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In this thesis we revisit two classical definitions of angle in an inner product space: real-part angle and Hermitian angle. Special attention is paid to Krein’s inequality and its analogue. Some applications are given, leading to a simple proof of a basic lemma for a trace inequality of unitary matrices and also its extension. A brief survey on recent results of angles between subspaces is presented. This naturally brings us to the world of majorization. After introducing the notion of majorization, we present some classical as well as recent results on eigenvalue majorization. Several new norm inequalities are derived by making use of a powerful decomposition lemma for positive semidefinite matrices. We also consider coneigenvalue majorization. Some discussion on the possible generalization of the majorization bounds for Ritz values is presented. We then turn to a basic notion in convex analysis, the Legendre-Fenchel conjugate. The convexity of a function is important in finding the explicit expression of the transform for certain functions. A sufficient convexity condition is given for the product of positive definite quadratic forms. When the number of quadratic forms is two, the condition is also necessary. The condition is in terms of the condition number of the underlying matrices. The key lemma in our derivation is found to have some connection with the generalized Wielandt inequality. A new inequality between angles in inner product spaces is formulated and proved. This leads directly to a concise statement and proof of the generalized Wielandt inequality, including a simple description of all cases of equality. As a consequence, several recent results in matrix analysis and inner product spaces are improved.

In this thesis we revisit two classical definitions of angle in an inner product space: real-part angle and Hermitian angle. Special attention is paid to Krein’s inequality and its analogue. Some applications are given, leading to a simple proof of a basic lemma for a trace inequality of unitary matrices and also its extension. A brief survey on recent results of angles between subspaces is presented. This naturally brings us to the world of majorization. After introducing the notion of majorization, we present some classical as well as recent results on eigenvalue majorization. Several new norm inequalities are derived by making use of a powerful decomposition lemma for positive semidefinite matrices. We also consider coneigenvalue majorization. Some discussion on the possible generalization of the majorization bounds for Ritz values is presented. We then turn to a basic notion in convex analysis, the Legendre-Fenchel conjugate. The convexity of a function is important in finding the explicit expression of the transform for certain functions. A sufficient convexity condition is given for the product of positive definite quadratic forms. When the number of quadratic forms is two, the condition is also necessary. The condition is in terms of the condition number of the underlying matrices. The key lemma in our derivation is found to have some connection with the generalized Wielandt inequality. A new inequality between angles in inner product spaces is formulated and proved. This leads directly to a concise statement and proof of the generalized Wielandt inequality, including a simple description of all cases of equality. As a consequence, several recent results in matrix analysis and inner product spaces are improved.

In this dissertation, we investigate the Riccati diagonal stability and explore some extensions of this notion. Riccati diagonal stability plays an important role in the stability analysis of linear time-delay systems. It is known that if a linear time-delay system is Riccati diagonally stable then it admits a diagonal Lyapunov-Krasovskii functional. The existence of such a functional implies the asymptotic stability of the linear time-delay system. This diagonal stability problem has other applications in applied areas such as physical sciences and population dynamics. We also study the Lyapunov diagonal stability, which has a clear connection to the Riccati diagonal stability. Using a separation theorem, we first provide new proofs for some existing results on the Lyapunov-type diagonal stability. We also construct a new, shorter, and more transparent proof for a well-known result by Kraaijevanger that gives explicit conditions for the Lyapunov diagonal stability on matrices in $\mathbb{R}^{3 \times 3}$. In addition, we give several necessary and sufficient conditions for matrices in $\mathbb{R}^{3 \times 3}$ to be Lyapunov diagonally stable. Furthermore, we present an extension of the so-called Riccati diagonal stability to the Riccati $\alpha$-scalar stability. We derive two new characterizations regarding the Riccati $\alpha$-scalar solution of the Riccati matrix inequality so as to expand and broaden the relevant existing results. We also generalize this notion to consider a common $\alpha$-scalar solution for a family of Riccati matrix inequalities. We shall refer to this new generalization as common Riccati $\alpha$-scalar stability. As an application for the main results, we further explore families of block triangular matrices. Finally, motivated by recent developments, we formulate the problem of Riccati $\alpha$-stability. We present a necessary and sufficient condition for this type of stability and study the connection between Riccati $\alpha$-stability of a pair of $\alpha$-block matrices and Riccati stability of the diagonal block pairs. Moreover, we generalize the Riccati $\alpha$-stability by considering a family of pairs of $\alpha$-block matrices and give a new characterization for this new case.

