In this work, prestressed elasticity problem as a model of the so-called glacial isostatic adjustment (GIA) process is studied. The model problem is described by a set of partial differential equations (PDE) and discretized with a mixed finite element (FE) formulation. In the presence of prestress the so-constructed system of equations is non-symmetric and indefinite. Moreover, the resulting system of equations is of the saddle point form. We focus on a robust and efficient block lower-triangular preconditioning method, where the lower diagonal block is and approximation of the so-called Schur complement. The Schur complement is approximated by the so-called element-wise Schur complement. The element-wise Schur complement is constructed by assembling exact local Schur complements on the cell elements and distributing the resulting local matrices to the global preconditioner matrix. We analyse the properties of the element-wise Schur complement for the symmetric indefinite system matrix and provide proof of its quality. We show that the spectral radius of the element-wise Schur complement is bounded by the exact Schur complement and that the quality of the approximation is not affected by the domain shape. The diagonal blocks of the lower-triangular preconditioner are combined with inner iterative schemes accelerated by (numerically) optimal and robust algebraic multigrid (AMG) preconditioner. We observe that on distributed memory systems, the top pivot block of the preconditioner is not scaling satisfactorily. The implementation of the methods is further studied using a general profiling tool, designed for clusters. For nonsymmetric matrices we use the theory of Generalized Locally Toeplitz (GLT) matrices and show the spectral behavior of the element-wise Schur complement, compared to the exact Schur complement. Moreover, we use the properties of the GLT matrices to construct a more efficient AMG preconditioner. Numerical experiments show that the so-constructed methods are robust and optimal.

The aggregate interference distribution in cognitive radio networks is studied in a rigorous and analytical way using the popular Poisson point process model. While a number of results are available for this model for non-cognitive radio networks, cognitive radio networks present extra levels of difficulties for the analysis, mainly due to the exclusion region around the primary receiver, which are typically addressed via various ad-hoc approximations (e.g., based on the interference cumulants) or via the large-deviation analysis. Unlike the previous studies, we do not use here ad-hoc approximations but rather obtain the asymptotic interference distribution in a systematic and rigorous way, which also has a guaranteed level of accuracy at the distribution tail. This is in contrast to the large deviation analysis, which provides only the (exponential) order of scaling but not the outage probability itself. Unlike the cumulant-based analysis, our approach provides a guaranteed level of accuracy at the distribution tail. Additionally, our analysis provides a number of novel insights. In particular, we demonstrate that there is a critical transition point below which the outage probability decays only polynomially but above which it decays super-exponentially. This provides a solid analytical foundation to the earlier empirical observations in the literature and also reveals what are the typical ways outage events occur in different regimes. The analysis is further extended to include interference cancelation and fading (from a broad class of distributions). The outage probability is shown to scale down exponentially in the number of canceled nearest interferers in the below-critical region and does not change significantly in the above-critical one. The proposed asymptotic expressions are shown to be accurate in the non-asymptotic regimes as well.

Object of presented dissertation is proposition of block of flats. Block of flats is based on wood technology with free stages without cellar. Block of flats is designed with 22°saddle roof based on rafters with tie beam. Object is situated in Uničov, Czech Republic.

This thesis deals with the project documentation of the accommodation facility. Guest house kapacity is 45 beds and 52 seated restaurant.The object is designed as a fourfloor with a partial basement. Basement floor will consist of storage, utility room. In the first floor is located main entrance, reception desk and restaurant with facilities. In the sekond and thirt floor are rooms for guests. On second floor has been situated room for invalids also. The building is walled with saddle roof.

This thesis deals with the project documentation of the accommodation facility.Guest house kapacity is 26 beds and 32 seated restaurant. The object is designed as a threefloor. In the first floor is located main entrance, reception desk and restaurant with facilities and wellness.In the sekond and thirt floor are rooms for guests and five other beds for a staffs. On second floor has been situated room for invalids also. The building is walled with saddle roof. The project was processed by a computer program ArchiCAD.

