The continuum function is a function which maps every infinite cardinal κ to 2κ. We say that a regular uncountable cardinal κ has the tree property if every κ-tree has a cofinal branch, or equivalently if there are no κ-Aronszajn trees. We say that a regular uncountable cardinal κ has the weak tree property if there are no special κ-Aronszajn trees. It is known that the tree property, and the weak tree property, have the following non-trivial effect on the continuum function: (∗) If the (weak) tree property holds at κ++, then 2κ ≥ κ++. In this thesis we show several results which suggest that (∗) is the only restriction which the tree property and the weak tree property put on the continuum function in addition to the usual restrictions provable in ZFC (monotonicity and the fact that the cofinality of 2κ must be greater than κ; let us denote these conditions by (∗∗)). First we show that the tree property at ℵ2n for every 1 ≤ n < ω, and the weak tree property at ℵn for 2 ≤ n < ω, does not restrict the continuum function below ℵω more than is required by (∗), i.e. every behaviour of the continuum function below ℵω which satisfies the conditions (∗) and (∗∗) is realisable in some generic extension. We use infinitely many weakly compact cardinals (for the tree property) and infinitely many Mahlo...

This thesis examines the interactions between the continuum function and large cardinals. It is know, by a result of Easton, that the continuum function on regular cardinals has great freedom in ZFC. However, large cardinals lay additional constraints to possible behaviour of the continuum function. We focus on weakly compact and measurable cardinal to point out the differences in interactions with the continuum function between various types of large cardinals. We also study the case of indescribable cardinals for the comparison, and the results lead us to conclude that it is not easy to pinpoint the reason for these differences. 1

Diese Arbeit liefert ein dreidimensionales numerisches Homogenisierungskonzept, welches beim Übergang von der Mikro- zur Makroskala einen Wechsel in der Kontinuumsbeschreibung beinhaltet. Während für die Beschreibung der Makroskala das verallgemeinerte Cosserat-Kontinuum verwendet wird, basiert die Mikroskala auf der klassischen Cauchy-Theorie. Um das homogene Cosserat-Ersatzmaterial im Rahmen numerischer Simulationen nutzen zu können, erfolgt die Implementierung geeigneter Finiter Elemente in das Programmsystem Abaqus und deren Verifikation. Neben der Diskussion der bei der Homogenisierung beobachteten Effekte werden anhand eines idealisierten Modells eines biaxialverstärkten Mehrlagengestrickes die Vorteile gegenüber der klassischen Herangehensweise aufgezeigt. / This contribution provides a threedimensional homogenization approach which includes the switch of the continuum theory during the scale transition. Whereas the microscopic scale is described in the framework of the classical Cauchy theory, the macroscopic scale is based on the generalized Cosserat continuum. In order to use the obtained homogeneous Cosserat material, suitable finite elements are implemented in the commercial program system Abaqus followed by an appropriate verification. Beside the discussion of the arising effects the advantages of this approach compared to the classical procedure are shown by means of an idealized model of a biaxial woven fabric.

This thesis explains important concepts, procedures and forms of assessment in current school with a focus on new trends in this area. The thesis aim is to find out how is formative assessment and learning progress maps represented in the school assessment, whether created by SCIO or interviewed teachers. The theoretical part deals primarily with the formative school assessment, its functions and specifics. The second area on which the theoretical part focuses are innovations in the field of evaluation in connection with technology steeped era. Emperical part presents a report on whether and how is worked with progress maps on basic schools. Whether the teachers at these schools know this concept and optionally use learning progress maps in whatever form. Keywords Assessment, formative assessment, constructivist approach in teaching, portfolio, progress maps, reading continuum

Molecular dynamics simulations are an important tool for the study of biological systems, such as biomembranes. The missing electronic polarization in classical non- polarizable force fields, however, produces significant inaccuracies in the interactions of membranes with charged particles, such as ions. In this work, we implement the missing electronic polarization effects into CHARMM36 force field for phospatidylcholine lipids. This implementation is done in the mean field way by using electronic continuum correction (ECC) model. We will validate the strength of ion-membrane interactions using the electrometer concept. This concept connects the response of choline order parameters of lipid molecules with the amount of charge present in the surface of the membrane. Keywords: phosphatydylcholine, calcium ions, sodium ions, electronic continuum cor- rection, electrometer concept 1

