<p>Noise-induced stabilization occurs when an unstable deterministic system is stabilized by the addition of white noise. Proving that this phenomenon occurs for a particular system is often manifested through the construction of a global Lyapunov function. However, the procedure for constructing a Lyapunov function is often quite ad hoc, involving much time and tedium. In this thesis, a systematic algorithm for the construction of a global Lyapunov function for planar systems is presented. The general methodology is to construct a sequence of local Lyapunov functions in different regions of the plane, where the regions are delineated by different behaviors of the deterministic dynamics. A priming region, where the deterministic drift is directed inward, is first identified where there is an obvious choice for a local Lyapunov function. This priming Lyapunov function is then propagated to the other regions through a series of Poisson equations. The local Lyapunov functions are lastly patched together to form one smooth global Lyapunov function.</p><p>The algorithm is applied to a model problem which displays finite time blow up in the deterministic setting in order to prove that the system exhibits noise-induced stabilization. Moreover, the Lyapunov function constructed is in fact what we define to be a super Lyapunov function. We prove that the existence of a super Lyapunov function, along with a minorization condition, implies that the corresponding system converges to a unique invariant probability measure at an exponential rate that is independent of the initial condition.</p> / Dissertation

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Rolling element bearing failure can cause problems for industries ranging from mild inconveniences such as simple replacement to catastrophic damage such as large production-line equipment failure. Rolling element bearing failure has plagued industries for many years. Bearings are currently monitored to determine whether or not there is a defect in the bearing, but the remaining lifetime of the bearing remains unknown. This research estimates the bearings remaining lifetime through digital signal processing in conjunction with a modified version of Pariss equationa fatigue-failure equation well known in rotating machinery prognostics. An energy quantity, coined the Power Spectrum Value (PSV), is the maximum amplitude of the frequencies within a relatively small band around the resonant frequency of the system. The current PSV is estimated and updated using a chronologically weighted least squares algorithm. It is this PSV which is implemented in the modified Paris equation to determine the remaining lifetime of the bearing. This research presents a non-intrusive method of determining the lifetime of the bearing so that the bearings utility is maximized and reactive maintenance procedures are minimized.

The main purpose of this study is to investigate eighth-grade students¡¦ understanding of the equal sign and analyzed error types of quadratic equation in one variable. To achieve this purpose, the investigator did a survey and development instruments. Participants were 215 eighth-grade students who formed a convenient sample. There are three results. First, participants with a relational definition of the equal sign added to about 80% of the sample. Second, the performance of students with relational definitions is higher than the performance of students with operational definitions. Third, students¡¦ understanding of the equal sign was related to their respective problem-solving performance on quadratic equation in one variable. In this study, participants with an operational definition of the equal sign tended to guess randomly or leave a blank. Problem-solving performance of participants with a relational definition of the equal sign involved multiple strategies. The researcher suggested that teachers should strengthen students¡¦ understanding of equal sign and related students¡¦ prior algebraic knowledge.

This study uses the Phase-field method to simulate the transient thermal current of the metal surface heated and molten by a massing energy. The flow field uses a two-dimension module, considered with the mass conservation equation, momentum equation, energy equation and level-set equation, to solve for the distribution in whole domain, including the interface, of temperature, velocity, pressure and level-set number. We ignore the effect of concentration diffusion, but consider about the effect of heat translation on the flow field. Finally the results will display the flows of air around molten area forced by buoyancy which is caused by high temperature, and the flows in molten area forced by thermocapillary which is caused by temperature gradient.

Abstract The purpose of this investigation is based on the revision model proposed by Ferris , Adams, Kolodinsky, Hochwarter, Ammeter,(2002).This research is deeply to examine the influence of perceptions of organizational politics on trust - organizational cynicism as mediator variable .The data were analyzed by SPSS 15.0 software and by structural equation modeling (SEM). The major results of this study are as following¡GThe perceptions of organizational politics were found have a significant negative relationship with trust. The perceptions of organizational politics were constructed from three patterns( general political behavior¡Bgo along to get ahead¡Bpay and promotion).Only general political behavior has a significant effect on trust.The other two patterns have no significant effect on trust. The perceptions of organizational politics were found have a significant positive relationship with organizationl cynicism . Organizationl cynicism has a significant negative relationship with trust.Organizationl cynicism has a mediating effect on the relationship between perceptions of organizational politics and trust. Key word¡Gperceptions of organizational politics , trust , organizationl cynicism , structural equation modeling