Taiwan has listed on developed countries, people in Taiwan are more and more emphasis on leisure activities following on the higher income, increased GNP and changed life style of aging society. Besides, 5-working-day scheme and promotion of tourism and leisure industries have become Taiwan government¡¦s important policy. Tourism and leisure industries is a tremendous potential market, which implies billions of dollars treasure there. Moreover, tourism and leisure industries can help Taiwan government to resolve high un-employee problems. I believe that this potential emerging market of leisure and tourism industries may draw more and more attention from authorities and interested parties. So as this paper hi-lights leisure industries and takes a case study of Shitzuwan Beach Resort. From business operational environment point of view, there are certain factors that cause an enterprise operates very successfully in its field, these certain factors are well known as key success factors. On the other hand, resource-based view is looking into and focusing an enterprise¡¦s internal resources and its capabilities, this theory has been implemented since 1990 and becomes a fad now a day. From resource-based view, the formation of competitive advantage of a firm is weather or not its resources and capabilities match with key success factors, this model of ¡uresource and core competence ¡÷ key success factors ¡÷ competitive advantage¡vhave been proved by the ¡ucompetitive advantage matrix analysis model¡v whereas the model created by the author. The main purpose of this paper therefore, is to contribute to the theoretical creation of competitive advantage matrix analysis model, this model is based on two dimensions of key success factors¡]KSF¡^and resource-based view¡]RBV¡^, through this competitive advantage matrix can illustrates the types of competitive advantage and intensive of competitive advantage of the designated enterprise. The result of matrix analysis also gives hints for the enterprises to overview and to reinforce his internal resources as well as core competence, so as to keep and create its competitive advantage. Key Words¡GKey Success Factor¡]KSF¡^, Resource-based View¡]RBV¡^, Core Competence, Competitive Advantage, Competitive Advantage Matrix Analysis.

The main focus of this thesis is a proposal of business development strategy for small company providing accomodation services in Slovakia. The first part is theoretical and defines basic concepts as strategy, strategic management, development and growth of small and medium-sized enterprises, as well as its characteristics. It also describes selected analytical-research methods which goal is to reveal the key factors influencing the current situation. These methods are then applied in the second part, the analytical, where the external and internal environment of the company is mapped and analyzed, together with the influencing factors. The third part, the proposing, interprets possible solutions and recommendations based on the results of selected analyzes, which aim to ensure the future development of the company.

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The aim of this thesis is to design a strategy for Vodafone Czech Republic, a.s. Using the open data an analysis of macroenvironment as well as microenvironment are performed, where a definition and a breakdown of telecommunication market into five segment is made. Following is the analysis of Porter five forces, which analyses competition forces on the market as well as to the Vodafone. Further on a financial analysis and product portfolio analysis is made, which serves as the basis of Ansoff matrix. In the conclusion a synthesis of the analyses is made and several strategies are designed.

The emerging interests in spatial pattern mining leads to the demand for a flexible spatial pattern mining language, on which easy to use and understand visual pattern language could be built. It is worthwhile to define a pattern mining language called LCSPM to allow users to specify complex spatial patterns. I describe a proposed pattern mining language in this paper. A visual interface which allows users to specify the patterns visually is developed. Visual pattern queries are translated into the LCSPM language by a parser and data mining process can be triggered afterwards. The visual language is based on and goes beyond the visual language proposed in literature. I implemented a prototype system based on the open source JUMP framework.

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