A study of impulsively started flow over cylindrical objects is made using the particle image velocimetry (PIV) technique for Reynolds numbers of Re = 200, 500 and 1000 in an X-Y towing tank. The cylindrical objects studied were a circular cylinder of diameter, D = 25.4 mm, and square and diamond cylinders each with side length, D = 25.4 mm. The aspect ratio, AR (= L/D) of the cylinders was 28 and therefore they were considered infinite. The development of the recirculation zone up to a dimensionless time of t* = 4 following the start of the motion was examined. The impulsive start was approximated using a dimensionless acceleration parameter, a*, and in this research, the experiments were conducted for five acceleration parameters, a* = 0.5, 1, 3, 5 and 10. The study showed that conditions similar to impulsively started motion were attained once a* ¡Ý 3.<p> A recirculation zone was formed immediately after the start of motion as a result of flow separation at the surface of the cylinder. It contained a pair of primary eddies, which in the initial stages (like in this case) were symmetrical and rotating in opposite directions. The recirculation zone was quantified by looking at the length of the zone, LR, the vortex development, both in terms of the streamwise location and the cross-stream spacing of the vortex centers, a and b, respectively, as well as the circulation (strength) of the primary vortices, ¦£.<p> For all types of cylinders examined, the length of the recirculation zone, the streamwise location of the primary eddies and the circulation of the primary eddies increase as time advances from the start of the impulsive motion. They also increase with an increase in the acceleration parameter, a*, until a* = 3, beyond which there is no more change, since the conditions similar to impulsively started conditions have been achieved. The cross-stream spacing of the primary vortices is relatively independent of Re, a* and t* but was different for different cylinders.<p> Irrespective of the type of cylinder, the growth of the recirculation zone at Re = 500 and 1000 is smaller than at Re = 200. The recirculation zone of a diamond cylinder is much larger than for both square and circular cylinders. The square and diamond cylinders have sharp edges which act as fixed separation points. Therefore, the cross-stream spacing of the primary vortex centers are independent of Re, unlike the circular cylinder which shows some slight variation with changes in Reynolds number.<p> The growth of the recirculation is more dependent on the distance moved following the start of the impulsive motion; that is why for all types of cylinders, the LR/D, a/D and ¦£/UD profiles collapse onto common curves when plotted against the distance moved from the start of the motion.

A study of impulsively started flow over cylindrical objects is made using the particle image velocimetry (PIV) technique for Reynolds numbers of Re = 200, 500 and 1000 in an X-Y towing tank. The cylindrical objects studied were a circular cylinder of diameter, D = 25.4 mm, and square and diamond cylinders each with side length, D = 25.4 mm. The aspect ratio, AR (= L/D) of the cylinders was 28 and therefore they were considered infinite. The development of the recirculation zone up to a dimensionless time of t* = 4 following the start of the motion was examined. The impulsive start was approximated using a dimensionless acceleration parameter, a*, and in this research, the experiments were conducted for five acceleration parameters, a* = 0.5, 1, 3, 5 and 10. The study showed that conditions similar to impulsively started motion were attained once a* ¡Ý 3.<p> A recirculation zone was formed immediately after the start of motion as a result of flow separation at the surface of the cylinder. It contained a pair of primary eddies, which in the initial stages (like in this case) were symmetrical and rotating in opposite directions. The recirculation zone was quantified by looking at the length of the zone, LR, the vortex development, both in terms of the streamwise location and the cross-stream spacing of the vortex centers, a and b, respectively, as well as the circulation (strength) of the primary vortices, ¦£.<p> For all types of cylinders examined, the length of the recirculation zone, the streamwise location of the primary eddies and the circulation of the primary eddies increase as time advances from the start of the impulsive motion. They also increase with an increase in the acceleration parameter, a*, until a* = 3, beyond which there is no more change, since the conditions similar to impulsively started conditions have been achieved. The cross-stream spacing of the primary vortices is relatively independent of Re, a* and t* but was different for different cylinders.<p> Irrespective of the type of cylinder, the growth of the recirculation zone at Re = 500 and 1000 is smaller than at Re = 200. The recirculation zone of a diamond cylinder is much larger than for both square and circular cylinders. The square and diamond cylinders have sharp edges which act as fixed separation points. Therefore, the cross-stream spacing of the primary vortex centers are independent of Re, unlike the circular cylinder which shows some slight variation with changes in Reynolds number.<p> The growth of the recirculation is more dependent on the distance moved following the start of the impulsive motion; that is why for all types of cylinders, the LR/D, a/D and ¦£/UD profiles collapse onto common curves when plotted against the distance moved from the start of the motion.

