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In politics and economics, and thus in the official statistics, the precise estimation of indicators for small regions or parts of populations, the so-called Small Areas or domains, is discussed intensively. The design-based estimation methods currently used are mainly based on asymptotic properties and are thus reliable for large sample sizes. With small sample sizes, however, this design based considerations often do not apply, which is why special model-based estimation methods have been developed for this case - the Small Area methods. While these may be biased, they often have a smaller mean squared error (MSE) as the unbiased design based estimators. In this work both classic design-based estimation methods and model-based estimation methods are presented and compared. The focus lies on the suitability of the various methods for their use in official statistics. First theory and algorithms suitable for the required statistical models are presented, which are the basis for the subsequent model-based estimators. Sampling designs are then presented apt for Small Area applications. Based on these fundamentals, both design-based estimators and as well model-based estimation methods are developed. Particular consideration is given in this case to the area-level empirical best predictor for binomial variables. Numerical and Monte Carlo estimation methods are proposed and compared for this analytically unsolvable estimator. Furthermore, MSE estimation methods are proposed and compared. A very popular and flexible resampling method that is widely used in the field of Small Area Statistics, is the parametric bootstrap. One major drawback of this method is its high computational intensity. To mitigate this disadvantage, a variance reduction method for parametric bootstrap is proposed. On the basis of theoretical considerations the enormous potential of this proposal is proved. A Monte Carlo simulation study shows the immense variance reduction that can be achieved with this method in realistic scenarios. This can be up to 90%. This actually enables the use of parametric bootstrap in applications in official statistics. Finally, the presented estimation methods in a large Monte Carlo simulation study in a specific application for the Swiss structural survey are examined. Here problems are discussed, which are of high relevance for official statistics. These are in particular: (a) How small can the areas be without leading to inappropriate or to high precision estimates? (b) Are the accuracy specifications for the Small Area estimators reliable enough to use it for publication? (c) Do very small areas infer in the modeling of the variables of interest? Could they cause thus a deterioration of the estimates of larger and therefore more important areas? (d) How can covariates, which are in different levels of aggregation be used in an appropriate way to improve the estimates. The data basis is the Swiss census of 2001. The main results are that in the author- view, the use of small area estimators for the production of estimates for areas with very small sample sizes is advisable in spite of the modeling effort. The MSE estimates provide a useful measure of precision, but do not reach in all Small Areas the level of reliability of the variance estimates for design-based estimators.

The startle response in psychophysiological research: modulating effects of contextual parameters
(2013)

Startle reactions are fast, reflexive, and defensive responses which protect the body from injury in the face of imminent danger. The underlying reflex is basic and can be found in many species. Even though it consists of only a few synapses located in the brain stem, the startle reflex offers a valuable research method for human affective, cognitive, and psychological research. This is because of moderating effects of higher mental processes such as attention and emotion on the response magnitude: affective foreground stimulation and directed attention are validated paradigms in startle-related research. This work presents findings from three independent research studies that deal with (1) the application of the established "affective modulation of startle"-paradigm to the novel setting of attractiveness and human mating preferences, (2) the question of how different components of the startle response are affected by a physiological stressor and (3) how startle stimuli affect visual attention towards emotional stimuli. While the first two studies treat the startle response as a dependent variable by measuring its response magnitude, the third study uses startle stimuli as an experimental manipulation and investigates its potential effects on a behavioural measure. The first chapter of this thesis describes the basic mechanisms of the startle response as well as the body of research that sets the foundation of startle research in psychophysiology. It provides the rationale for the presented studies, and offers a short summary of the obtained results. Chapter two to four represent primary research articles that are published or in press. At the beginning of each chapter the contribution of all authors is explained. The references for all chapters are listed at the end of this thesis. The overall scope of this thesis is to show how the human startle response is modulated by a variety of factors, such as the attractiveness of a potential mating partner or the exposure to a stressor. In conclusion, the magnitude of the startle response can serve as a measure for such psychological states and processes. Beyond the involuntary, physiological startle reflex, startle stimuli also affect intentional behavioural responses, which we could demonstrate for eye movements in a visual attention paradigm.