This research is based on the framework of revision model proposed by Ferris et al. (2002), discussing the influence organization politics consciousness to staff's from Machiavellianism and type A personality. The sample consisted of 1890 employee selected from 40 organizations covering 9 industrial sectors in Taiwan. The data were analyzed by descriptive statistics, reliability analysis, confirmatory factor analysis, correlation analysis and structural equation modeling and the summarized findings are in the following sections. The major results of this study are as fallowing: 1. Machiavellianism has a significant effect on employees¡¦ general political behavior of organizational politics perceptions. 2. Machiavellianism has a significant effect on employees¡¦ benefits of remaining silence of organizational politics perceptions. 3. Machiavellianism has a significant effect on employees¡¦ salary and promotion policies of organizational politics perceptions. 4. Type A personality has a significant effect on employees¡¦ general political behavior of organizational politics perceptions. 5. Type A personality has a significant effect on employees¡¦ benefits of remaining silence of organizational politics perceptions. 6. Type A personality has a significant effect on employees¡¦ salary and promotion policies of organizational politics perceptions.

The perceptions of organizational politics and organizational citizenship behavior are neither regulated nor indentified in any organization. But, they are exactly existed in organization. This study is based on the revise model of Perceptions of Organizational Politics (POP) proposed by Ferris et al. (2002). We investigate the relationship between the perceptions of organizational politics and the organizational citizenship behavior. Furthermore, we investigate the indirect effect between the perceptions of organizational politics and the subordinates of organizational citizenship behavior. This study used the scales of 35 items collected by Dr. Chin-ming Ho and the other members of the last research team of POP in 2008. The research is based on the revision model of POP and questionnaire survey. The sample consisted of 1,890 employee selected from 40 organizations covering 9 industrial sectors in Taiwan. The method, path analysis with latent variables of the structural equation modeling (SEM) is used to measure the relationship among the constructs. The major result of this study is as following: 1. The perceptions of organizational politics have negative effect on the organizational citizenship behavior. 2. The perceptions of organizational politics have negative effect on the altruism toward colleagues 3. The perceptions of organizational politics have negative effect on the conscientiousness 4. The perceptions of organizational politics have negative effect on the identification with company 5. The perceptions of organizational politics have negative effect on the interpersonal harmony 6. The perceptions of organizational politics have negative effect on the protecting company resources

This research investigated the thermal properties of the polarization switching (PS) in vertical-cavity surface-emitting lasers (VCSELs). The investigations were performed by experiments and numerical simulations. In the experiments, the current modulation frequency and ambient temperature of VCSELs were varied to study their thermal effects on PS, resulting in rich dynamics. The current-heating effect on PS was also investigated by a step function current experiment. Based on an assumption that PS is activated as the temperature in the active region reaches a certain temperature, we model a simplified temperature rate equation to simulate the experiment of the step function. The consistency of the experiments and simulations concludes that the thermal effect plays a major role in PS and PS¡¦s hysteresis. These results contribute to the understanding of the mechanism of VCSEL¡¦s polarization switching.

A Ce:YAG-doped glass phosphor layer instead of conventional Ce:YAG-doped silicone phosphor layer as phosphor-converted white-light emitting diodes (PC-WLEDs) is demonstrated. The advantage of employing doped glass encapsulation in high power PC-WLEDs could be explained the material property of glass transition temperature of 750¢J was higher than silicone of 150¢J. The lumen degradation, chromaticity shift, color temperature change, transmittance, and fluorescence spectrum in glass and silicone based high-power PC-WLEDs under thermal aging at 150¢J, 200¢J, and 250¢J is compared and presented. Under highest temperature of 250¢J, the glass and silicone encapsulation base d PC-WLEDs exhibited 8.15% and 38.85% in lumen loss, 1.07 and 7.32 in chromaticity shift, 856 K and 3666 K in color temperature change, 4.21% and 28.1% in transmittance loss, respectively. However, the excitation spectrum altered as slight as emission spectrum before and after experiments. After aging test, the mean-time-to-failure (MTTF) evaluation of glass and silicone encapsulation materials for PC-WLEDs in accelerated thermal tests is also compared and presented by the using of Weibull distribution and Arrhenius equation. The MTTF of PC-WLEDs is defined the lumen decayed to 90%. The results showed that the glass as encapsulation material of PC-WLEDs exhibited higher MTTF than the silicone encapsulation by about 4.81, 5.92, and 7.53 times in lumen loss at 150¢J, 200¢J, and 250¢J, respectively. The results of the lumen loss, chromaticity shift, and MTTF investigations demonstrated that the thermal-stability performance of the glass based PC-WLEDs were better than silicone based PC-WLEDs at 150¢J, 200¢J, and 250¢J. A better thermal stability phosphor layer of glass as encapsulation material may be beneficial to the many applications where the LED modules with high power and high reliability are demanded.