This study explores the dynamics of salt finger convection which occurs when warm, salty water overlies cool and fresh. Salt finger convection is generally observed in mid-latitude regions, particularly in the Atlantic Ocean and Mediterranean Sea, between the base of the mixed layer and the top of the intermediate water. Active salt fingering is characterized by the appearance of well mixed layers separated by thin high-gradient interfaces, known as thermohaline staircases. The data from the CSALT, SFTRE and moored profiler experiments are analyzed to determine the origin of the thermohaline staircases and the mechanism for selection of the preferred layer thickness. Comparisons between these observations and models suggested by Radko are made. We use a combination of data analysis and analytical considerations to estimate the vertical heat/salt mixing rates and their dependencies on the large-scale environmental parameters. The three dimensional structure of these staircases and their evolution in time is explained by considering the secondary instabilities of a series of diffusive interfaces and the temporal and spatial structure of the high resolution data. Using a Parabolic Equation model we have investigated the influence of thermohaline staircases on acoustic propagation Also we experiment the sensitivity of the acoustic variations to changes in frequency and source depth. / Royal Australian Navy author

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. May 30, 2016. / In this dissertation, we consider a number of modi ed Black-Scholes equations being either non-linear or given in higher dimensions. In particular we focus on the non-linear Black-Scholes equation describing option pricing with hedging strategies in one case, and two dimensional models in the other. Classical Lie point symmetry techniques are employed in an attempt to construct exact solutions. Some large symmetry algebras are admitted. We proceeded by determining the one dimensional optimal systems of sub-algebras for the admitted Lie algebras. The elements of the optimal systems are used to reduce the number of variables by one. In some cases, exact solutions are constructed. For the cases for which exact solutions are di cult to construct, we employed the numerical solutions. Some simulations are observed and interpreted / MT2016

A project report submitted to the Faculty of Mining Engineering, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. / A strategy to determine the probability that a mining induced seismic event will occur with magnitude which exceeds some specified value within a given time is investigated. The model allows for a non-linear frequency-magnitude relationship and a Poissonian distribution of seismic events in time. The procedure is also independent of the method of mining and of the mining geometry. The model was applied to clusters of various sizes) starting from small areas on a single reef and ending up with the entire mine as a single entity. It was shown that the model works well with large populations of events, but to be successful with small clusters, the retention of the Poisson distribution is too restrictive and a non-stationary model of seismicevent occurrence in time will have to be developed. / AC2018

