In this paper we present a finite volume method for a two-dimensional Black-Scholes equation with stochastic volatility governing European option pricing. In this work, we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conversative form. We then present a finite volume method for the resulting equation, based on a fitting technique proposed for a one-dimensional Black-Scholes equation. We show that the method is monotone by proving that the system matrix of the discretized equation is an M-matrix. Numerical experiments, performed to demonstrate the usefulness of the method, will be presented.

Magnetic resonance spectroscopy has been widely used in medical applications, rendering precise evaluation and diagnosis in clinics. As the development of various tools for automatic spectra analysis, providing objective quantification of metabolites, absolute concentrations has been playing an important role in clinical studies and applications as well. In this study, we investigate the reliability and accuracy of absolute concentration quantified by LCModel. Ten healthy subjects were included. We compared the resultant concentrations calculated by internal water scaling and phantom calibration, both of which are provided by LCModel. Partial volume effect was also taken into account to improve the accuracy of absolute concentrations. Automatic segmentation was applied to volume of interest in order to separate gray matter and white matter, which will facilitate the further partial volume correction and thus better accuracy of absolute quantification.

The purpose of the study is to investigate the problem-solving strategies of children in fourth-grade, fifth-grade and sixth-grade. The investigators tried to guide children through a variety of problem-solving strategies that were in written, figural, or symbolic forms. Then the investigators examined the variation of children¡¦s spatial concepts by analyzing the problem-solving strategies used in calculating the volumes of various solids. In order to improve the teaching materials, the investigator identified the performance of spatial concepts by referring to QCAI (QUASAR Cognitive Assessment Instrument). For the purpose of designing future lessons, the investigator examined the relationship between children¡¦s problem-solving strategies level and the performance in the seven content areas in the curriculum. There are two results of this study: The first result is on the problem-solving strategies found within the same grade (4th; 5th; and 6th) and there are 3 findings. First, strategies of fourth-graders are focused on low-levels and middle-levels; strategies of fifth-graders focused on middle-level geometric space concept, and finally, strategies of sixth-grades students focused on middle-levels and high-levels. Second, there are no significant differences relating to gender. Third, the higher the grade of children is the higher the levels of their spatial concepts. In addition, the second result is the relationship between strategy levels and performance in seven content areas: revealing position corrections, and having mathematics as the most significant, and the rest in order: social studies, language arts, science and technology, arts and humanities, integrative activities, health and physical education.

In the era of explosive information, storage subsystem is becoming more and more important in our daily life and commercial markets. Because more and more data are recorded in the digital form and stored in the storage device, an intelligent mechanism is required to make the management of the digital data and storage devices more eficiently rather than simply keep increasing more storage equipment into a system. The concept of storage virtualization was introduced to solve this problem, by aggregating all the physical devices into a single virtual storage device and hidding the complexity of underlying block devices. Through this virtual layer, users can dynamically allocate and resize their virtual storage device to satisfy their need, and they can also use the methods provided by the virtual layer to organize data more efficiently. Linux Logical Volume Manager 2 (LVM2) is an implementation of storage virtualization on the Linux operation system. It includes three components: the kernel-space devicemapper, the user-space device-mapper support library (libdevmapper), and the user-space LVM2 toolset. This thesis will focus on the kernel-space device-mapper, which provides virtualization mechanism for user-space logical volume manager. The organization of this thesis is composed of : (1) Introduce novel technologies in the recent years, (2) Provide an advanced document about the internals of device-mapper, (3) Try optimizing the mapping table algorithm, and (4) Evaluate the performance of device-mapper.

The purpose of this study is improve the cage net volume deformation during typhoon attacking. A special bottom collar system is to substitute the sinkers system. The Research contents include the numerical development and the hydrodynamic physical model test in a wave tank. The numerical model is based on the lumped mass method to set up the equation of motion of the whole cage net system; meanwhile the solutions of equation have been solved through the Runge-Kutta fifth order method. The hydrodynamic physical model tests have been carried out to verify the goodness of the numerical model. The research results are as follows. The sinker system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is about 4.54% higher than the physical model results, and the error of net deformation rate is about 8.04% higher. While the bottom collar system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is 6.34% lower than physical model results, and the error of net deformation rate is 3.82% lower. The physical model show that the minimum side projection area deformation rates of net in the bottom collar system is about 4~6% higher than the sinker system¡¦s. According to the conclusions of this study, the presented numerical model is capable to predict the whole cage net system performance and indicates that the bottom collar system is practically feasible in improving the cage net volume deformation.