The Hadamard product of two holomorphic functions which is defined via a convolution integral constitutes a generalization of the Hadamard product of two power series which is obtained by pointwise multiplying their coefficients. Based on the integral representation mentioned above, an associative law for this convolution is shown. The main purpose of this thesis is the examination of the linear and continuous Hadamard convolution operators. These operators map between spaces of holomorphic functions and send - with a fixed function phi - a function f to the convolution of phi and f. The transposed operator is computed and turns out to be a Hadamard convolution operator, too, mapping between spaces of germs of holomorphic functions. The kernel of Hadamard convolution operators is investigated and necessary and sufficient conditions for those operators to be injective or to have dense range are given. In case that the domain of holomorphy of the function phi allows a Mellin transform of phi, certain (generalized) monomials are identified as eigenfunctions of the corresponding operator. By means of this result and some extract of the theory of growth of entire functions, further propositions concerning the injectivity, the denseness of the range or the surjectivity of Hadamard convolution operators are shown. The relationship between Hadamard convolution operators, operators which are defined via the convolution with an analytic functional and differential operators of infinite order is investigated and the results which are obtained in the thesis are put into the research context. The thesis ends with an application of the results to the approximation of holomorphic functions by lacunary polynomials. On the one hand, the question under which conditions lacunary polynomials are dense in the space of all holomorphic functions is investigated and on the other hand, the rate of approximation is considered. In this context, a result corresponding to the Bernstein-Walsh theorem is formulated.

This study examines the relationship between media content, its production, and its reception in Japanese popular culture with the example of the so-called yuri ("lily") genre that centers on representations of intimate relationships between female characters. Based on contemporary genre theory, which posits that genres are not inherent properties of texts, the central question of this study is how the yuri genre is discursively produced in Japan. To examine this question, the study takes a variety of sources into consideration: Firstly, it discusses ten exemplary texts from the 1910s to 2010s that in the Japanese discourse on the yuri genre are deemed the milestone texts of the yuri genre's historical development (Hana monogatari, Otome no minato, Secret Love, Shiroi heya no futari, BishÅjo senshi Sailor Moon, Maria-sama ga miteru, ShÅjo Sect, Aoi hana, Yuru yuri, and Yuri danshi). Secondly, interviews with ten editors working for Japanese manga magazines shed light on their assessment of the yuri genre. Finally, the results of an online survey among Japanese fans of the yuri genre, which returned 1,352 completed questionnaires, question hitherto assumptions about the fans and their reasons for liking the yuri genre. The central argument of this study is that the yuri genre is for the most part constructed not through assignments on part of the genre's producers but through interpretations on part of the genre's fans. The intimacy portrayed in the texts ranges from "friendship" to "love," and often the ideas of "innocence" and "beauty" are emphasized. Nevertheless, the formation of the yuri genre occurs outside the bounds of the texts, most importantly in fan works, i.e. derivative texts created by fans. The actual content of the originals merely serves as a starting point for these interpretations. Located at the intersection of Japanese studies, cultural studies, media studies, and sociology, this study contributes to our understanding of contemporary Japanese popular culture by showing the mutual dependencies between media content, production, and reception. It provides a deeper look at these processes through first-hand accounts of both producers and fans of the yuri genre.

In a paper of 1996 the british mathematician Graham R. Allan posed the question, whether the product of two stable elements is again stable. Here stability describes the solvability of a certain infinite system of equations. Using a method from the theory of homological algebra, it is proved that in the case of topological algebras with multiplicative webs, and thus in all common locally convex topological algebras that occur in standard analysis, the answer of Allan's question is affirmative.

Religion, churches and religious communities have growing importance in the Law of the European Union. Since long a distinct law on religion of the European Union is developing. This collection of those norms of European Union Law directly concerning religion mirrors today's status of this dynamic process.

