Partial differential equations on domains presenting point singularities have always been of interest for applied mathematicians; this interest stems from the difficulty to prove regularity results for non-smooth domains, which has important consequences in the numerical solution of partial differential equations. In my thesis I address those consequences in the case of conforming and penalty finite element methods. The main results here contained concerns a priori error estimates for conforming and penalty finite element methods with respect to the energy norm, the $\mathcal{L}^2(\Omega)$ norm in both the standard and weighted setting.

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Finite element simulation of contact/impact problems using the penalty method is a well-established capability. The automatic penalty stiffness provides an easy way to implement the contact analysis. However, this way in which the penalty stiffness is associated with the material property and geometry of the master surface can lead to inappropriate distributions of contact pressure at edges or mesh transitions, or even cause much numerical noise. A new method of defining the penalty stiffness, which is associated with geometry of the slave surface, the reference penetration and reference contact pressure, is developed to consistently relate forces on contacting nodes with the contact pressure. This technique is successfully applied to several examples as the clamping simulation during the punch test and the rolling process. The results of such applications of new contact stiffness model demonstrate the effectiveness of such a model in avoiding the stress edge effect and the accompanying numerical noise. As an alternative approach to define the penalty stiffness, this new model provides another option for the contact analysis and gives the users more possibilities to control the contact performance. / Thesis / Master of Engineering (ME)

Resumé The right to life and the capital punishment Death penalty or capital punishment, or extreme penalty, is a punishment that assumes killing (or execution) of condemned person for a criminal offence provided it is possible to impose this sentence in accordance with the criminal law in force. At former times these crimes were called capital or hanging crimes. With regard to its definitiveness (impossibility of any redress after its execution) it is very controversial punishment. Its supporters argue that it is the sole just sentence for homicide and other felonies, that it excludes recurrence and it has significant deterrent (preventive) effects. On the other hand, the opponents allege not only moral arguments concerning the right of each person to life but they also mention the danger of judicial error which is incorrigible in this case. Furthermore, the objectors point out that the death sentence is not so intimidating. In addition, the costs of the execution use to be more expensive than life imprisonment. Since 1970s the capital punishment has been gradually cancelled in the majority of European and South American countries. Some states of the USA and the People's Republic of China are among countries that still make practise of the death penalty. I deal with the capital sentence in the first part...

Contractual Penalty under the Commercial Code (with focus on the discretionary power of a judge to reduce a contractual penalty) Contractual penalty is a concept frequently used by the parties to consolidate the position of the creditor as well as to motivate the debtor to fulfill the obligation as agreed. Not different from the other institutes of private law, the practical application of contractual penalty arises many questions with no uniform answers. The purpose of the thesis is to analyze selected contentious issues concerning the contractual penalty, especially discretionary power of a judge to reduce its unreasonable amount, to confront controversial theoretical opinions as well as non-conforming conclusions drawn from the juristic theory and established practice of the courts and add own opinion on the discussed matters. The paper does not include the exhaustive construction of contractual penalty, and therefore the general aspects are outlined only to the necessary extent. Greater attention is paid to the creation and existence of the right and claim to the contractual penalty. The study shifts the focus on the discretionary power of a judge to mitigate its inappropriate amount comprising different opinions on the related issues. The concept of contractual penalty has been used in private...

Esse trabalho sintetiza a busca por uma orientação alternativa para o tratamento teórico-prático da determinação judicial da pena, com destaque especial para as particularidades referentes à fixação da pena-base. Para tanto, de saída, foi revisitado o discurso tradicional sobre a punição, de sorte a explicitar, já a partir desse campo de legitimação da pena, algumas das principais limitações das abordagens ditas oficiais a respeito dos fundamentos e finalidades atribuídos à reprimenda penal. Em seguida, buscou-se empreender uma crítica materialista da punição, o que foi feito por meio de uma abordagem histórico-social da pena e das instituições penais, das quais se examinou a origem e consolidação, até o desaguar no atual quadro de encarceramento em massa. Por fim, analisou-se as principais contribuições teóricas ao debate sobre a determinação da punição, de maneira a que fossem aduzidas as suas mais graves insuficiências, e, ao cabo, esboçou-se indicações, ainda que gerais, voltadas a uma atuação penal fundamentalmente referenciada na necessidade de se minorar os efeitos reconhecidamente dessocializadores do cárcere. / This paper summarizes the search for an alternative orientation to the theoretical and practical treatment of judicial sentencing, with particular attention to the particularities regarding the base sentencing. To do so, the traditional discourse on punishment was revisited, in order to clarify, from this field of penalty legitimacy, some of the main limitations of the so called official approach concerning the foundations and purposes attributed to criminal reprimand. Next, we sought to undertake a materialist critique of punishment, which was done through a socio-historical approach of sentences and penal institutions, whose origin and consolidation was examined, to the current flow of mass incarceration. Finally, the main theoretical contributions to the debates on the determination of punishment were analyzed, so that they were put forward to its most serious shortcomings, and indications were laid out, albeit general, geared primarily to a criminal action referenced on the need to mitigate the well known disocialisating effects of the jail.

