Filtern
Erscheinungsjahr
Dokumenttyp
- Dissertation (832)
- Wissenschaftlicher Artikel (219)
- Buch (Monographie) (113)
- Beitrag zu einer (nichtwissenschaftlichen) Zeitung oder Zeitschrift (108)
- Arbeitspapier (62)
- Ausgabe (Heft) zu einer Zeitschrift (24)
- Teil eines Buches (Kapitel) (22)
- Konferenzveröffentlichung (17)
- Sonstiges (16)
- Rezension (10)
- Masterarbeit (9)
- Habilitation (6)
- Bericht (3)
- Retrodigitalisat (3)
- Bachelorarbeit (2)
- Lehrmaterial (2)
- Vorlesung (2)
- Examensarbeit (1)
Sprache
- Deutsch (842)
- Englisch (518)
- Französisch (75)
- Mehrsprachig (15)
- Russisch (1)
Schlagworte
- Deutschland (84)
- Luxemburg (52)
- Stress (40)
- Schule (37)
- Schüler (33)
- Politischer Unterricht (29)
- Modellierung (28)
- Fernerkundung (25)
- Geschichte (24)
- Demokratie (23)
Institut
- Raum- und Umweltwissenschaften (213)
- Psychologie (212)
- Politikwissenschaft (132)
- Universitätsbibliothek (83)
- Rechtswissenschaft (77)
- Wirtschaftswissenschaften (66)
- Mathematik (65)
- Fachbereich 4 (57)
- Medienwissenschaft (57)
- Fachbereich 6 (50)
In this thesis, we investigate the quantization problem of Gaussian measures on Banach spaces by means of constructive methods. That is, for a random variable X and a natural number N, we are searching for those N elements in the underlying Banach space which give the best approximation to X in the average sense. We particularly focus on centered Gaussians on the space of continuous functions on [0,1] equipped with the supremum-norm, since in that case all known methods failed to achieve the optimal quantization rate for important Gauss-processes. In fact, by means of Spline-approximations and a scheme based on the Best-Approximations in the sense of the Kolmogorov n-width we were able to attain the optimal rate of convergence to zero for these quantization problems. Moreover, we established a new upper bound for the quantization error, which is based on a very simple criterion, the modulus of smoothness of the covariance function. Finally, we explicitly constructed those quantizers numerically.
This dissertation deals with consistent estimates in household surveys. Household surveys are often drawn via cluster sampling, with households sampled at the first stage and persons selected at the second stage. The collected data provide information for estimation at both the person and the household level. However, consistent estimates are desirable in the sense that the estimated household-level totals should coincide with the estimated totals obtained at the person-level. Current practice in statistical offices is to use integrated weighting. In this approach consistent estimates are guaranteed by equal weights for all persons within a household and the household itself. However, due to the forced equality of weights, the individual patterns of persons are lost and the heterogeneity within households is not taken into account. In order to avoid the negative consequences of integrated weighting, we propose alternative weighting methods in the first part of this dissertation that ensure both consistent estimates and individual person weights within a household. The underlying idea is to limit the consistency conditions to variables that emerge in both the personal and household data sets. These common variables are included in the person- and household-level estimator as additional auxiliary variables. This achieves consistency more directly and only for the relevant variables, rather than indirectly by forcing equal weights on all persons within a household. Further decisive advantages of the proposed alternative weighting methods are that original individual rather than the constructed aggregated auxiliaries are utilized and that the variable selection process is more flexible because different auxiliary variables can be incorporated in the person-level estimator than in the household-level estimator.
In the second part of this dissertation, the variances of a person-level GREG estimator and an integrated estimator are compared in order to quantify the effects of the consistency requirements in the integrated weighting approach. One of the challenges is that the estimators to be compared are of different dimensions. The proposed solution is to decompose the variance of the integrated estimator into the variance of a reduced GREG estimator, whose underlying model is of the same dimensions as the person-level GREG estimator, and add a constructed term that captures the effects disregarded by the reduced model. Subsequently, further fields of application for the derived decomposition are proposed such as the variable selection process in the field of econometrics or survey statistics.
This thesis is concerned with two classes of optimization problems which stem
mainly from statistics: clustering problems and cardinality-constrained optimization problems. We are particularly interested in the development of computational techniques to exactly or heuristically solve instances of these two classes
of optimization problems.