In this thesis, global surrogate models for responses of expensive simulations are investigated. Computational fluid dynamics (CFD) have become an indispensable tool in the aircraft industry. But simulations of realistic aircraft configurations remain challenging and computationally expensive despite the sustained advances in computing power. With the demand for numerous simulations to describe the behavior of an output quantity over a design space, the need for surrogate models arises. They are easy to evaluate and approximate quantities of interest of a computer code. Only a few number of evaluations of the simulation are stored for determining the behavior of the response over a whole range of the input parameter domain. The Kriging method is capable of interpolating highly nonlinear, deterministic functions based on scattered datasets. Using correlation functions, distinct sensitivities of the response with respect to the input parameters can be considered automatically. Kriging can be extended to incorporate not only evaluations of the simulation, but also gradient information, which is called gradient-enhanced Kriging. Adaptive sampling strategies can generate more efficient surrogate models. Contrary to traditional one-stage approaches, the surrogate model is built step-by-step. In every stage of an adaptive process, the current surrogate is assessed in order to determine new sample locations, where the response is evaluated and the new samples are added to the existing set of samples. In this way, the sampling strategy learns about the behavior of the response and a problem-specific design is generated. Critical regions of the input parameter space are identified automatically and sampled more densely for reproducing the response's behavior correctly. The number of required expensive simulations is decreased considerably. All these approaches treat the response itself more or less as an unknown output of a black-box. A new approach is motivated by the assumption that for a predefined problem class, the behavior of the response is not arbitrary, but rather related to other instances of the mutual problem class. In CFD, for example, responses of aerodynamic coefficients share structural similarities for different airfoil geometries. The goal is to identify the similarities in a database of responses via principal component analysis and to use them for a generic surrogate model. Characteristic structures of the problem class can be used for increasing the approximation quality in new test cases. Traditional approaches still require a large number of response evaluations, in order to achieve a globally high approximation quality. Validating the generic surrogate model for industrial relevant test cases shows that they generate efficient surrogates, which are more accurate than common interpolations. Thus practical, i.e. affordable surrogates are possible already for moderate sample sizes. So far, interpolation problems were regarded as separate problems. The new approach uses the structural similarities of a mutual problem class innovatively for surrogate modeling. Concepts from response surface methods, variable-fidelity modeling, design of experiments, image registration and statistical shape analysis are connected in an interdisciplinary way. Generic surrogate modeling is not restricted to aerodynamic simulation. It can be applied, whenever expensive simulations can be assigned to a larger problem class, in which structural similarities are expected.

Chemical communication in the reproductive behaviour of Neotropical poison frogs (Dendrobatidae)
(2013)

Chemical communication is the evolutionary oldest communication system in the animal kingdom that triggers intra- and interspecific interactions. It is initiated by the emitter releasing either a signal or a cue that causes a reaction of the receiving individual. Compared to other animals there are relatively few studies regarding chemical communication in anurans. In this thesis the impact of chemical communication on the behaviour of the poison frog Ranitomeya variabilis (Dendrobatidae) and its parental care performance was investigated. This species uses phytotelmata (small water bodies in plants) for both clutch and tadpole depositions. Since tadpoles are cannibalistic, adult frogs do not only avoid conspecifics when depositing their eggs but also transport their tadpoles individually into separated phytotelmata. The recognition of already occupied phytotelmata was shown to be due to chemical substances released by the conspecific tadpoles. In order to gain a deeper comprehension about the ability of adult R. variabilis to generally recognize and avoid tadpoles, in-situ pool choice experiments were conducted, offering chemical substances of tadpole of different species to the frogs (Chapter I). It turned out that they were able to recognize all species and avoid their chemical substances for clutch depositions. However, for tadpole depositions only dendrobatid tadpoles occurring in phytotelmata were avoided, while those species living in rivers were not. Additionally, the chemical substances of a treefrog tadpole (Hylidae) were recognized by R. variabilis. Yet, they were not avoided but preferred for tadpole depositions; thus these tadpoles might be recognized as a potential prey for the predatory poison frog larvae. One of the poison frog species which was avoided for both tadpole and clutch depositions, was the phytotelmata breeding Hyloxalus azureiventris. The chemical substances released by its tadpoles were analysed together with those of the R. variabilis tadpoles (Chapter II). After finding a suitable solid-phase extraction sorbent (DSC-18), the active chemical compounds from the water of both tadpole species were extracted and fractionated. In order to determine which fractions triggered the avoidance behaviour of the frogs, in-situ bioassays were conducted. It was found that the biologically active compounds differed between both species. Since the avoidance of the conspecific tadpoles is not advantageous to the releaser tadpoles (losing a potential food resource) the chemicals released by them might be defined as chemical cues. However, as it turned out that the avoidance of the heterospecific tadpoles was not triggered by a mere byproduct based on the close evolutionary relationship between the two species, the chemical compounds released by H. azureiventris tadpoles might be defined as chemical signals (being advantageous to the releasing tadpoles) or, more specifically as synomones, interspecificly acting chemicals that are advantageous for both emitter and receiver (since R. variabilis avoids a competition situation for its offspring, too). Another interspecific communication system investigated in this thesis was the avoidance of predator kairomones (Chapter III). Using chemical substances from damselfly larvae, it could be shown that R. variabilis was unable to recognize and avoid kairomones of these tadpole predators. However, when physically present, damselfly larvae were avoided by the frogs. For the recognition of conspecific tadpoles in contrast, chemical substances were necessary, since purely visible artificial tadpole models were not avoided. If R. variabilis is also capable to chemically communicate with adult conspecifics was investigated by presenting chemical cues/signals of same-sex or opposite-sex conspecifics to the frogs (Chapter IV). It was suggested that males would be attracted to chemical substances of females and repelled by those of conspecific males. But instead all individuals showed avoidance behaviour towards the conspecific chemicals. This was suggested to be an artefact due to confinement stress of the releaser animals, emitting disturbance cues that triggered avoidance behaviour in their conspecifics. The knowledge gained about chemical communication in parental care thus far, was used to further investigate a possible provisioning behaviour in R. variabilis. In-situ pool-choice experiments with chemical cues of conspecific tadpoles were carried out throughout the change from rainy to dry season (Chapter V). With a changepoint analysis, the exact seasonal change was defined and differences between frogs" choices were analysed. It turned out that R. variabilis does not avoid but prefer conspecific cues during the dry season for tadpole depositions, what might be interpreted as a way to provide their tadpoles with food (i.e. younger tadpoles) in order to accelerate their development when facing desiccation risk. That tadpoles were also occasionally fed with fertilized eggs could be shown in a comparative study, where phytotelmata that contained a tadpole deposited by the frogs themselves received more clutch depositions than freshly erected artificial phytotelmata containing unfamiliar tadpoles (i.e. their chemical cues; Chapter VI). Conducting home range calculations with ArcGIS, it turned out that R. variabilis males showed unexpectedly strong site fidelity, leading to the suggestion that they recognize their offspring by phytotelmata location. However, in order to test if R. variabilis is furthermore able to perform chemical offspring recognition, frogs were confronted in in-situ pool-choice experiments with chemical cues of single tadpoles that were found in their home ranges (Chapter VII). Genetic kinship analyses were conducted between those tadpoles emitting the chemical cues and those deposited together with or next to them. The results, however, indicated that frogs did not choose to deposit their offspring with or without another tadpole due to relatedness, i.e. kin recognition by chemical cues could not be confirmed in R. variabilis.

