Studien undersöker läromedlen PM och Livsviktigt, som används i religionskunskap och i social och emotionell träning (SET). Och fokuserar på hur dessa belyser existentiella frågor i jämförelse med de riktlinjer som Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011, (Lgr 11)[1] tar upp. Syftet är att se hur dessa läromedel svarar mot Lgr 11 och om läromedlen tar upp de områden som Lgr 11 säger ska ingå i undervisningen. För att nå information om detta genomfördes en innehållsanalys av läromedlen som används i religionskunskap och SET undervisningen. Läromedlen jämfördes med Lgr 11, för att se om dessa belyser samma områden som styrdokumentet. Resultatet visar att det finns likheter i innehållet i läromedlen och Lgr 11 inom det existentiella området. Enskilt belyser läromedlen en liten del av allt som Lgr 11 tar upp. Tillsammans täcker de upp betydligt mer av alla punkter som beskrivs i styrdokumentet. Slutsatsen är att det krävs fler källor som inspirerar eleven i sökandet och identitetsskapandet inom existentiella frågor, för att uppfylla kraven i Lgr 11. [1]Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011, Skolverket, Stockholm, 2011

An interface-preserving level set method is incorporated into the Reynolds- Averaged Navier-Stokes (RANS) numerical method for the time-domain simulation of green water effects. This generalized method can be used to evaluate two- and three-dimensional, laminar and turbulent, free surface flows in moving non-orthogonal grids. In the method, free surface flows are modeled as immiscible two-phase (air and water) flows. A level set function is used to mark the individual fluids and the free surface itself is represented by the zero level set function. The level set evolution equation is coupled with the conservation equations for mass and momentum, and solved in the transformed plane. Chimera domain decomposition technique is employed to handle embedding, overlapping, or matching grids. To demonstrate the feasibility of the method, calculations are performed in several bench mark free surface flows including dam break flows, free jets, solitary wave propagations and the impingement of dam break flow on a fixed structure. The comparisons between the simulations and the experimental data provide a thorough validation of the present method. The results also show the potential capability of level-set RANS method in much more complicated free surface flow simulations. After validations, the method is applied to simulate sloshing flows in LNG tank and green water over the platform. In sloshing flows, the level-set RANS method captures the large impact pressure accurately on LNG tank walls. It also generates a plunging breaker successfully in front of a platform in the numerical wave tank. The good agreements between numerical and experimental results prove the level set RANS method is a powerful and accurate CFD methodology in free surface flow simulations.

This dissertation considers a class of closely related NP-hard otpimization problems on graphs that arise in many important applications, including network-based data mining, analysis of the stock market, social networks, coding theory, fault diagnosis, molecular biology, biochemistry and genomics. In particular, the problems of interest include the classical maximum independent set problem (MISP) and maximum clique problem (MCP), their vertex-weighted vesrions, as well as novel optimization models that can be viewed as practical relaxations of their classical counterparts. The concept of clique has been a popular instrument in analysis of networks, and is, essentially, an idealized model of a “closely connected group”, or a cluster. But, at the same time, the restrictive nature of the definition of clique makes the clique model impractical in many applications. This motivated the development of clique relaxation models that relax different properties of a clique. On the one hand, while still possessing some clique-like properties, clique relaxations are not as “perfect” as cliques; and on the other hand, they do not exhibit the disadvantages associated with a clique. Using clique relaxations allows one to compromise between perfectness and flexibility, between ideality and reality, which is a usual issue that an engineer deals with when applying theoretical knowledge to solve practical problems in industry. The clique relaxation models studied in this dissertation were first proposed in the literature on social network analysis, however they have not been well investigated from a mathematical programming perspective. This dissertation considers new techniques for solving the MWISP and clique relaxation problems and investigates their effectiveness from theoretical and computational perspectives. The main results obtained in this work include (i) developing a scale-reduction approach for MWISP based on the concept of critical set and comparing it theoretically with other approaches; (ii) obtaining theoretical complexity results for clique relaxation problems; (iii) developing algorithms for solving the clique relaxation problems exactly; (iv) carrying out computational experiments to demonstrate the performance of the proposed approaches, and, finally, (v) applying the obtained theoretical results to several real-life problems.