The minimum sum-of-squares clustering (MSSC) problem is widely used
to find clusters within a set of data points. The problem is also known as
the $k$-means problem, since the most prominent heuristic to compute a feasible
point of this optimization problem is the $k$-means method. In many modern
applications, however, the clustering suffers from uncertain input data due to,
e.g., unstructured measurement errors. The reason for this is that the clustering
result then represents a clustering of the erroneous measurements instead of
retrieving the true underlying clustering structure. We address this issue by
applying robust optimization techniques: we derive the strictly and $\Gamma$-robust
counterparts of the MSSC problem, which are as challenging to solve as the
original model. Moreover, we develop alternating direction methods to quickly
compute feasible points of good quality. Our experiments reveal that the more
conservative strictly robust model consistently provides better clustering solutions
than the nominal and the less conservative $\Gamma$-robust models.
In the context of clustering problems, however, using only a heuristic solution
comes with severe disadvantages regarding the interpretation of the clustering.
This motivates us to study globally optimal algorithms for the MSSC problem.
We note that although some algorithms have already been proposed for this
problem, it is still far from being “practically solved”. Therefore, we propose
mixed-integer programming techniques, which are mainly based on geometric
ideas and which can be incorporated in a
branch-and-cut based algorithm tailored
to the MSSC problem. Our numerical experiments show that these techniques
significantly improve the solution process of a
state-of-the-art MINLP solver
when applied to the problem.
We then turn to the study of cardinality-constrained optimization problems.
We consider two famous problem instances of this class: sparse portfolio optimization and sparse regression problems. In many modern applications, it is common
to consider problems with thousands of variables. Therefore, globally optimal
algorithms are not always computationally viable and the study of sophisticated
heuristics is very desirable. Since these problems have a discrete-continuous
structure, decomposition methods are particularly well suited. We then apply a
penalty alternating direction method that explores this structure and provides
very good feasible points in a reasonable amount of time. Our computational
study shows that our methods are competitive to
state-of-the-art solvers and heuristics.
In this thesis we focus on the development and investigation of methods for the computation of confluent hypergeometric functions. We point out the relations between these functions and parabolic boundary value problems and demonstrate applications to models of heat transfer and fluid dynamics. For the computation of confluent hypergeometric functions on compact (real or complex) intervals we consider a series expansion based on the Hadamard product of power series. It turnes out that the partial sums of this expansion are easily computable and provide a better rate of convergence in comparison to the partial sums of the Taylor series. Regarding the computational accuracy the problem of cancellation errors is reduced considerably. Another important tool for the computation of confluent hypergeometric functions are recurrence formulae. Although easy to implement, such recurrence relations are numerically unstable e.g. due to rounding errors. In order to circumvent these problems a method for computing recurrence relations in backward direction is applied. Furthermore, asymptotic expansions for large arguments in modulus are considered. From the numerical point of view the determination of the number of terms used for the approximation is a crucial point. As an application we consider initial-boundary value problems with partial differential equations of parabolic type, where we use the method of eigenfunction expansion in order to determine an explicit form of the solution. In this case the arising eigenfunctions depend directly on the geometry of the considered domain. For certain domains with some special geometry the eigenfunctions are of confluent hypergeometric type. Both a conductive heat transfer model and an application in fluid dynamics is considered. Finally, the application of several heat transfer models to certain sterilization processes in food industry is discussed.
Pour pouvoir développer une compétence médiatique, les élèves ont besoin d’une réflexion, mais également d’une pratique personnelle des médias afin de devenir des producteur(trice)s et des concepteur(trice)s d’offres médiatiques. Ce compte rendu pratique relate la réalisation d’un programme télévisé d’une heure avec des élèves du Lycée de Garçons Esch.
One of the main tasks in mathematics is to answer the question whether an equation possesses a solution or not. In the 1940- Thom and Glaeser studied a new type of equations that are given by the composition of functions. They raised the following question: For which functions Ψ does the equation F(Ψ)=f always have a solution. Of course this question only makes sense if the right hand side f satisfies some a priori conditions like being contained in the closure of the space of all compositions with Ψ and is easy to answer if F and f are continuous functions. Considering further restrictions to these functions, especially to F, extremely complicates the search for an adequate solution. For smooth functions one can already find deep results by Bierstone and Milman which answer the question in the case of a real-analytic function Ψ. This work contains further results for a different class of functions, namely those Ψ that are smooth and injective. In the case of a function Ψ of a single real variable, the question can be fully answered and we give three conditions that are both sufficient and necessary in order for the composition equation to always have a solution. Furthermore one can unify these three conditions to show that they are equivalent to the fact that Ψ has a locally Hölder-continuous inverse. For injective functions Ψ of several real variables we give necessary conditions for the composition equation to be solvable. For instance Ψ should satisfy some form of local distance estimate for the partial derivatives. Under the additional assumption of the Whitney-regularity of the image of Ψ, we can give sufficient conditions for flat functions f on the critical set of Ψ to possess a solution F(Ψ)=f.