The present thesis addresses the validity of Binge Eating Disorder (BED) as well as underlying mechanisms of BED from three different angles. Three studies provide data discriminating obesity with BED from obesity without BED. Study 1 demonstrates differences between obese individuals with and without BED regarding eating in the natural environment, psychiatric comorbidity, negative affect as well as self reported tendencies in eating behavior. Evidence for possible psychological mechanisms explaining increased intake of BED individuals in the natural environment was given by analyzing associations of negative affect, emotional eating, restrained eating and caloric intake in obese BED compared to NBED controls. Study 2 demonstrated stress-induced changes in the eating behavior of obese individuals with BED. The impact of a psychosocial stressor, the Trier Social Stress Test (TSST, Kirschbaum, Pirke, &amp;amp; Hellhammer, 1993), on behavioral patterns of eating behavior in laboratory was investigated. Special attention was given to stress-induced changes in variables that reflect mechanisms of appetite regulation in obese BED individuals compared to controls. To further explore by which mechanisms stress might trigger binge eating, study 3 investigated differences in stress-induced cortisol secretion after a socially evaluated cold pressure test (SECPT, Schwabe, Haddad, &amp;amp; Schachinger, 2008) in obese BED as compared to obese NBED individuals.

This work investigates the industrial applicability of graphics and stream processors in the field of fluid simulations. For this purpose, an explicit Runge-Kutta discontinuous Galerkin method in arbitrarily high order is implemented completely for the hardware architecture of GPUs. The same functionality is simultaneously realized for CPUs and compared to GPUs. Explicit time steppings as well as established implicit methods are under consideration for the CPU. This work aims at the simulation of inviscid, transsonic flows over the ONERA M6 wing. The discontinuities which typically arise in hyperbolic equations are treated with an artificial viscosity approach. It is further investigated how this approach fits into the explicit time stepping and works together with the special architecture of the GPU. Since the treatment of artificial viscosity is close to the simulation of the Navier-Stokes equations, it is reviewed how GPU-accelerated methods could be applied for computing viscous flows. This work is based on a nodal discontinuous Galerkin approach for linear hyperbolic problems. Here, it is extended to non-linear problems, which makes the application of numerical quadrature obligatory. Moreover, the representation of complex geometries is realized using isoparametric mappings. Higher order methods are typically very sensitive with respect to boundaries which are not properly resolved. For this purpose, an approach is presented which fits straight-sided DG meshes to curved geometries which are described by NURBS surfaces. The mesh is modeled as an elastic body and deformed according to the solution of closest point problems in order to minimize the gap to the original spline surface. The sensitivity with respect to geometry representations is reviewed in the end of this work in the context of shape optimization. Here, the aerodynamic drag of the ONERA M6 wing is minimized according to the shape gradient which is implicitly smoothed within the mesh deformation approach. In this context a comparison to the classical Laplace-Beltrami operator is made in a Stokes flow situation.

