The delimitation of the very fines lithologies from seismic data is a crucial problem in geophysics, indeed the presence of the noise in seismic traces can deteriorate information and hide important hydrocarbons accumulations. For that we have to try in this paper to use a recent technique developed by A.Arneodo and his collaborators which is the wavelet transform modulus maxima lines (WTMM) combined with the discrete wavelet transform (DWT), to denoising traces and characterize each amplitude in the seismic trace by an exponent of Holder. In order to separate information that is of a significant geological lithology variation with the various noises. Our application at VSP data shows that this technique is a powerful tool of processing.

The numerical path integration method for solving stochastic differential equations is extended to solve systems up to six spatial dimensions, angular variables, and highly nonlinear systems - including systems that results in discontinuities in the response probability density function of the system. Novel methods to stabilize the numerical method and increase computation speed are presented and discussed. This includes the use of the fast Fourier transform (FFT) and some new spline interpolation methods. Some sufficient criteria for the path integration theory to be applicable is also presented. The development of complex numerical code is made possible through automatic code generation by scripting. The resulting code is applied to chaotic dynamical systems by adding a Gaussian noise term to the deterministic equation. Various methods and approximations to compute the largest Lyapunov exponent of these systems are presented and illustrated, and the results are compared. Finally, it is shown that the location and size of the additive noise term affects the results, and it is shown that additive noise for specific systems could make a non-chaotic system chaotic, and a chaotic system non-chaotic.

An analog controller has been analyzed and built for an electrostatic micro-cantilever beam. The closed loop MEMS device can be used as both actuator and sensor. As an actuator it will have the advantage of large stable travel range up to 90% of the gap. As a sensor the beam is to be driven into chaotic motion which is very sensitive changes in the system parameters. Two versions of the controller have been analyzed and implemented, one for the actuator and one for the sensor. For the actuator, preliminary experiments show good matching with the model. As for the sensor, the dynamic behavior have been studied and the best operating regions have been determined.

Voltage (lighting) flicker is mainly caused by the electric arc furnaces (EAF) facility supplied by the medium and high voltage power network. In addition to that, because of the increase of wind power generation in both quantity and capacity, intermittent power output of wind turbines under wind speed variation could also cause voltage flickers that affect the performance of lighting and electronics devices in the neighboring feeder buses. Successful voltage flicker prediction and propagation estimation would help both utility and customers in dealing with the problem. This dissertation presents a nonlinear model for the short term prediction of voltage flicker due to EAF operations. In this study, synchronized voltage flicker measurement was conducted at several EAF facilities to understand the stochastic behavior of voltage flicker. The electric loading condition during EAF melting process shows a long term qualitative behavior of a dynamic system and illustrates a special structure of a fractal system. With the fractal structure identification, the behavior hidden behind the voltage flicker time series measurement could be grasped. Using a phase space reconstruction technique and Lyapunov exponent (LE) of state trajectory in the phase space, based on actual voltage flicker measurements, it is proved that the voltage flicker time series is chaos. By using LE, three formulations are adopted to build the prediction models and illustrate the feasibility of short term EAF voltage flicker prediction. Currently, some Asian countries are using the Japanese £GV10 flicker voltage standard. Due to the adoption of IEC standard by IEEE and European countries, a rational conversion of flicker planning limits between different standards would help utilities consider revising or changing their voltage flicker standards and planning limits. Statistical analyses of Pst and £GV10 measurement are conducted in this study. Under different EAF types and operation conditions, reasonable conversion factors between Pst and £GV10 standards are derived, and the flicker transfer factor between different voltage levels of the power supply system are presented.

Abstract The impenetrable movement and crash of the stock market is always the most intriguing research task of any financial researcher. Nowadays, it has been proved that the movements of financial asset have the property of non-linearity or near-chaos and shows some tendency within a given period. We used the R/S analysis as the tool to indicate the tendency, and those stocks as our researching objects. We then combined purely price technical analysis indicators and genetic algorithms to form a predicting model. Then we compared our genetic predicting model with the traditional ARIMA analysis and hope to find out the invisible pattern under price volatility. And we hope our model could assist investors in assessing the stock markets more objectively and reduce the risk of stock investment. The researching target is TSMC(2330). We covered the period from 5 September 1994 to 28 December 1999, resulting in 1490 trading days. Historical data are available from Taiwan Economic Journal (TEJ). We execute the researching comparison by bear-market, bull-market, and bull-then-bear market and concluded as follows. 1. After the R/S analysis, we got the Hurst exponent of TSMC to be 0.849855 and the trending cycle was 940. It has proved that the market has tendency and indirectly showed that the Taiwan stock market was not efficient. 2. According to directional precision, our predicting model apparently outpaced the ARIMA model in these three periods. The reason was that our model grabbed more information than the ARIMA model. 3. If we only think about the inputs and outputs, our model seems to be a proper framework for explaining the relationships among variables in comparison with the neural network model having the same input and output variables. 4. We can deduce the invisible relationships of price technical indicators and the closing price. 5. Genetic predicting model can detect the prevailing trend of the learning periods. 6. The shorter the learning period, the better the predicting effects. As a whole and conservatively speaking, we have 70% confidence in directional precision. 7. If we combine proper trading strategy with genetic predicting model and deduct the transaction cost, we still get a better profit than buy-and-hold strategy and have some maneuvering flexibility. 8. After hypothesis testing, our predicting model seems to have some potential of ex ante prediction, but the stability and usability still need further study. In short, we proposed the ex post stock price movement learning model and the viable direction of ex ante prediction. Investors can take advantage of the flexibility of the predicting model and avoid using the over-complex and rigid trading strategies.