An interface-preserving level set method is incorporated into the Reynolds-Averaged Navier-Stokes (RANS) numerical method to simulate the application of the green water phenomena around a platform and the breaking wave above the deck. In the present study, this method is used to evaluate the laminar in two dimension plane with fixed orthogonal grids. In this method, it is assumed that the free surface is modeled as immiscible two-phase flow (air and water). A level set function can present the individual fluids, and the interface between two-phase is represented by the zero level set. In addition, the level set evolution equation is coupled with the conservation equations for mass and momentum, which will be solved in the transformed plane. For different purposes, there are several block domains in the application grid. Chimera domain decomposition technique is employed to handle such embedding, overlapping, or matching grids. Several simple test cases were performed to demonstrate the feasibility of this method. The comparisons between the ENO scheme and the WENO scheme will be illustrated in the Zalesak's disk case and will further prove that the WENO scheme is superior to the ENO scheme. The propagation of continuous wave case will validate some properties of wave and determine the importance of some parameters in code. Moreover, the method will be applied in simulation of green water around a two dimensional platform. By configuring different deck heights, some distinct phenomena can be represented. Lastly, it is crucial to observe the green water phenomena around the platform deck by applying the velocity-extrapolation routine.

Domestic production of bioenergy by utilizing set-aside land in Taiwan can reduce Taiwan’s reliance on expensive and politically insecure foreign fossil fuels while also reducing the combustion of fossil fuels, which emit substantial amounts of greenhouse gases. After joining the World Trade Organization, Taiwan’s agricultural sector idled about one-third of the national cropland, hereafter called “set-aside land”. This potentially provides the land base for Taiwan to develop a bioenergy industry. This dissertation examines Taiwan’s potential for bioenergy production using feedstocks grown on set-aside land and discusses the consequent effects on Taiwan’s energy security plus benefits and greenhouse gas (GHG) emissions. The Taiwan Agricultural Sector Model (TASM) was used to simulate different agricultural policies related to bioenergy production. To do this simulation the TASM model was extended to include additional bioenergy production possibilities and GHG accounting. We find that Taiwan’s bioenergy production portfolio depends on prices of ethanol, electricity and GHG. When GHG prices go up, ethanol production decreases and electricity production increases because of the relatively stronger GHG offset power of biopower. Results from this pyrolysis study are then incorporated into the TASM model. Biochar from pyrolysis can be used in two ways: burn it or use it as a soil amendment. Considering both of these different uses of biochar, we examine bioenergy production and GHG offset to see to what extent Taiwan gets energy security benefits from the pyrolysis technology and how it contributes to climate change mitigation. Furthermore, by examining ethanol, electricity and pyrolysis together in the same framework, we are able to see how they affect each other under different GHG prices, coal prices and ethanol prices. Results show that ethanol is driven out by pyrolysis-based electricity when GHG price is high. We also find that when biochar is hauled back to the rice fields, GHG emission reduction is higher than that when biochar is burned for electricity; however, national electricity production is consequently higher when biochar is burned.

Clustering is the unsupervised classification of patterns into groups, which is easy provided the data of patterns are consistent. However, real data are almost always tempered with inconsistencies, which make it a hard problem, and actually, the most widely studied formulations, correlation clustering and hierarchical clustering, are both NP-hard. In the graph representation of data, inconsistencies also frequently present themselves as cycles, also called deadlocks, and to break cycles by removing vertices is the objective of the classical feedback vertex set (FVS) problem. This dissertation studies the three problems, correlation clustering, hierarchical clustering, and disjoint-FVS (a variation of FVS), from a kernelization approach. A kernelization algorithm in polynomial time reduces a problem instance provably to speed up the further processing with other approaches. For each of the problems studied, an efficient kernelization algorithm of linear or sub-quadratic running time is presented. All the kernels obtained in this dissertation have linear size with very small constants. Better parameterized algorithms are also designed based on the kernels for the last two problems. Finally, some concluding remarks on possible directions for future research are briefly mentioned.

As a series of financial crisis and accounting scandals occur around the world, the government, many institutions and the public have put great emphasis on corporate governance. Most of the prior research focus on how the corporate governance monitoring system can enhance the firm value and reduce the financial crisis. This empirical analysis includes investment opportunity set (IOS) as an environmental factor and tests the interaction between IOS, firm performance and external corporate governance mechanisms (audit quality and institutional investor ownership) as well as internal corporate governance mechanisms (CEO duality and pledged shares ratio of directors and supervisors) in Taiwan. The sample consists of 999 Taiwan publicly listed companies both in electronics industry and non-electronics industries in 2003. This empirical study uses common factor analysis, Pearson¡¦s correlation analysis and regression analysis to test four hypotheses. The hypotheses are as follows: (1) the relationship between IOS and firm performance will be affected if the auditor is from the Big 4 auditing firm. (2) The relationship between IOS and firm performance will be changed due to the institutional investor ownership. (3) The CEO duality will influence the relationship between IOS and firm performance. (4) The pledged shares ratio of directors and supervisors has an influence on the relationship between IOS and firm performance. The results show that audit quality has no influence on the association of IOS and firm performance, but the institutional investor ownership has a negative and significant influence on that relationship. In non-electronics industries, CEO duality won¡¦t change the firm performance but a negative influence is reported in this study. Eventually, while many companies with financial distress have a higher pledged shares ratio than other normal companies, a positive influence is shown in this study when the investment opportunity set is considered.