Competitive analysis is a well known method for analyzing online algorithms.
Two online optimization problems, the scheduling problems and the list accessing problems, are considered in the thesis of Yida Zhu in the respect of this method.
For both problems, several existing online and offline algorithms are studied. Their performances are compared with the performances of corresponding offline optimal algorithms.
In particular, the list accessing algorithm BIT is carefully reviewed.
The classical proof of its worst case performance get simplified by adapting the knowledge about the optimal offline algorithm.
With regard to average case analysis, a new closed formula is developed to determine the performance of BIT on specific class of instances.
All algorithm considered in this thesis are also implemented in Julia.
Their empirical performances are studied and compared with each other directly.
Educational researchers have intensively investigated students" academic self-concept (ASC) and self-efficacy (SE). Both constructs are part of the competence-related self-perceptions of students and are considered to support students" academic success and their career development in a positive manner (e.g., Abele-Brehm & Stief, 2004; Richardson, Abraham, & Bond, 2012; Schneider & Preckel, 2017). However, there is a lack of basic research on ASC and SE in higher education in general, and in undergraduate psychology courses in particular. Therefore, according to the within-network and between-network approaches of construct validation (Byrne, 1984), the present dissertation comprises three empirical studies examining the structure (research question 1), measurement (research question 2), correlates (research question 3), and differentiation (research question 4) of ASC and SE in a total sample of N = 1243 psychology students. Concerning research question 1, results of confirmatory factor analysis (CFAs) implied that students" ASC and SE are domain-specific in the sense of multidimensionality, but they are also hierarchically structured, with a general factor at the apex according to the nested Marsh/Shavelson model (NMS model, Brunner et al., 2010). Additionally, psychology students" SE to master specific psychological tasks in different areas of psychological application could be described by a 2-dimensional model with six factors according to the Multitrait-Multimethod (MTMM)-approach (Campbell & Fiske, 1959). With regard to research question 2, results revealed that the internal structure of ASC and SE could be validly assessed. However, the assessment of psychology students" SE should follow a task-specific measurement strategy. Results of research question 3 further showed that both constructs of psychology students" competence-related self-perceptions were positively correlated to achievement in undergraduate psychology courses if predictor (ASC, SE) corresponded to measurement specificity of the criterion (achievement). Overall, ASC provided substantially stronger relations to achievement compared to SE. Moreover, there was evidence for negative paths (contrast effects) from achievement in one psychological domain on ASC of another psychological domain as postulated by the internal/external frame of reference (I/E) model (Marsh, 1986). Finally, building on research questions 1 to 3 (structure, measurement, and correlates of ASC and SE), psychology students" ASC and SE were be differentiated on an empirical level (research question 4). Implications for future research practices are discussed. Furthermore, practical implications for enhancing ASC and SE in higher education are proposed to support academic achievement and the career development of psychology students.
Mechanical and Biological Treatment (MBT) generally aims to reduce the amount of solid waste and emissions in landfills and enhance the recoveries. MBT technology has been studied in various countries in Europe and Asia. Techniques of solid waste treatment are distinctly different in the study areas. A better understanding of MBT waste characteristics can lead to an optimization of the MBT technology. For a sustainable waste management, it is essential to determine the characteristics of the final MBT waste, the effectiveness of the treatment system as well as the potential application of the final material regarding future utilization. This study aims to define and compare the characteristics of the final MBT materials in the following countries: Luxembourg (using a high degree technology), Fridhaff in Diekirch/Erpeldange, Germany (using a well regulated technology), Singhofen in Rhein-Lahn district, Thailand (using a low cost technology): Phitsanulok in Phitsanulok province. The three countries were chosen for this comparative study due to their unique performance in the MBT implementation. The samples were taken from the composting heaps of the final treatment process prior to sending them to landfills, using a random sampling standard strategy from August 2008 onwards. The size of the sample was reduced to manageable sizes before characterization. The size reduction was achieved by the quartering method. The samples were first analyzed for the size fraction on the day of collection. They were screened into three fractions by the method of dry sieving: small size with a diameter of <10 mm, medium size with a diameter of 10-40 mm and large size with a diameter of >40 mm. These fractions were further analyzed for their physical and chemical parameters such as particle size distribution (total into 12 size fractions), particle shape, porosity, composition, water content, water retention capacity and respiratory activity. The extracted eluate was analyzed for pH-value, heavy metals (lead, cadmium and arsenic), chemical oxygen demand, ammonium, sulfate and chloride. In order to describe and evaluate the potential application of the small size material as a final cover of landfills, the