Periodic and chaotic dynamical systems follow deterministic equations such as Newton's laws of motion. To distinguish the difference between two systems, the initial conditions have an important role. Chaotic behaviors or dynamics are characterized by sensitivity to initial conditions. Mathematically, a chaotic system is defined as a system very sensitive to initial conditions. A small difference in initial conditions causes unpredictability in the final outcome. If error is measured from the initial state, the relative error grows exponentially. Prediction becomes impossible and finally, chaotic systems can come to become stochastic system. To make chaotic motion, the number of variables in the system should be above three and there should be non-linear terms coupling several of the variables in the equation of motion. Phase space is defined as the space spanned by the coordinate and velocity vectors. In our case, mixing zone is phase space. With the above characteristics - the initial condition sensitivity of a chaotic system, our plan is to find most efficient chaotic stirrer. In this thesis, we present four methods to measure mixing state based on the chaotic dynamics theory. The Lyapunov exponent is a measure of the sensitivity to initial conditions and can be used to calculate chaotic strength. We can decide the chaotic state with one real number and measure efficiency of the chaotic mixer and find the optimum frequency. The Poincare section method provides a means for viewing the phase space diagram so that the motion is observed periodically. To do this, the trajectory is sectioned at regular intervals. With the Poincare section method, we can find 'islands' considered as bad mixed zones so that the mixing state can be measured qualitatively. With the chaotic dynamics theory, the initial length of the interface can grow exponentially in a chaotic system. We will show the above characteristics of the chaotic system to prove as fact that our model is an efficient chaotic mixer. The final goal for making chaotic stirrer is how to implement efficient dispersed particles. The box counting method is focused on measurement of the particles dispersing state. We use snap shots of the mixing process and with these snap shots, we devise a plan to measure particles' dispersing rate using the box-counting method.

The first part of this work gives an introduction into aperiodic order in general and the lines of research pursued. The second part consists of eight manuscripts.

Οι ασθενείς λύσεις μιας διαφορικής εξίσωσης βρίσκονται σε μια ένα προς ένα αντιστοιχία με τα κρίσιμα σημεία ενός κατάλληλου συναρτησιοειδούς. Οι χώροι Sobolev που θα αναφερθούμε εδώ, για την ύπαρξη των ασθενών λύσεων, είναι υπόχωροι Χ του Η1=Η1(M,g). Οι άλλοι χώροι Ηqk αναφέρονται διότι θα χρησιμοποιηθούν για το πέρασμα των ασθενών λύσεων σε C2 κλασικές λύσεις. / --

An analog controller has been analyzed and built for an electrostatic micro-cantilever beam. The closed loop MEMS device can be used as both actuator and sensor. As an actuator it will have the advantage of large stable travel range up to 90% of the gap. As a sensor the beam is to be driven into chaotic motion which is very sensitive changes in the system parameters. Two versions of the controller have been analyzed and implemented, one for the actuator and one for the sensor. For the actuator, preliminary experiments show good matching with the model. As for the sensor, the dynamic behavior have been studied and the best operating regions have been determined.

In the first part of this thesis, we present the first non-trivial small value estimate that applies to an algebraic group of dimension 2 and which involves large sets of points. The algebraic group that we consider is the product ℂ× ℂ*, of the additive group ℂ by the multiplicative group ℂ*. Our main result assumes the existence of a sequence (PD)D ≥1 of non-zero polynomials in ℤ [X1, X2] taking small absolute values at many translates of a fixed point (ξ, η) in ℂ × ℂ* by consecutive multiples of a rational point (r, s) ∈ (ℚ*)2 with s = ±1. Under precise conditions on the size of the coefficients of the polynomials PD, the number of translates of (ξ, η) and the absolute values of the polynomials PD at these points, we conclude that both ξ and η are algebraic over ℚ. We also show that the conditions that we impose are close from being best possible upon comparing them with what can be achieved through an application of Dirichlet’s box principle. In the second part of the thesis, we consider points of the form θ = (1,θ1 , . . . ,θd-1 ,ξ) where {1,θ1 , . . . ,θd-1 } is a basis of a real number field K of degree d ≥ 2 over ℚ and where ξ is a real number not in K. Our main results provide sharp upper bounds for the uniform exponent of approximation to θ by rational points, denoted λ ̂(θ), and for its dual uniform exponent of approximation, denoted τ ̂(θ). For d = 2, these estimates are best possible thanks to recent work of Roy. We do not know if they are best possible for other values of d. However, in Chapter 2, we provide additional information about rational approximations to such a point θ assuming that its exponent λ ̂(θ) achieves our upper bound. In the course of the proofs, we introduce new constructions which are interesting by themselves and should be useful for future research.