Well-posedness and Ill-posedness of the Nonlinear Beam Equation

The dissertation consists of two parts, Well-posedness and ill-posedness for the nonlinear beam equation and Strichartz estimates of the beam equation on the domains. In the first part, we will work to introduce the further studies of Strichartz estimates with initial data both in homogeneous Sobolev spaces $\\dot{H}^s\ imes\\dot{H}^{s-2}$ and in inhomogeneous Sobolev space ${H}^s\ imes{H}^{s-2}$. We take advantage of the Strichartz estimates to build well-posedness theorems of the nonlinear beam equations for rough data by the Picard iteration method. We will apply these methods on the nonlinear beam equation with ``energy critical, subcritical and ``energy supercritical cases. Since the beam equation does not satisfy finite speed propagation, we introduce the further result of the fractional chain rule to deal with the ``energy super critical case. We obtain the global well-posedness with initial data in homogeneous Sobolev space $\\dot{H}^s\ imes\\dot{H}^{s-2}$ and local well-posedness with initial data in inhomogeneous Sobolev space ${H}^s\ imes{H}^{s-2}$. At the same time, we extend the range of order $s$. With the global existence for small data, we prove the scattering and asymptotic completeness result for the nonlinear beam equation. Last we prove the nonlinear beam equation is ill-posed in defocusing case $\\omega=-1$ when $

Suppression of Fracture Failure of Structures by Composite Design Based on Fracture Mechanics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/84743/1/Li_ICF11.pd

Examining Intrinsic and Extrinsic Motivation Factors among Graduate Employees in China

The aim of this study is to examine the intrinsic and extrinsic factors that motivate graduate employees in China. Graduate employees play an important role especially in China. Thus, it is necessary for contemporary organizations to discover the difference between intrinsic and extrinsic motivation factor and adopt appropriate methods to motivate graduate employees, improve their performance and inspire their potentials. This study adopts quantitative research methods, using a 5-point Likert scale questionnaire to investigate 200 Chinese graduate employees. The data is analyzed by using SPSS software. The result shows that adequate earning is the most significant motivation factor for graduate employees in China followed by job security. Meanwhile, this study found that gender, organization type and education level are significantly related to motivation preference. This study will also discuss recommendation, limitations and future suggestions

Examining Intrinsic and Extrinsic Motivation Factors among Graduate Employees in China

The aim of this study is to examine the intrinsic and extrinsic factors that motivate graduate employees in China. Graduate employees play an important role especially in China. Thus, it is necessary for contemporary organizations to discover the difference between intrinsic and extrinsic motivation factor and adopt appropriate methods to motivate graduate employees, improve their performance and inspire their potentials. This study adopts quantitative research methods, using a 5-point Likert scale questionnaire to investigate 200 Chinese graduate employees. The data is analyzed by using SPSS software. The result shows that adequate earning is the most significant motivation factor for graduate employees in China followed by job security. Meanwhile, this study found that gender, organization type and education level are significantly related to motivation preference. This study will also discuss recommendation, limitations and future suggestions

Offline Equilibrium Finding

Offline reinforcement learning (Offline RL) is an emerging field that has recently begun gaining attention across various application domains due to its ability to learn behavior from earlier collected datasets. Using logged data is imperative when further interaction with the environment is expensive (computationally or otherwise), unsafe, or entirely unfeasible. Offline RL proved very successful, paving a path to solving previously intractable real-world problems, and we aim to generalize this paradigm to a multi-agent or multiplayer-game setting. Very little research has been done in this area, as the progress is hindered by the lack of standardized datasets and meaningful benchmarks. In this work, we coin the term offline equilibrium finding (OEF) to describe this area and construct multiple datasets consisting of strategies collected across a wide range of games using several established methods. We also propose a benchmark method -- an amalgamation of a behavior-cloning and a model-based algorithm. Our two model-based algorithms -- OEF-PSRO and OEF-CFR -- are adaptations of the widely-used equilibrium finding algorithms Deep CFR and PSRO in the context of offline learning. In the empirical part, we evaluate the performance of the benchmark algorithms on the constructed datasets. We hope that our efforts may help to accelerate research in large-scale equilibrium finding. Datasets and code are available at https://github.com/SecurityGames/oef