Design and structural optimization has become a very important field in industrial applications over the last years. Due to economical and ecological reasons, the efficient use of material is of highly industrial interest. Therefore, computational tools based on optimization theory have been developed and studied in the last decades. In this work, different structural optimization methods are considered. Special attention lies on the applicability to three-dimensional, large-scale, multiphysic problems, which arise from different areas of the industry. Based on the theory of PDE-constraint optimization, descent methods in structural optimization require knowledge of the (partial) derivatives with respect to shape or topology variations. Therefore, shape and topology sensitivity analysis is introduced and the connection between both sensitivities is given by the Topological-Shape Sensitivity Method. This method leads to a systematic procedure to compute the topological derivative by terms of the shape sensitivity. Due to the framework of moving boundaries in structural optimization, different interface tracking techniques are presented. If the topology of the domain is preserved during the optimization process, explicit interface tracking techniques, combined with mesh-deformation, are used to capture the interface. This techniques fit very well the requirements in classical shape optimization. Otherwise, an implicit representation of the interface is of advantage if the optimal topology is unknown. In this case, the level set method is combined with the concept of the topological derivative to deal with topological perturbation. The resulting methods are applied to different industrial problems. On the one hand, interface shape optimization for solid bodies subject to a transient heat-up phase governed by both linear elasticity and thermal stresses is considered. Therefore, the shape calculus is applied to coupled heat and elasticity problems and a generalized compliance objective function is studied. The resulting thermo-elastic shape optimization scheme is used for compliance reduction of realistic hotplates. On the other hand, structural optimization based on the topological derivative for three-dimensional elasticity problems is observed. In order to comply typical volume constraints, a one-shot augmented Lagrangian method is proposed. Additionally, a multiphase optimization approach based on mesh-refinement is used to reduce the computational costs and the method is illustrated by classical minimum compliance problems. Finally, the topology optimization algorithm is applied to aero-elastic problems and numerical results are presented.

Cortisol exhibits typical ultradian and circadian rhythm and disturbances in its secretory pattern have been described in stress-related pathology. The aim of this thesis was to dissect the underlying structure of cortisol pulsatility and to develop tools to investigate the effects of this pulsatility on immune cell trafficking and the responsiveness of the neuroendocrine system and GR target genes to stress. Deconvolution modeling was set up as a tool for investigation of the pulsatile secretion underlying the ultradian cortisol rhythm. This further allowed us to investigate the role of the single cortisol pulses on the immune cell trafficking and the role of induced cortisol pulses on the kinetics of expression of GR target genes. The development of these three tools, would allow to induce and investigate in future the significance of single cortisol pulses for health and disease.