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Abstract Most of the enterprises evaluate the effects of advertisement by analyzing the sales volume. However, there are plenty of elements which contributes to the sales volume, and advertisement is only one of them. Wherefore, how to precisely measure the effects of advertisement becomes the key issue. Besides, we have to mention that the manufacturer and the retailer have different strategic point of view on doing advertisement. Compared to manufacturer, retailer focuses more on regional market segmentation and emphasizes more on immediately. The attributions and advertisement cooperative strategies exist different interpretations between manufacturer and retailer. Concerning about business model of the convenient store, making too much order of bento could cause the wastage due to the short shelf life. On the other hand, making less order of bento could lead to unsatisfaction of consumer demands, losing sales. There are many factors that affect making orders such as climate, regional business activity, advertisement, promotion and so on. This research aims to investigate how the series of bento advertisement affect consumers by checking advertisement contact percentage, memory recall and hurried consuming behavior in order to make the retail realize the consumers¡¦ wants and fulfill the demands. The methodology in this study has been divided into two sections. The first section is mainly about the advertisement strategies of seven-eleven Taiwan. Three examples will be taken as case studies: ¡§citizen bento¡¨ represents the rational appealing, ¡§ railway obento¡¨ represents the perceptual appealing, and ¡§rice harvest¡¨ represents mixture of both rational and perceptual. In investigating the three former case studies, three elements are attempted to identify advertisement related-factors which are advertisement contact percentage, advertisement memory recall and how advertisement promote the consuming. The second section is to evaluate how importance advertisement influence the ordering. It is intended that the research will enhance the understanding of different perceptions in creating new products and suggestion the advertisement strategies.

The effects on heat transfer in a two-dimensional parallel plate channel with sixteen porous baffles in a staggered arrangement with a uniform heat flux heating applied to the top and bottom walls has been numerically investigated. Developing Flow (DF) was considered for this study. The Brinkman-Forchheimer-extended Darcy model was used for modeling the heat transfer and fluid flow through the porous baffles. The flow was assumed to be laminar. A finite volume based method in conjunction with the SIMPLEC algorithm was used to solve the model equations. Calculations were made by varying several independent parameters such as Reynolds number (Re), Darcy number ⎞ (Da), thermal conductivity ratio ⎛⎜ k e kf ⎠⎟ , baffle thickness ( * ) , non-dimensional w ⎝ baffle spacing ( * ) , and non-dimensional baffle height ( * ) . w The results of the study established that porous baffles out perform solid baffles from a pressure drop point of view. However, porous baffles under perform solid baffles from a heat transfer point of view. The ratio representing increase in heat transfer per unit increase in pumping power (heat transfer performance ratio) was found to be less than unity for all cases. Increasing the Darcy number was found to produce less desirable heat transfer enhancement ratios. Increasing the non-dimensional baffle spacing (d/w) and the baffle aspect ratio (H/w) were found to enhance heat transfer.

Empirical models of airflow output and power consumption were developed for series and parallel fan powered variable air volume terminal units at typical design pressure conditions. A testing procedure and experimental setup were developed to test sets of terminal units from three different manufacturers. Each set consisted of two series and two parallel units, each with 8 in. (203 mm) and 12 in. (304 mm) primary air inlets, for a total of four units in each set. Generalized models were developed for the series and parallel units, with coefficients varying by size and manufacturer. Statistical modeling utilized SAS software (2002). Fan power and airflow data were collected at downstream static pressures over a range from 0.1 to 0.5 in. w.g. (25 to 125 Pa) for the parallel terminal units. Downstream static pressure was held constant at 0.25 in. w.g. (62 Pa) for the series units. Upstream static pressures of all variable air volume (VAV) terminal units ranged from 0.1 to 2.0 in. w.g. (25 to 498 Pa). Data were collected at four different primary air damper positions. Data were also collected at four different terminal unit fan speeds, controlled by a silicon controlled rectifier (SCR). The models utilized the RMS voltage entering the terminal unit fan, the 'rake' sensor velocity pressure, and the downstream static pressure. In addition to the terminal unit airflow and power models, a model was developed to quantify air leakage in parallel terminal units, when the unit fan was off. In all but two of the VAV terminal units, the resulting models of airflow and power had R2 values greater than 0.90. In the two exceptions, there appeared to be manufacturing defects: either excessive air leakage or a faulty SCR that limited the effectiveness of the airflow and power models to capture the variation in the data.

Magnetic resonance spectroscopy is now in widespread use, which with various tools of spectra analysis can provide concentrations of metabolites. The influence of metabolites on human physiology is greatly. Due to the tiny variation of the concentration in various metabolites, the analytic method used in the quantitative determination of the absolute concentrations of metabolites plays an important role in this research area. In this thesis we present an analysis tool for segmentation of white matter, gray matte and cerebrospinal fluid using region growing with spatial space, and provide manual interaction for exception handling in this subject. Then we use this tool to analyze different percentages of white matter and gray matter with the default parameter by LCModel and correct partial volume effect. The results show that the proposed tool can improve significantly the accuracy in absolute quantitative analysis of concentration.