according to different frequencies in the range 5 to 50 Hz. After that, I find a reference 1-D layered P and S-wave velocity model from the measured Rayleigh wave dispersion curve, and put 6 sets of Gaussian perturbations into the reference velocity structure to invert for the actual temporal change of velocity structure in the experiment. I find a clear increase of S-wave velocity in the water injection area, and the S-wave velocity gradually recovers to the initial value after we stop pumping water. In the second part, I analyze temporal changes in fault zone site response along the Karadere-Düzce branch of the North Anatolian Fault, starting 8 days before and ending 72 days after the 1999 Mw7.1 Düzce, Turkey, earthquake. The analysis involves comparisons of strong motion seismic records at station VO inside the Karadere fault and station FP about 300 m away from the fault. I compare all available seismic waveforms at these stations, including those generated by foreshocks, the mainshock, aftershocks and seismic noise, and cut them into 10 s windows with a 5 s overlap. Fourier amplitude spectra are computed for seismic data in each window, and the average amplitude spectra for the two horizontal components are used to obtain the spectral ratio for each on/off fault pair of seismic records. The spectral ratios are smoothed over every 10 points in the frequency domain (0.5 Hz). The results show a shift of the spectral peak to lower frequencies during the main shock. The peak frequency reduces from 4.3 Hz several days before the main shock to 2.9 Hz (67.4% of the pre mainshock value) right after the mainshock. It quickly recovers to 3.8 Hz (64% recovery of the dropped value) after a day, and then gradually recovers to 4.0 Hz (79% recovery of the dropped value) after 72 days. I also compare the results from all the seismic data including direct S-wave, S coda waves and seismic noise and from coda waves only and find that the results from coda waves which are generally less scattered than those from all the data, and show lower amplitude of spectra ratio with higher peak frequencies. The observations suggest a nonlinear behavior of the fault zone material under strong ground motion of nearby major earthquakes. Finally I attempt to link the two parts by identifying their implications for the nonlinear site effects.