Brilleslyper et al. analyzed a one-parameter family of harmonic trinomials, and Brooks and Lee analyzed a one-parameter family of harmonic functions with poles. Each family was explored to find the relationship between the size of the parameter and the number of zeros of the harmonic function. In this thesis, we examine convex combinations of members of these families. We determine conditions under which the critical curves separating the sense-preserving and sense-reversing regions are circular. We show that the number of zeros of a convex combination can be greater than the maximum number of zeros of either part.

Discontinuous dynamical systems and multiagent systems are encountered in numerous engineering applications. This dissertation develops stability and dissipativity of nonlinear dynamical systems with discontinuous right-hand sides, optimality of discontinuous feed-back controllers for Filippov dynamical systems, almost consensus protocols for multiagent systems with innaccurate sensor measurements, and adaptive estimation algorithms using multiagent network identifiers. In particular, we present stability results for discontinuous dynamical systems using nonsmooth Lyapunov theory. Then, we develop a constructive feedback control law for discontinuous dynamical systems based on the existence of a nonsmooth control Lyapunov function de fined in the sense of generalized Clarke gradients and set-valued Lie derivatives. Furthermore, we develop dissipativity notions and extended Kalman-Yakubovich-Popov conditions and apply these results to develop feedback interconnection stability results for discontinuous systems. In addition, we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear-nonquadratic performance functional for Filippov dynamical systems. Then, we provide connections between dissipativity and optimality of nonlinear discontinuous controllers for Filippov dynamical systems. Furthermore, we address the consensus problem for a group of agent robots with uncertain interagent measurement data, and show that the agents reach an almost consensus state and converge to a set centered at the centroid of agents initial locations. Finally, we develop an adaptive estimation framework predicated on multiagent network identifiers with undirected and directed graph topologies that identifies the system state and plant parameters online.

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and a new probability type reduced reasoning method for the interval-valued fuzzy logic system are proposed in this thesis. In order to optimize this particle system’s performance, we adopt genetic algorithm (GA) to adjust parameters. The applications for the new system are performed and results have shown that the developed method is more accurate and robust to design a reliable fuzzy logic system than type-1 method and the computation of our proposed method is more efficient.

Quivers (directed graphs) and species (a generalization of quivers) as well as their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this thesis, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field). Namely, we show that the category of K-species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles that do not appear in the literature. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K-species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.

中國大陸自1994年採用生產型增值稅後，重複課稅阻礙了產業結構的發展，使企業成長受到抑制，故2009年轉型為消費型增值稅，雖已有學者針對法治層面進行研究，然而尚無文獻針對增值稅轉型對於增值稅實質稅負之影響進行實證研究。本研究初以產業結構、股權結構與地區結構之差異探討對於中國大陸為轉型消費型增值稅後對於實質稅率產生之影響，並輔以企業規模、銷貨毛利率、股東權益報酬率、資本資產密集度……等變數的控制，期以降低對主要測量變數之影響。 實證結果發現: （1）中國大陸上市公司之有效稅率在增值稅體系中享有租稅優惠而使實際繳納之有效稅率降低，2009年後實施消費型增值稅，其實質稅率亦從4.79％降至4.02％，顯見實施後的實質稅率確能降低租稅負擔。（2）資本密集度較高之產業，其實質稅率亦較高，2009增值稅轉型後，無論是資本密集度高之產業抑或資本密集度低之產業，其實質稅率之影響並不顯著，顯見此次轉型因增值稅與營業稅並存而無法真正體現消費型增值稅所帶來稅負公平性。（3）內資持股比例超過50％之上市公司（內資企業）經過此次轉型後其實質稅率並未下降，顯見此次轉型並非全面而使成效有限。（4）中部和西部地區相較於東部地區之實質稅率較高，在2009年轉型為消費型增值稅後有降低之趨勢。 / This study investigates the effect of the effective tax rate after china began the transition from production-type valued-added tax to consumption-type VAT. Some researchers explore the pros and cons from the institutional level, but it is rarely to analyze the impact of the effective tax rate when the authorized implemented the consumption valued-added tax. This paper analyzes the effect of the effective tax rate on the transformation of valued-added tax by means of the empirical study. The empirical findings indicate that: 1) The effective tax rate of china listed companies declined from 4.79% to 4.02% after the transition of the VAT(Valued-added Tax),Therefore, the transition of the valued-added tax can decrease the burden of tax. 2) This study divided industries into capital intensive industries with high and low indicates it is not obvious in the regression. Because valued-added tax and business tax co-exist which results in the lack of fairness in consumption-type VAT. 3) The listed companies whose proportion of domestic ownership is above 50%(defined as domestic enterprises)increase rather than decrease effective tax rate after transition of VAT in 2009. 4) The listed companies which belong to area with middle and western region have decreasing tendency toward effective tax rate after transition of VAT in 2009.

Quivers (directed graphs) and species (a generalization of quivers) as well as their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this thesis, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field). Namely, we show that the category of K-species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles that do not appear in the literature. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K-species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.

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Quivers (directed graphs) and species (a generalization of quivers) as well as their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this thesis, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field). Namely, we show that the category of K-species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles that do not appear in the literature. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K-species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.

Quivers (directed graphs) and species (a generalization of quivers) as well as their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this thesis, we discuss the most important results in the representation theory of species, such as Dlab and Ringel’s extension of Gabriel’s theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field). Namely, we show that the category of K-species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles that do not appear in the literature. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as “crushed” species, and we show that if K is a perfect field, then the tensor algebra of a K-species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23673号 / 理博第4763号 / 新制||理||1683(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 市野 篤史, 教授 雪江 明彦, 教授 池田 保 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM