Real-time system refers to the computing, communication, and information system with deadline requirements. To meet these deadline requirements, most systems use a mechanism known as the schedulability test which determines whether each of the admitted tasks can meet its deadline. A new task will not be admitted unless it passes the schedulability test. Schedulability tests can be either direct or indirect. The utilization based schedulability test is the most common schedulability test approach, in which a task can be admitted only if the total system utilization is lower than a pre-derived bound. While the utilization bound based schedulability test is simple and effective, it is often difficult to derive the bound. For its analytical complexity, utilization bound results are usually obtained on a case-by-case basis. In this dissertation, we develop a general framework that allows effective derivation of schedulability bounds for different workload patterns and schedulers. We introduce an analytical model that is capable of describing a wide range of tasks' and schedulers'€™ behaviors. We propose a new definition of utilization, called workload rate. While similar to utilization, workload rate enables flexible representation of different scheduling and workload scenarios and leads to uniform proof of schedulability bounds. We introduce two types of workload constraint functions, s-shaped and r-shaped, for flexible and accurate characterization of the task workloads. We derive parameterized schedulability bounds for arbitrary static priority schedulers, weighted round robin schedulers, and timed token ring schedulers. Existing utilization bounds for these schedulers are obtained from the closed-form formula by direct assignment of proper parameters. Some of these results are applied to a cluster computing environment. The results developed in this dissertation will help future schedulability bound analysis by supplying a unified modeling framework and will ease the implementation practical real-time systems by providing a set of ready to use bound results.

In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.

The bending of an orthotropic cusped plate in energetic and weighted Sobolev spaces has been considered. The existence and uniqueness of generalized and weak solutions of admissible boundary value problems (BVPs) have been investigated.

It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.

Green operators on manifolds with edges are known to be an ingredient of parametrices of elliptic (edge-degenerate) operators. They play a similar role as corresponding operators in boundary value problems. Close to edge singularities the Green operators have a very complex asymptotic behaviour. We give a new characterisation of Green edge symbols in terms of kernels with discrete and continuous asymptotics in the axial variable of local model cones.

We study elliptic boundary value problems in a wedge with additional edge conditions of trace and potential type. We compute the (difference of the) number of such conditions in terms of the Fredholm index of the principal edge symbol. The task will be reduced to the case of special opening angles, together with a homotopy argument.

On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.

The Kappa coefficient is widely used in assessing categorical agreement between two raters or two methods. It can also be extended to more than two raters (methods).  When using Kappa, the shortcomings of this coefficient should be not neglected.  Bias and prevalence effects lead to paradoxes of Kappa. These problems can be avoided by using some other indexes together, but the solutions of the Kappa problems are not satisfactory. This paper gives a critical survey concerning the Kappa coefficient and gives a real life example. A useful alternative statistical approach, the Rank-invariant method is also introduced, and applied to analyze the disagreement between two raters.

- Rückblick Simulation-News in Creo 1.0 & Creo 2.0 - Ausblick Simulation-News in Creo 3.0 - Gewichtete Verbindungen: „Tips & Tricks“ mit konkreten Beispielen: o Lagersteifigkeiten (z.B. Wälzlager) o Mechanismus Verbindungen (Dreh-, Schub-, Zylinder, .... Gelenke) o Vorgespannte Schrauben (mit Schalen-/Balken-Elementen) o Aufbringung einer momentfreien Zwangsverschiebung o „Gesamtlast auf Punkt“: Messen der Punktverschiebung o Verbinden von Massen-Elementen o Verhindern von Singularitäten - Live-Präsentation in Creo 2.0 o Lagersteifigkeiten (z.B. Wälzlager) o Mechanismus Verbindungen (Dreh-, Schub-, Zylinder, .... Gelenke)

China has undergone significant urban growth and industrialization over the last 30 years and its incredible development continues to move ahead at an increasingly rapid pace. In terms of urban expansion, China has just recently surpassed the world’s average urbanization rate of 50%, as it moves its massive population from rural to urban areas at an astonishing speed. It’s massive population and fast urbanizing speed aside, China is also unique in terms of its socio-political system and historical-cultural context: it is a hybrid of government planning and market forces. Since it encompasses a large part of the global population and has had a vastly different urbanization experience than that of Western countries, around which most theories are based, studying China’s urbanization is an opportunity to contribute to the field of urban studies in an unprecedented manner. However, these differences also make it difficult to develop a comprehensive study of China’s urban system since the predominant theories in the field are best suited to Western cities. This research rises to this challenge by systematically studying the relationship between the socioeconomic and biophysical processes in the Chinese urban system to understand the interaction between human and physical factors, and the landscape patterns that result from these interactions. This complex urban system is examined using a hierarchical, top-down approach. At the highest level is a Macro-scale analysis of the national urban system, followed by a study of the regional urban system: the JingJinJi Metropolitan Area at the Meso-scale, and finally a Micro-scale examination with a focus on the city of Beijing. Since urban systems develop over both time and space, the urban system is analyzed spatio-temporally on all three levels. Research at the national scale is composed of two parts. First, the challenges and opportunities of China’s urban development since the foundation of the People’s Republic of China in 1949 are investigated in a general context. The institutional barriers that impede the management and continuation of China’s urban development are also discussed. Rank-size Analysis and satellite images are used to present the structural transitions of city scaling and urban clusters. These changes come with a series of challenges that are also iterated and discussed. This is followed by an analysis of the spatial distribution and transition patterns of China’s urban system using Centrographic Analysis, particularly since the post-1979 reforms. Second, the Macro-scale research focuses on a study of the urban hierarchy that is based on inter-city interactions as determined by the Synthesized Gravity Model (SGM). Under this model socioeconomic variables are synthesized and represented by the Influential Factor, while the Function Distance is derived from a Network Analysis that is based on multiple transportation methods. As an improvement on the conventional Gravity Model (GM), the SGM is used to accurately establish and represent the nodal structure of China’s urban system, the evolution of its hierarchical structure, and the relationships that exist between the nodal structure and socioeconomic factors. The results based on the SGM indicate that China’s national urban system is characterized by the emergence of urban clusters with stronger inter-city interactions since the 1990s. However, development among cities within certain urban clusters is not even, although the general pattern indicates a lessening inequality among cities. Spatially, while most cities at the top of the hierarchy are located in the east of China, cities in the middle and west of the country are also gaining higher positions in the hierarchy over time. On the Meso-scale, the applicability of the Cellular Automata (CA)-based SLEUTH model for regional urban growth pattern is studied through a focus on the JingJinJi Metropolitan Area (Beijing-Tianjin-Hebei). By integrating socioeconomic factors into a modified SLEUTH model, the urban growth dynamics and future development scenarios of the area are simulated and predicted. The results based on the CA model show that this region is characterized by a dynamic development pattern with high spreading and breeding growth rules that relies greatly on the growing transportation systems. It also allows for the projection of three possible future urban growth scenarios, each occurring under different environmental and development conditions, showing the future urban growth with or without further intervention. This research confirms that four factors play essential roles in the formulation of the urban growth mechanism of the JingJinJi Metropolitan Area: Urban policies, Industry restructuring, Rural-urban migration, and Reclassification of urban boundaries. The Micro-scale study of Beijing is conducted from two perspectives: the social and natural. The social aspect adopts the factorial ecology approach to identify the social landscape patterns and the factors that have shaped Beijing’s social space in 1990 and 2000. The social mosaic has experienced a significant change due to suburbanization, resulting in a more dynamic and complex internal structure since the 2000s. From a natural perspective, Beijing’s physical landscape patterns are extracted by processing remotely sensed images that have the same temporal span. The physical change through landscape metrics demonstrates that Beijing’s expansion has generated a more complex and fragmented land use/cover pattern. Meanwhile, transportation systems play a significant role in urban expansion, although the expansion across the space (zonal rings and directional sectors) is not even. Finally, the relationship between the social and physical landscapes is quantitatively defined by the Geographically Weighted Regression (GWR) technique, using physical landscape metrics as dependent variables and social areas as independent variables. The GWR is able to demonstrate the relationship between the social and physical landscapes at this level: as a city’s social mosaic becomes more varied over time it results in the fragmentation of that city’s physical space.