This diploma thesis focuses on a development of the executive documentation of a dormitory for secondary school students, namely a youth home located in the cadastral area of Nové Sady u Olomouce. The project as well as the addenda is elaborated according to the current legislature and standards. The youth home is located on the plot number 132/23, in the cadastral area of Nové Sady u Olomouce in the district of Olomouc. There are all necessary infrastructures near the plot and the plot is well accessible via the local road. The youth home is a four-floor building without a cellar and with a saddle roof. The bed capacity of the youth home is 31 and the number of accommodation units is 12.

Title: Numerical Optimization Methods for the Falsification of Hybrid Dynamical Systems Author: Jan Kuřátko Department: Department of Numerical Mathematics Supervisor: Stefan Ratschan, Institute of Computer Science, The Czech Academy of Sciences Abstract: This thesis consists of three published papers that contribute to the finding of error trajectories of hybrid dynamical systems. A hybrid dynamical system is a dynamical system that has both discrete and continuous state. For example, one can use it as a model for a thermostat in a room: Such a thermostat may have two discrete states, one where the heating is off, and another one, where the heating is on. Its continuous state is the temperature in the room. For such a model one may be interested in finding an error trajectory, that is, an evolution of the system that reaches an unsafe state that is to be avoided. Industry is in need of methods for automatized testing and verification of safety conditions in order to identify flaws in the design of systems. The thesis contains several contributions to finding error trajectories that are based on numerical optimization. Keywords: optimization, dynamical systems, saddle-point matrix

Coronavirus disease 2019 (COVID-19), which is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has emerged as a global pandemic with an unprecedented death toll worldwide. Although it primarily affects the respiratory tract presenting as pneumonia or acute respiratory failure, it is also known to cause significant cardiovascular complications, including acute coronary syndrome (ACS), arrhythmia, myopericarditis, cardiomyopathy, venous thromboembolism, heart failure, and cardiogenic shock. Morbidity and mortality secondary to cardiovascular complications are higher in patients with preexisting cardiovascular risk factors. Here, we present a case report of a 69-year-old male who was recently diagnosed with COVID-19 illness presenting with ST-elevation myocardial infarction (STEMI) and eventually with Takotsubo cardiomyopathy (TTC), and the course was complicated by right atrial thrombus and a pulmonary embolism (PE).

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This thesis is concerned with the fast iterative solution of linear systems of equations of saddle point form. Saddle point problems are a ubiquitous class of matrices that arise in a host of computational science and engineering applications. The focus here is on improving the convergence of iterative methods for these problems by preconditioning. Preconditioning is a way to transform a given linear system into a different problem for which iterative methods converge faster. Saddle point matrices have a very specific block structure and many preconditioning strategies for these problems exploit this structure. The preconditioners considered in this thesis are constraint preconditioners. This class of preconditioner mimics the structure of the original saddle point problem. In this thesis, we prove norm- and field-of-values-equivalence for constraint preconditioners associated to saddle point matrices with a particular structure. As a result of these equivalences, the number of iterations needed for convergence of a constraint preconditioned minimal residual Krylov subspace method is bounded, independent of the size of the matrix. In particular, for saddle point systems that arise from the finite element discretization of partial differential equations (p.d.e.s), the number of iterations it takes for GMRES to converge for theses constraint preconditioned systems is bounded (asymptotically), independent of the size of the mesh width. Moreover, we extend these results when appropriate inexact versions of the constraint preconditioner are used. We illustrate this theory by presenting numerical experiments on saddle point matrices that arise from the finite element solution of coupled Stokes-Darcy flow. This is a system of p.d.e.s that models the coupling of a free flow to a porous media flow by conditions across the interface of the two flow regions. We present experiments in both two and three dimensions, using different types of elements (triangular, quadrilateral), different finite element schemes (continuous, discontinuous Galerkin methods), and different geometries. In all cases, the effectiveness of the constraint preconditioner is demonstrated. / Mathematics