Service providers often use various types of ¡§punishments¡¨ or ¡§penalties¡¨ to reduce the frequency of customers¡¦ violations and to balance their potential loss, but researchers does not pay much attention to ¡§customer penalties¡¨. Existing studies of customer penalties focus on the relationships between the service provider (the executor) and customers (the recipients) who violate company¡¦s policy, especially on the effects of punishment toward recipients. However, studies in ¡§organizational punishments¡¨ had enlarge the scope of research by including observers, and developed a framework for studying the effects of punishments on observers which is called ¡§a framework for understanding the social effects of organizational punishment¡¨. This study is based on customer penalties, and the researcher cites the viewpoints and theories from this framework to enlarge the scope of research in bilateral to tripartite. This study examines observers¡¦ responses, including their perception of justice, violate intension, and affective commitment to the service provider, when they obtain the information about service provider punishing a violated customer by experimental design. The result shows that social learning effect will exists if observers receive information about punishments. Observers prefer service providers whose punishments with lower severity, higher flexibility, and adequate explanations. The result also shows that perceived justice has a partial mediating effect on ¡§punishments-responses¡¨ relation.

Esse trabalho sintetiza a busca por uma orientação alternativa para o tratamento teórico-prático da determinação judicial da pena, com destaque especial para as particularidades referentes à fixação da pena-base. Para tanto, de saída, foi revisitado o discurso tradicional sobre a punição, de sorte a explicitar, já a partir desse campo de legitimação da pena, algumas das principais limitações das abordagens ditas oficiais a respeito dos fundamentos e finalidades atribuídos à reprimenda penal. Em seguida, buscou-se empreender uma crítica materialista da punição, o que foi feito por meio de uma abordagem histórico-social da pena e das instituições penais, das quais se examinou a origem e consolidação, até o desaguar no atual quadro de encarceramento em massa. Por fim, analisou-se as principais contribuições teóricas ao debate sobre a determinação da punição, de maneira a que fossem aduzidas as suas mais graves insuficiências, e, ao cabo, esboçou-se indicações, ainda que gerais, voltadas a uma atuação penal fundamentalmente referenciada na necessidade de se minorar os efeitos reconhecidamente dessocializadores do cárcere. / This paper summarizes the search for an alternative orientation to the theoretical and practical treatment of judicial sentencing, with particular attention to the particularities regarding the base sentencing. To do so, the traditional discourse on punishment was revisited, in order to clarify, from this field of penalty legitimacy, some of the main limitations of the so called official approach concerning the foundations and purposes attributed to criminal reprimand. Next, we sought to undertake a materialist critique of punishment, which was done through a socio-historical approach of sentences and penal institutions, whose origin and consolidation was examined, to the current flow of mass incarceration. Finally, the main theoretical contributions to the debates on the determination of punishment were analyzed, so that they were put forward to its most serious shortcomings, and indications were laid out, albeit general, geared primarily to a criminal action referenced on the need to mitigate the well known disocialisating effects of the jail.

In this research effort, we study three exterior penalty function approaches for solving linear programming problems. These methods are an active set l2 penalty approach (ASL2), an inequality-equality based l2 penalty approach (IEL2), and an augmented Lagrangian approach (ALAG). Particular effective variants are presented for each method, along with comments and experience on alternative algorithmic strategies that were empirically investigated. Our motivation is to examine the relative performance of these different approaches based on the basic l2 penalty function in order to provide insights into the viability of these methods for solving linear programs. To test the performance of these algorithms, a set of randomly generated problems as well as a set of NETLIB test problems from the public domain are used. By way of providing a benchmark for comparisons, we also solve the test problems using CPLEX 6.0, an advanced simplex implementation. While a particular variant (ALAG2) of ALAG performed the best for randomly generated test problems, ASL2 performed the best for the NETLIB test problems. Moreover, for test problems having only equality constraints, IEL2, and ASL2 (which is a finer-tuned version of IEL2 in this case) were comparable and yielded a second-best performance in comparison with ALAG2. Furthermore, a set of problems with relatively higher density parameter values, as well as a set of low-density problems were used to determine the effect of density on the relative performances of these methods. This experiment revealed that for linear programs with a high density parameter, ASL2 is the best alternative among the tested algorithms; whereas, for low-density problems ALAG2 is the fastest method. Moreover, although our implementation was rudimentary in comparison with CPLEX, all of the tested methods attained a final solution faster than CPLEX for the set of large-scale low-density problems, sometimes as fast as requiring only 16-23% of the effort consumed by CPLEX. Average rank tests based on the computational results obtained are performed using two different statistics, that assess the speed of convergence and the quality or accuracy of the solution, in order to determine the relative effectiveness of the algorithms and to validate our conclusions. Overall, the results provide insights into selecting algorithmic strategies based on problem structure and indicate that while this class of methods is viable for computing near optimal solutions, more research is needed to design robust and competitive exterior point methods for solving linear programming problems. However, the use of the proposed variant of the augmented Lagrangian method to solve large-scale low-density linear programs is promising and should be explored more extensively. / Master of Science

The thesis seeks to enhance understanding of the recent reform of capital punishment law, policies and institutions in China by studying its causes, significance, and limits. The research surveys the reform initiated by China’s top judiciary – the Supreme People’s Court - around 2006-2007. It demonstrates a changing domestic socio-political context, within which the external and internal impetus to reform is inevitable. Drawn from elite interview evidence with penal policy makers including judges, prosecutors, and legislators, the thesis concludes that Europe-inspired, cross-border abolitionist sentiments created motivation for change in China through soft mechanisms of shaming and persuasion, albeit to a limited degree. In the domestic realm, the research identified three pairs of interrelated tensions – the contradiction between elites and the public, the conflict between political intervention and judicial autonomy, and the divergent interests and priorities between top judicial organs and lower courts. These tensions are useful social, political and legal indicators to explain why and how China reformed its capital punishment machinery.