Suppose Gamma is a group acting on a set X. An r-labeling phi: X to {1, 2, ..., r} of X is distinguishing (with respect to the action of Gamma) if for any sigma in Gamma, sigma not equal id_X, there exists an element x in X such that phi(x) not equal phi(sigma(x)). The distinguishing number, D_{Gamma}(X), of the action of Gamma on X is the minimum r for which there is an r-labeling which is distinguishing. Given a graph G, the distinguishing number of G, D(G),is defined as D(G) = D_{Aut(G)}(V(G)). This thesis determines the distinguishing numbers of all actions of S_5. As a consequence, we determine all the possible values of the distinguishing numbers of graphs G with Aut(G)=S_5, confirming a conjecture of Albertson and Collins.

In this thesis, we study two new inverse nodal problems introduced by Yang, Shen and Shieh respectively. Consider the classical Sturm-Liouville problem: $$ left{ egin{array}{c} -phi'+q(x)phi=la phi phi(0)cosalpha+phi'(0)sinalpha=0 phi(1)coseta+phi'(1)sineta=0 end{array} ight. , $$ where $qin L^1(0,1)$ and $al,ein [0,pi)$. The inverse nodal problem involves the determination of the parameters $(q,al,e)$ in the problem by the knowledge of the nodal points in $(0,1)$. In 1999, X.F. Yang got a uniqueness result which only requires the knowledge of a certain subset of the nodal set. In short, he proved that the set of all nodal points just in the interval $(0,b) (frac{1}{2}<bleq 1)$ is sufficient to determine $(q,al,e)$ uniquely. In this thesis, we show that a twin and dense subset of all nodal points in the interval $(0,b)$ is enough to determine $(q,al,e)$ uniquely. We improve Yang's theorem by weakening its conditions, and simplifying the proof. In the second part of this thesis, we will discuss an inverse nodal problem for the vectorial Sturm-Liouville problem: $$ left{egin{array}{c} -{f y}'(x)+P(x){f y}(x) = la {f y}(x) A_{1}{f y}(0)+A_{2}{f y}'(0)={f 0} B_{1}{f y}(1)+B_{2}{f y}'(1)={f 0} end{array} ight. . $$ Let ${f y}(x)$ be a continuous $d$-dimensional vector-valued function defined on $[0,1]$. A point $x_{0}in [0,1]$ is called a nodal point of ${f y}(x)$ if ${f y}(x_{0})=0$. ${f y}(x)$ is said to be of type (CZ) if all the zeros of its components are nodal points. $P(x)$ is called simultaneously diagonalizable if there is a constant matrix $S$ and a diagonal matrix-valued function $U(x)$ such that $P(x)=S^{-1}U(x)S.$ If $P(x)$ is simultaneously diagonalizable, then it is easy to show that there are infinitely many eigenfunctions which are of type (CZ). In a recent paper, C.L. Shen and C.T. Shieh (cite{SS}) proved the converse when $d=2$: If there are infinitely many Dirichlet eigenfunctions which are of type (CZ), then $P(x)$ is simultaneously diagonalizable. We simplify their work and then extend it to some general boundary conditions.

Presently, there are a lot of applications of gear sets with skew axes, some of them, especially worm gear sets and hypoid gear sets, are widely used. Take hypoid gear as example, gear sets produced by different gear factories can¡¦t fit to each other. Due to the lacking in common properties among different systems, it is disadvantageous to integrated application of development of gear researches. Therefore, a common mathematical constructive model is necessary to be established. The main content of this thesis is to construct the mathematical parametric model and the partial differential constraint equation according to the rigid-body transformation theory and General Theorem of Conjugate Surfaces. After finding out the solution from the partial differential constraint equation, a new line-contacted type of tooth profile of gear sets with skew axes, quality analyses to the parameters of gear profile rendered are proceeded. Finally, utilize the software of motion simulation to simulate the operating situation of the linear contacted type of gear sets with skew axes constructed, and supply the demonstration of the theory of tooth profile of gear sets and properties of gear sets.