fraction of small size samples were tested for the geotechnical properties as well. The geotechnical parameters were the compaction test, permeability test and shear strength test. The detailed description of the treatment facilities and methods of the study areas were included in the results. The samples from the three countries are visibly smaller than waste without pretreatment. Maximum particle size is found to be less than 100 mm. The samples are found to consist of dust to coarse fractions. The small size with a diameter of <10 mm was highest in the sample from Germany (average 60% by weight), secondly in the sample from Luxembourg (average 43% by weight) and lowest in the sample from Thailand (average 15% by weight). The content of biodegradable material generally increased with decreasing particle sizes. Primary components are organic, plastics, fibrous materials and inert materials (glass and ceramics). The percentage of each components greatly depends on the MBT process of each country. Other important characteristics are significantly reduced water content, reduced total organic carbon and reduced potential heavy metals. The geotechnical results show that the small fraction is highly compact, has a low permeability and lot of water adsorbed material. The utilization of MBT material in this study shows a good trend as it proved to be a safe material which contained very low amounts of loadings and concentrations of chemical oxygen demand, ammonium, and heavy metals. The organic part can be developed to be a soil conditioner. It is also suitably utilized as a bio-filter layer in the final cover of landfill or as a temporary cover during the MBT process. This study showed how to identify the most appropriate technology for municipal solid waste disposal through the study of waste characterization.
Comparing the results of the phylogeographies of the four species included in this thesis, some accordances have been found, even though certain patterns are only represented in one or two species. In all cases, the findings of the studied species strongly support the existence of forests or forest-like ecosystems beyond the classic forest refugia in the Mediterranean areas (Iberian, Apennine and Balkan peninsulas) during glacial times. However, evidence of glacial refugial areas in Southeastern Europe, especially the Balkans, have been found in this study as well. The analysed populations of Aposeris foetida, Melampyrum sylvaticum and Erebia euryale showed high genetic diversity values and mostly higher private fragments in this area, which is a strong indicator for centres of glacial survival during Würm and, regarding the results of M. sylvaticum, even during the Riss ice age. Three of the analysed species (A. foetida, M. sylvaticum and Colias palaeno) supported a second main glacial refuge area located along the Northern Alps. Again, high genetic diversity values and the uniqueness of the populations living in this region today prove the importance of this area as a glacial centre of survival. Those results confirm several recently published studies on forest species and strongly indicate the persistence of forest-like structures or even forests during the ice ages along the foothills of the Northern Alps. Additionally, the persistence of C. palaeno in this area furthermore supports the existence of peatlands north of the Alps, at least during the last glacial. The results of M. sylvaticum and E. euryale further indicate the vicinity of the Tatra Mountains as core areas for glacial survival. However, the genetic patterns found for E. euryale are ambiguous. Due to an intermediate position of two genetic lineages (originating in the Eastern Alps and Southeastern Europe), the Tatras could also reflect a postglacial mixture zone of those lineages. Moreover, the glacial and postglacial importance of this area for woodland species was accentuated, supporting other phylogeographic studies published. Besides the congruities among the results of the study species, some unique patterns and therefore further potential glacial refugia have also been illuminated in this thesis. For instance, the calcicole species, A. foetida, most probably had further survival area at both sides of the Dinaric Alps, supported by high genetic diversity values and a high number of private fragments found in Croatian populations. Furthermore, the surroundings of the German Uplands and the margin of the Southern Alps provided suitable conditions for glacial survival for M. sylvaticum, while the Eastern and Southeastern Alpine region most probably sheltered the Large Ringlet E. euryale during ice ages. Additionally, this butterfly species survived at least the glaciation along the foothills of the Massif Central, whose present populations showed a unique genetic lineage and their genetic diversity values have been measurably higher than in other populations for this species. Finally, a large and continuous Würm distribution is highly likely south of the Fennoscandian glaciers in Central Europe for C. palaeno, which might indicate extended peatland areas during Würm glacial. With all the patterns found in this study, the understanding of glacial persistence of forest, respectively forest-like structures and peatlands during Würm or even Riss glacial in Europe could be advanced. The congruencies among the analysed woodland and bog species illustrate the importance and location of extra-Mediterranean refugia for European mountain forests and the glacial presence of Central European peatlands. Thus, already postulated theories could be supported and further pieces of the overall puzzle could be added. The varieties of the different survival centres once more clarified that further phylogeographic studies on mountain forest of different habitat requirements and especially peatland species have to be implemented to get a clearer picture of the glacial history of these habitats.