Abstract Optical fiber communications have been become one of the most popular researches since 1970s. In this field, there are many studies on the coupling between semiconductor lasers and fibers and many conclusions are demonstrated. In this thesis we build a 2-D numerical model to simulate energy coupling between laser diodes (LDs) and tapered optical fibers. Our model is based on the spectral domain integral equation (SDIE) formulation which is derived from Maxwell equations and the principle of mode matching. Through this numerical model we will be able to show the field distribution in LD waveguide junctions. We may also use this tool to study the coupling parameters such as the separation distance and tapered fiber geometry.

We extend the classical Ambarzumyan's theorem for the Sturm-Liouville equation, which is concerned only with the Neumann boundary conditions, to the general boundary conditions, by imposing an additional condition on the potential function. Our result supplements Poschel-Trubowitz's inverse spectral theory. We also have parallel results for the vectorial Sturm-Liouville system.

The relationship between budgetary participation, budgetary slack and performance has received a great deal of attention in the literatures of management accounting. However, there is a little consistent conclusion in the relationship between budgetary participation, budgetary slack and performance. Behavior accounting researchers using the Contingent Theory in order to conciliate these inconsistent conclusions also confound contrary results (such as Merchant (1985) and Dunk (1993)). This study suggested that the perceived cause of budgetary participation and the cognitive functions of budgetary participation are important determinants of propensity to create budgetary slack and performance. In addition, this study considered the influence of procedural justice about budgetary decision on budgetary slack and performance. We proposed that there are three actions of participator in the process of participation. The first, subordinate would review the surroundings around themselves like environment uncertainty, task uncertainty, budgetary emphasis, role ambiguity and information asymmetry. The second, subordinates will think the need of functions of participation. The surrounding variables will influence the cognitive functions of participation. Finally, they will decide the subsequent action (in this study we discuss the propensity of budgetary slack and performance). We gathered data from 174 subordinate managers working in the publicly owned companies in Taiwan and used LISREL to test our hypotheses. The results of this study revealed that 1.The cause of budgetary of participation is imperative factor influencing the need of the functions of budgetary participation. The environment uncertainty, task uncertainty, role ambiguity and information asymmetry has positively direct influence on the need of informational effect of budgetary participation respectively. Budgetary emphasis has positively direct influence on the need of affective/motivational effect of budgetary participation. 2.The informational effect of budgetary participation was directive associated with budgetary slack. However, the affective/motivational effect of budgetary participation was indirectly related to budgetary slack through procedural justice. 3. The affective/motivational effect of budgetary participation was directive associated with performance. However, the informational effect of budgetary participation was indirectly related to performance through procedural justice and affective/motivational effect of budgetary participation. We anticipated that the result of this study could offer insight into the relationship between budgetary participation, slack and performance. In addition, we expect to give some suggestions to firms that implement participatory budgeting system to avoid dysfunctional behavior of employees and to encourage performance.

Cracked beam problem is an elliptic boundary value problem with singularity. It is often used as a testing model for numerical methods. We use numerical and symbolic boundary approximation methods and boundary collocation method to compute its extremely high accurate solution with global error $O(10^{-100})$. This solution then can be regarded as the exact solution. On the other hand, we vary the boundary conditions of this problem to obtain several related models. Their numerical solutions are compared to those of cracked beam and Motz problems, the prototypes of singularity problems. From the comparison we can conclude the advantage of each model and decide the best testing model for numerical methods.

In this thesis, we consider the Laplace quation on sector with various constant Dirichlet or Numann boundary conditions. Most of such problems have singularity in the solution. We first analyze the type of singularity on the corner and then survey some known methods to solve these problems. The boundary approximation method is used to compute some of their solutions with two singularities. Besides, a Laplace equation on a triangle with multiple solutions is solved by the method of separation of variables.