Diese Arbeit liefert ein dreidimensionales numerisches Homogenisierungskonzept, welches beim Übergang von der Mikro- zur Makroskala einen Wechsel in der Kontinuumsbeschreibung beinhaltet. Während für die Beschreibung der Makroskala das verallgemeinerte Cosserat-Kontinuum verwendet wird, basiert die Mikroskala auf der klassischen Cauchy-Theorie. Um das homogene Cosserat-Ersatzmaterial im Rahmen numerischer Simulationen nutzen zu können, erfolgt die Implementierung geeigneter Finiter Elemente in das Programmsystem Abaqus und deren Verifikation. Neben der Diskussion der bei der Homogenisierung beobachteten Effekte werden anhand eines idealisierten Modells eines biaxialverstärkten Mehrlagengestrickes die Vorteile gegenüber der klassischen Herangehensweise aufgezeigt. / This contribution provides a threedimensional homogenization approach which includes the switch of the continuum theory during the scale transition. Whereas the microscopic scale is described in the framework of the classical Cauchy theory, the macroscopic scale is based on the generalized Cosserat continuum. In order to use the obtained homogeneous Cosserat material, suitable finite elements are implemented in the commercial program system Abaqus followed by an appropriate verification. Beside the discussion of the arising effects the advantages of this approach compared to the classical procedure are shown by means of an idealized model of a biaxial woven fabric.

We study nonlinear stability of steady state solutions of partial differential equations governing the thermomechanical evolution of viscoelastic fluids; materials that exhibit both viscous as well as elastic response when undergoing deformation. It is well-known that thermodynamical concepts can be gainfully exploited in the construction of Lya- punov functionals for nonlinear stability analysis of spatially homogeneous equilibrium rest states in thermodynamically closed systems. We show that the thermodynamically oriented approach can be utilized in the nonlinear stability analysis of spatially inhomo- geneous non-equilibrium steady states in thermodynamically open systems as well. The thesis consists of two parts. In the first part, we revisit the classical construction of Lyapunov functionals in thermodynamically closed systems and we apply the nonlinear stability theory to compressible heat-conducting viscoelastic fluids modeled by a multi- scale, as well as a purely macroscopic approach. In the second part, we focus on two special instances of thermodynamically open systems. First, we show that the spatially inhomogeneous non-equilibrium steady state of an incompressible heat-conducting vis- coelastic fluid, which occupies a mechanically isolated vessel with walls kept at spatially non-uniform...

Thesis deals with solving the problems of continuum mechanics by method of Isogeometric analysis. This relatively young method combines the advantages of precise NURBS geometry and robustness of the classical finite element method. The method is described on procedure of solving a plane Poissons boundary value problem. Solver is implemented in MatLab and algorithms are attached to the text.

This Master's thesis relates to continuum mechanics and its connection with selected directions of modern differential geometry, which deal with geometric structures and objects. These are mainly tensors, bundles, varieties and jets. The first part is devoted to the mechanics of the continuum itself and its description in several areas, others deal with mathematical concepts and their possible application in mechanics.

Práce se zabývá tvárným lomem, který je výsledkem víceosého kvazi-statického monotónního namáhání doprovázeného rozsáhlými plastickými deformacemi, přičemž pro degradaci materiálu je uvažován lokální přístup. Ve výpočtech o rozvoji poškození rozhodují použité mezní podmínky tvárného lomu. Tyto byly teoreticky studovány v úvodu práce a po výběru vhodné mezní podmínky byl stanoven postup kalibrace. Dále byl rozpracován plán měření a realizovány zkoušky při pokojové teplotě na slitině hliníku 2024-T351, zahrnující tah, krut a tlak, pro studium rozvoje poškození a věrohodnou kalibraci vybraného fenomenologického modelu tvárného porušování, vyjádřeného pomocí lomového přetvoření a závislého na hydrostatickém tlaku a deviátoru tenzoru napětí. Mezní podmínka tvárného lomu byla posléze svázána s podmínkou plasticity. Plasticita byla pro zkoumaný materiál uvažována ve tvaru zohledňujícím i stav třetího invariantu deviátoru tenzoru napětí. Celý navržený přístup, plně aplikovatelný na víceosé úlohy, byl implementován pomocí uživatelské rutiny do komerčního programu založeného na explicitní variantě metody konečných prvků. V závěru práce je předložena aplikace navrženého přístupu k modelování tvárného porušování v podobě verifikace na vybraných zkušebních testech, z níž plynou závěry a doporučení pro další práci.