A research report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in partial fulfillment of the requirements for the Degree of Masters of Science. / Owing to the complexity of hedging against the unfavourable price movements, derivatives came into being to solve this problem if used in an effective and appropriate manner. Movements in share or stock prices, foreign exchange rates, interest rates, etc., make it difficult to anticipate or guess the next price or exchange rate or interest rates. Hence hedging ones'self against these movements becomes a hurdle that is difficult to overcome. Coming to the fore of the derivatives markets made a relief to many traders, but still then, no one could be certain about the move of the market which he is trading in. Forecasting appeared as an educated guess as to which direction and by how much the market will move. This research report focusses on how to forecast the foreign exchange rates using the Dollar/Rand as an example. I have gathered the historical daily data for the DoIIar/Rand spot rates which includes the mayhem period that happened in February 1996. The data was obtained from one of the biggest banks of South Africa; it was drawn from the Reuters historical data giving the open, high, low and close prices of the Dollar/Rand (USD/ZAR) spot rates. The data was then downloaded and copied to the spreadsheet for the calculation of the historical volatilities for different periods. To have a genuine comparison with the implied volatilities, a data of historical implied volatilities tor approximately the same period was gathered from the SAIMB (South African International Money Brokers). The only snag with the data was that it only catered for specific traded periods, like 1 month, 2 months, 3 months, 6 months, 9 months and 12 months only. Most financial institutinns are using these implied volatilities for their pricing and end-of-day or -month or -year revaluation. By the same token the data was downloaded to the spreadsheet for further analysis and arrangement. Chapter 1 gives the purpose and the meaning of'forecasting, together with different methods that this process can be achieved. Views from Makridakis et al., (1983) are used to beautify the world of forecasting and its importance. In Chapter 2 the concept of volatility and its causes, is discussed in detail. Besides the implied and historical volatility discussions, volatility 'smile' concept is discussed and expanded. Volatility slope trading strategies and constraints on the slope of the volatility term structure are discussed in detail. Chapter 3 discusses different models used to calculate both the historical and the implied volatility. This includes models by Kawaller et al., (1994) and Figlewski et al., ( 1990). The Newton-Raphson method is among of the methods that can be used to get a good estimate of the implied volatility. For a lot accurate estimates the Method of Bisection can be used in place of the Newton-Raphson method. Mayhew (1995) even suggest a method, which involves the use of more weighting with higher vegas (Latane and Rendleman 1976) or weighting not by vegas but elasticity (Chiras and Manaster 1978). Chapter 4 dwells on different forecasting models for foreign exchange markets. This includes models by Engle (1993), who is one of the pioneers of the autoregression theory, He discusses the ARCH, GARCH and EGARCH models; Heynen et al., (1994,1995) discusses the models for the term structure of volatility implied by foreign exchange. In the 1995 article he dwells on the specifications of the different autoregressive conditional heteroskedastic models. U.A. Muller et al., (1990,1993) discusses some of the models for the changing time scale for short-term forecasting in financial markets. This includes discussion of some statistical properties of FX rates time-series. Xu and Taylor (1994) also discuss the term structure of volatility as implied, in particular, by FX options. Regression is used in computation of implied volatility Chapter 5 dwells on the empirical evidence and the market practice. This includes the statistical analysis of the data; applying the scaling law; proprietary model which depicts the edge between the historical volatility and implied volatility; empirical tests and the volatility forecast evaluation applied to historical USD/ZAR daily data, using different models. In the statistical analysis, using U.A. Muller et al., (1993) theory, the scaling law, which involves the absolute price changes, which are directly related to the interval At, is discussed. Using my GSD/ZAR data Imanaged to calculate the parameters described by the scaling law, using At as one day since my data is a daily data Icould not calculate the activity model function, which calculates the intra-day and intra-hour trading using tick-by-tick data, because of the nature of my data. Had it not been the case, f would have been able to calculate the intra-day and intra-hour volatilities. These statistics would have been able to depict the daily volatility, more especially on volatile days, like the day when the Rand took its first knock in February 1996. In the second section of the chapter the proprietary model is discussed, where an edge between the actual volatility and implied volatility was identified. There is a positive correlation between the actual and implied volatility although the latter is always higher than the former; hence traders can play with this situation for arbitrage purposes. To get the estimates of historical volatility, I used the Well-known formula of using the log-relatives of the returns of any two consecutive days. Annnalised standard deviation of these log-relatives resulted into the required historical volatility estimates. Moving averages were used to get estimates of different periods, as can be seen in the text. The main theme of the research report is to expose forecasting models that can be used in foreign exchange currencies using DolIar/Rand as an example. Random walk model was used as benchmark to other models like stochastic volatility, ARCH, GARCH( 1,1), and EGARCH (1,1). Due to the complexity of the specifications of these models, I used the SHAZAM 7.0 econometric program to generate the necessary parameters. Complex formulas of these models are given in the Appendices at the end of the report, together with the program itself. The significance of the forecasted volatility estimates was checked using the p-value correlation statistic and the Akaike Information Criterion (AIC). The p-value gives us the significance of the parameters and the AlC gives us an indication of the goodness-of-fit of the model. The formulas used to calculate these statistics are given at the end of the report as part of the Appendices. An account of where and how shese results can be of help in the practical situation is given under the section of market practice. One of the areas worth mentioning is in risk management, where estimates of the historical volatility can be used together with correlation in risk-metrics to calculate VArt (value-at-risk). VAR is defined in simple terms as the 5thpercentile (quantile) of the distribution of value changes. The beau.y of working with the percentile rather than, say the variance of a distribution, is that a percentile corresponds to both a magnitude e.g., dollar amount at risk, and exact probability e.g., the probability that the magnitude will not be exceeded. This roughly the gist of the research report. / Andrew Chakane 2018

University of Macau / Faculty of Science and Technology. / Department of Mathematics

