Matematicko-fyzikální fakulta: Poslední příspěvky
Zobrazují se záznamy 1-20 z 12516
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Erdős space
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 29. 6. 2026This thesis explores the topological properties and characterizations of Erdős space (E) and complete Erdős space (Ec). Originally introduced by Paul Erdős in 1940 as examples of totally disconnected yet one-dimensional ... -
Veta o izomorfizme štandardných borelovských priestorov
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 29. 6. 2026The subject of this bachelor's thesis is the complete classification of standard Borel spaces formulated in the Borel Isomorphism Theorem. This theorem states that standard Borel spaces with the same cardinality are identical ... -
Soulution of one-dimensional scalar variational problems
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 29. 6. 2026This thesis studies the optimal shape of a plant stem balancing bending stiffness, gravity, and light-seeking. We combine the Beer-Lambert law with Euler-Bernoulli beam theory to formulate a fourth-order nonlinear boundary ... -
Double Oracle Algorithm for Games with Non-compact Strategy Sets
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 29. 6. 2026The Double Oracle algorithm computes an equilibrium of a game by iteratively finding an equilibrium of a subgame and updating strategy sets via best responses to the current equilibrium. Convergence is known for infinite ... -
Separované a ekvilaterální množiny v Banachových prostorech
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 29. 6. 2026In this thesis, we investigate the conditions under which the unit ball of a Banach space contains an infinite or uncountable separated/equilateral set. We review results from several recent papers, most notably one by ... -
Mumford-Shah funkcional v jedné dimenzi
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 29. 6. 2026In this bachelor's thesis we investigate a one-dimensional version of the Mumford-Shah functional and the associated minimisation problem. We first present selected concepts and results from functional analysis, measure ... -
Přirozené objekty, které jsou složité
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 29. 6. 2026In this bachelor's thesis, we focus on sets of "high complexity" in the Borel hierarchy of the form Σ0 n(X) \ Π0 n(X) and Π0 n(X) \ Σ0 n(X) for n ∈ N and a given space X. We study their basic properties and demonstrate ... -
Hierarchical matrices
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026This thesis defines hierarchical matrices in the HODLR format and funda- mental algebraic operations on them. Subsequently, it describes methods for solving linear systems using these matrices via the Cholesky decomposition ... -
Zlehčito - Modulární platforma pro generování a procvičování otázek s využitím umělé inteligence
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 18. 6. 2026Generative artificial intelligence models open up new possibilities in the creation and practice of study materials. However, current platforms are often paid or require manda- tory registration, which poses a barrier, ... -
Využití digitálních technologií při výuce diferenciálního počtu
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026This rigorous thesis focuses on the use of digital technologies in teaching the fundamental concepts of differential calculus at secondary school level. The theoretical part defines key teaching methods in mathematics, ... -
Global Newton's Method on Quantum Computers
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026This thesis proposes a global Newton's method for solving systems of equations on post-NISQ quantum computers using floating-point arithmetic. While requiring a cur- rently unobtainable number of qubits, the thesis proposes ... -
Blokový CG a Lanczosův algoritmus
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026The basic method for solving a system with a symmetric positive-definite matrix and a single right-hand side is the conjugate gradient (CG) method. If there are multiple right-hand sides, we can use the block conjugate ... -
Comparison of iterative regularization methods based on short recurrences
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026In this thesis, we study a linear inverse problem Ax = b, where A is a linear operator with smoothing properties, and b represents measured data polluted by noise. First, we give a theoretical background to inverse problems ... -
Comparison of performance characteristics of ORM frameworks in Java over relational database system
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2025)Datum obhajoby: 4. 9. 2025This thesis presents a benchmarking system to compare the performance of six Java ORM frameworks, namely JDBC, Spring Data JPA, Ebean, jOOQ, MyBatis, and Cayenne, over a relational database system MySQL using a microservices ... -
Recognizing Hamiltonian systems by means of machine learning
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026Direct Poisson Neural Networks (DPNNs) offer a data-driven framework for learning Hamiltonian system dynamics on Poisson manifolds. A key strength is their capability of modeling non-canonical and degenerate systems. ... -
Numerical linear algebra in POSIT arithmetic
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026In recent years, several new number formats have emerged. Although most of which are specialized for concrete applications. Posits and Takums are two recent standards for computer arithmetic which aim to be universal ... -
Numerické řešení obyčejných diferenciálních rovnic pomocí rekonstrukcí vyššího řádu
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 26. 6. 2026Title: Numerical solution of ordinary differential equations using reconstructions of higher order Author: Svatopluk Vaňous Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vít Dolejší, Ph.D., DSc., ... -
Compositionality and Disentanglement: Structured Representations in Simple Neural Models
Výsledek obhajoby: OBHÁJENO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 30. 3. 2026Title: Compositionality and Disentanglement: Structured Representations in Simple Neural Models Author: Michal Auersperger Department: Institute of Formal and Applied Linguistics Supervisor: doc. RNDr. Pavel Pecina, Ph.D., ... -
Towards improved orographic gravity wave parameterization in chemistry-climate models.
Výsledek obhajoby: UZNÁNO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 9. 7. 2026Orographic gravity waves are ubiquitous in our atmosphere, having a large impact on the energy and momentum transport. Their scales reflect scales of the orography and as such global circulation models cannot resolve them ... -
Statistical processing of pollutant concentration projections
Výsledek obhajoby: UZNÁNO(Univerzita Karlova, Matematicko-fyzikální fakulta, 2026)Datum obhajoby: 9. 7. 2026Many factors and processes are expected to be altered in the troposphere under the on- going climate change. This is likely to affect the regime of concentrations of tropospheric species. In the case of ozone, the situation ...