ABSTRACT This dissertation constructs three strategic trade models. The first model is a single-shot two-stage game model of intra-industry trade with trade retaliation against government provided export subsidies and lobbying by foreign firm on domestic government¡¦s import tariff. The second model is an infinite repeated game model of intra-industry where the history of government and firm interaction is the basis for constructing trade strategies. The third model is a single-shot three-stage game model of intra-industry trade with the linkage between domestic and foreign intermediate-input and final-good industries and the choice of optimal export subsidies in the two industries for two governments. Chapter 1 introduces the motivation, objectives, framework, and literature review of this dissertation. The literature review is organized as follows. Initially we review the foundations of the basic intra-industry trade model, where our model is rooted. Next we present the more significant papers that describe the sensitivity of the basic model, because our repeated game model will show yet another way that the basic model is sensitive. Next we present some dynamic game theoretic results, which we use to construct our repeated game model. Finally, we review some papers related to intermediate input and strategic trade. The first model is developed in Chapter 2. We discover that there are two perfect strategy subgame perfect equilibria in this model. And then an import tariff is available, and using that tariff will remove the benefits originally conferred by an export subsidy. Active trade policy is not eliminated by the two governments and tariff policy is larger than subsidy policy. Hence, an import tariff will more than offset the anticipated gains from a subsidy policy. There is no reason to believe that one equilibrium is better or more likely than another, because the highest payoffs equilibrium of the two governments and domestic firm is not the best payoff equilibrium of the foreign firm. We used the single-shot game model of Chapter 2 and molded it into a repeated game in Chapter 3. First, we found the set of Nash equilibria toward solving the repeated game model. Second, we only focused on the subgame perfect equilibria from the infinite Nash equilibria¡¦s set. We used the result in Fudenberg and Maskin (1986) to define the subgame perfect equilibria. Third, we showed that in the repeated game a subgame perfect strategy of free trade can increase all players¡¦ payoffs which are better than the single-shot game equilibrium payoffs. Chapter 4 develops the third model. We observe how domestic and foreign governments choose their optimum export subsidy policies for their intermediate input and final good production by using the linkage between domestic and foreign intermediate-input and final-good industries under the condition of vertical specialization. The result indicates that under the condition of vertical specialization, the two governments will choose positive export subsidies for their final goods while they will give no subsidies for their intermediate inputs. Chapter 5 presented the implications of vertical specialization on the cross-strait economy and trade. To maintain the competitive advantage of Taiwan economy and smoothly upgrade industry structure, transferring the labor-intensive industry and the labor-intensive production sections to China seems an optimum choice under the principle of comparative advantages. Nevertheless, for Taiwan, the upgrade of local industries has never stopped, but with the acceleration of industrial relocation, the transformation of production and trade structures are also taking place. The impact carried by this transformation is extensive and profound. In addition to obvious impact on the economic perspective, if the structure of employment market cannot react in time, a great social cost may be incurred. How to utilize the edge of industrial specialization between the Strait to strengthen Taiwanese industries¡¦ competitive, enhance product development ability through cooperation with multinational enterprises, dominate product development, and establish a center of task division for regional industries can be one of the main focuses in the development of Taiwan¡¦s industrial policy.

The paper investigates problems of designing controllers to linear time-invariant continuous descriptor systems subject to norm-bounded structured uncertainty so that the closed-loop systems are admissible or D-admissible with their transfer matrices having H-infinite norm bounded by a prescribed value. The constant state feedback and the dynamic output feedback designs are addressed. In both design methods, sufficient LMI conditions are derived to guarantee achievement of the desired specifications, such as robust H-infinite norm and pole-clustering constraints. Finally, two numerical examples are shown for the illustration.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 71-78). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 129-133). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 129-133). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 71-78). Also available on the Internet.

The thesis offers an investigation into the analysis of so-called iterated generating functions and the schemes that produce them. Beginning with the study of some ad hoc scheme formulations, the notion of an iterated generating function is introduced and a mechanism to produce arbitrary finite sequences established. The development of schemes to accommodate infinite sequences leads – in the case of the Catalan sequence – to the discovery of what are termed Catalan polynomials whose properties are examined. Results are formulated for these polynomials through the algebraic adaptation of classical root-finding algorithms, serving as a basis for the synthesis of new generalised results for other infinite sequences and their associated polynomials.

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