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Micro ring-cavity, like the Fabry-Perot cavity, is an optical device that resonates at certain frequencies. It is used as a phase compensator, and filter. Easily fabricated, the micro ring-cavity can be mass-produced, the ring-cavity is becoming evermore important as integrated opto-electronic technology advances. In this thesis, we begin with a novel one-dimensional theory that considers bi-directional traffic in the micro-ring cavity. By separating the device into easily manageable regions, and employing only fundamental modes in each of the sections, we obtain a closed-form formula for the transmission and reflection coefficient of this device. Under certain circumstances, when the directional coupler length is short but its coupling strength is strong, we observed a significant amount of reflection of optical energy at some frequencies. This phenomena is currently unknown to the opto-electronic industry. To further study this, we developed a more rigorous multi-mode propagation method for two-dimensional bi-directional ring cavities. The problem at hand is first being sliced into regions of multi-layered sections. Within each section, we can express the fields in terms of the underlying waveguide modes of the structure. At the interfaces of these sections, we construct coupled integral equations, which are derived from the continuity requirement of the tangential fields. We have complete formulations for both TE and TM cases, down to the coupled matrix equation for the unknown modal coefficients at each junction.

The causal system is more practical then the noncausal system in the world. Causality implies only the past input can effect the future output. As a consequence, noncausal system is seldom investigation. The purpose of this thesis is to study the signal recury for a noncausal system. The principle of signal estimation is based upon the Wiener-Hopf equation. Therefore, the correlation computation is very important. By transforming the noncausal dynamic equations to a causal equation, we achieve a partial recursive computation structure for correlation computation. However the current input is not independent of the past signal in the noncausal system. Hence, the Mason Rule is applied to solved this problem to make the above recursive structure complete. Furthermore, a recursive computation of Mason Rule for stage propagation is developed in this thesis to accelerating the processing speed. Our algorithm is applied to image restoration. We first segment the image to find the required generating input ponen for each correlated region. Secondly, we extend our 1-D algorithms to 2-D algorithm to restore the image. Our method is compared with the method developed base upon the Gaussian Markov model. The experiments results demonstrate the advantage of method in both visual quailty and numerical results.

An experimental and numerical investigation of heat transfer enhancement in a three dimensional channel using wall mounted porous baffles was conducted. The module average heat transfer coefficients were measured in a uniformly heated rectangular channel with staggered positioned porous baffles. A numerical procedure was implemented, in conjunction with a commercially available Navier-Stokes solver, to model the turbulent flow in porous media. The Brinkman-Forchheimer-Extended Darcy model was used for modeling fluid flow through the porous baffles. Conventional, oneequation, and two-equation models were used for heat transfer modeling. The accuracy and characteristics of each model were investigated and discussed. The results were compared with experimental data. Baffles were mounted alternatively on the top and bottom walls. Heat transfer coefficients and pressure loss for periodically fully developed flow and heat transfer were obtained for different pore densities (10, 20, and 40 pores per inch (PPI)) with two different baffle heights ( / h h B D = 1/3 and 2/3), and two baffle thicknesses ( / t h B D = 1/3 and 1/12). The Reynolds number (Re) was varied from 20,000 to 50,000. To compare the effect of foam metal baffles, the data for conventional solid-type baffles was obtained for ( / t h B D =1/3). The maximum uncertainties associated with the module Nusselt number and friction factor were 5.8% and 4.3%, respectively. The experimental procedure was validated by comparing the data for the straight channel without baffles ( / h h B D = 0) with those in the literature. The use of porous baffles resulted in heat transfer enhancement as high as 300% compared to heat transfer in straight channels without baffles. However, the heat transfer enhancement per unit increase in pumping power was less than one for the range of parameters studied in this work. Correlation equations were developed for the heat transfer enhancement ratio and the heat transfer enhancement per unit increase in pumping power in terms of Reynolds number. The conventional theoretical model, the dispersion conductivity model, and the modified two-phase model using the local thermal non-equilibrium theory were considered. The results from each model were compared against the experimental data, and compared to each other to investigate the efficiency of each model. Also, the characteristics of each model were discussed.