A big challenge for agriculture in the 21st century is the provision of food safety to fast growing world- population, which not only demands the well utilisation of the available agricultural resources but also to develop new advancements in the mass production of food crops. Wheat is the third largest food crop of the world and Pakistan is the eighth largest wheat producing country globally. Rice is the second most important staple food of Pakistan after wheat, grown in all provinces of the country. Maize is the world- top ranking food crop followed by wheat and rice. The harvested produts have to be stored in different types of storage structures on small or large scale for food as well as seed purpose. In Pakistan, the harvested grains are stored for the whole year till the introduction of fresh produce in order to ensure the regular food supply throughout the year. However, it is this extended storage period making the commodity more vulnerable to insect attacks. Rhyzopertha dominica (Coleoptera: Bostrychidae), Cryptolestes ferrugineus (Coleoptera: Laemophloeidae), Tribolium castaneum (Coleoptera: Tenebrionidae) and Liposcelis spp. (Psocoptera: Liposcelididae) are the major and most damaging insect pests of stored products all around the world. Various management strategies have been adopted for stored grain insect pests mostly relying upon the use of a broad spectrum of insecticides, but the injudicious use of these chemicals raised various environmental and human health related issues, which necessitate the safe use of the prevailing control measures and evaluation of new and alternative control methods. The application of new chemical insecticides, microbial insecticides (particularly entomopathogenic fungi) and the use of inert dusts (diatomaceous earths) is believed amongst the potential alternatives to generally used insecticides in stored grain insect management system. In the current investigations, laboratory bioassays conducted to evaluate the effects of combining Imidacloprid (new chemistry insecticide) with and without Protect-It (diatomaceous earth formulation) against R. dominica, L. paeta, C. ferrugineus and T. castaneum, on three different grain commodities (i.e. wheat, maize and rice) revealed differences in adult mortality levels among grains and insect species tested. Individually, Imidacloprid was more effective as compared with Protect-It alone and the highest numbers of dead adults were recorded in wheat. The insecticidal efficacy of B. bassiana with Protect-It and DEBBM was also assessed against all test insect species under laboratory conditions. The findings of these studies revealed that the more extended exposure period and the higher combined application rate of B. bassiana and DEs provided the highest mortality of the test insect species. The progeny emergence of each insect species was also greatly suppressed where the highest dose rates of the combined treatments were applied. The residual efficacy of all three control measures Imidacloprid, B. bassiana and DEBBM formulation was also evaluated against all test insect species. The bioassays were carried out after grain treatments and monthly for 6 months. The results indicated that the adult mortality of each test insect species was decreased within the six month storage period, and the integarted application of the test grain protectants enhanced the mortality rates than their alone treatments. The maximum mortality was noted in the combined treatment of DEBBM with Imidacloprid. At the end, the effectiveness of B. bassiana, DEBBM and Imidacloprid applied alone as well as in combinations, against all above mentioned test insect species was also evaluated under field conditions in trials conducted in four districts of Punjab, Pakistan. For each district, a significant difference was observed between treatments, while the combined treatments gave better control of test species as compared with them alone. The least number of surviving adults and minimum percentage of grain damage was observed for the DEBBM and Imidacloprid combination, but DEBBM with B. bassiana provided the best long-term protection as compared with the remaining treatments.

Copositive programming is concerned with the problem of optimizing a linear function over the copositive cone, or its dual, the completely positive cone. It is an active field of research and has received a growing amount of attention in recent years. This is because many combinatorial as well as quadratic problems can be formulated as copositive optimization problems. The complexity of these problems is then moved entirely to the cone constraint, showing that general copositive programs are hard to solve. A better understanding of the copositive and the completely positive cone can therefore help in solving (certain classes of) quadratic problems. In this thesis, several aspects of copositive programming are considered. We start by studying the problem of computing the projection of a given matrix onto the copositive and the completely positive cone. These projections can be used to compute factorizations of completely positive matrices. As a second application, we use them to construct cutting planes to separate a matrix from the completely positive cone. Besides the cuts based on copositive projections, we will study another approach to separate a triangle-free doubly nonnegative matrix from the completely positive cone. A special focus is on copositive and completely positive programs that arise as reformulations of quadratic optimization problems. Among those we start by studying the standard quadratic optimization problem. We will show that for several classes of objective functions, the relaxation resulting from replacing the copositive or the completely positive cone in the conic reformulation by a tractable cone is exact. Based on these results, we develop two algorithms for solving standard quadratic optimization problems and discuss numerical results. The methods presented cannot immediately be adapted to general quadratic optimization problems. This is illustrated with examples.

Krylov subspace methods are often used to solve large-scale linear equations arising from optimization problems involving partial differential equations (PDEs). Appropriate preconditioning is vital for designing efficient iterative solvers of this type. This research consists of two parts. In the first part, we compare two different kinds of preconditioners for a conjugate gradient (CG) solver attacking one partial integro-differential equation (PIDE) in finance, both theoretically and numerically. An analysis on mesh independence and rate of convergence of the CG solver is included. The knowledge of preconditioning the PIDE is applied to a relevant optimization problem. The second part aims at developing a new preconditioning technique by embedding reduced order models of nonlinear PDEs, which are generated by proper orthogonal decomposition (POD), into deflated Krylov subspace algorithms in solving corresponding optimization problems. Numerical results are reported for a series of test problems.

In his article, the author asks how legitimacy of law and the concept of rules of law can be described taking into account the interaction between aspects of philosophy and sociology as well as the will of the state in states' constitutions. As the rule of law, versus other kinds of rules in our society, should be regarded as a rule of &amp;quot;three-dimensionality&amp;quot; " an interaction between the will of the state, the social, historical, and economic factors, and the idea or concept of justice ", the author focuses his interest on the examination of these three factors always taking into account that law is the will of the state, but that not every decision of the state can be considered as law.