University of Macau / Faculty of Science and Technology. / Department of Mathematics

Photocopy of typescript. / Digitized by Kansas Correctional Industries

In today's information age, companies collect massive amount of asymmetric flow data at individual customer level. Examples include customer-by-customer data (e.g., money, phone call and email flows among customers), product-by-product data (e.g., sequential purchase data), and web traffic data, etc. Asymmetric flow data carries meaningful customer intelligence and yet, it is under-explored. When combined with other data (such as customer profile and sales, etc.), this flow data can provide valuable understanding on individual customers, and thus enable marketers to trigger marketing actions at individual-customer level. / Simulation results show that the proposed algorithms yield promising model fitting performance within reasonable time. The LAS algorithm can successfully analyze 100,000 subjects in less than 10 hours. The CAS algorithm analyzes 50,000 subjects in 18 hours. The TAS algorithm analyzes 5,000 subjects within one hour. The proposed models are also applied on two real datasets (i.e., email data and web log data) to investigate the network structure among researchers and web pages. Results of simulation experiments and real data analyses suggest the proposed asymmetric scaling methods are viable ways of analyzing massive asymmetric flow data in marketing. / This thesis proposes three asymmetric scaling methods to analyze asymmetric flow data in marketing, namely Linear Asymmetric Scaling (LAS), Circular Asymmetric Scaling (CAS), and Two-dimensional Asymmetric Scaling (TAS). To visualize and analyze the asymmetric relationship among subjects, we assume that each subject has two relationship roles (i.e., as a source and as a destination of relationship flows). The LAS, CAS and TAS models represent asymmetric relationship among subjects by linear, circular and two-dimensional representations respectively. / Ho Ying. / "February 2007." / Adviser: Kin-Nam Lau. / Source: Dissertation Abstracts International, Volume: 68-09, Section: A, page: 3969. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 230-241). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Finally, we investigate the motion of a general form rigid body with smooth boundary by an incompressible perfect fluid occupying R3 . Due to the domain occupied by the fluid depending on the time, this problem can be transformed into a new systems of the fluid in a fixed domain by the frame attached with the body. With the aid of Kato-Lai's theory, we construct a sequence of successive solutions to this problem in some unform time interval. Then by a fixed point argument, we have proved that the existence, uniqueness and persistence of the regularity for the solutions of original fluid-structure interaction problem. / In the first part, we study the issue of the inviscid limit of the incompressible Navier-Stokes equations on the general smooth domains for completely slip boundary conditions. We verify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in the Prantle's theory. We improve the better regularity for the boundary layer and obtain the uniform Lp--estimates (3 < p ≤ 6) of the remainder. Then we improved these estimates to H 1--estimates. It is shown that the viscous solution converges to the solution of Euler equation in C([0, T]; H1(O)) as the viscosity tends to zero. / In the second part, we consider the non-stationary problems of a class of non-Newtonian fluid which is a power law fluid with p > 3nn+2 in the half space with slip boundary conditions. We present the local pressure estimate with the Navier's slip boundary conditions. Using these estimates and an Linfinity -- truncation method, we can obtain that this system has at least one required weak solution. / In this thesis, we study several issues involving incompressible viscous fluids with the slip boundary conditions and the motions of fluid-solid interactions. / Zang, Aibin. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 128-141). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Traditional cointegration analysis asserts that the observed series are unit root processes, but a linear combination among these series is a short-memory stationary process. By allowing deviations from equilibrium to follow a fractionally integrated process, fractional cointegration analysis captures a wider range of mean-reverting behavior than traditional cointegration. Under the assumption that the integration orders of the underlying series are equal, based on the memory estimates from observed series and the regression residual, we propose a residual-based test for the null hypothesis of no fractional cointegration against the alternative of fractional cointegration. Under some regular conditions, the test statistic has an asymptotic standard normal distribution under the null and diverges under the alternative. The test is easy to implement and performs well in Monte Carlo experiments. A necessary condition for fractional cointegration is that the integrated orders of underlying series are equal. We present a procedure to test for the equality of integration orders of the underlying series. / Wang, Bin. / Adviser: Ngai Hang Chan. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3589. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 50-54). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.