Hae

A graph consists of vertices that are connected by edges. A resolving set of a graph is a subset of its vertices that gives a unique combination of distances to every vertex of the graph. We can use the distances we are ...

The research area of this thesis is nonlinear functional analysis, a branch of Mathematics which examines questions related to qualitative aspects of solution of a differential equation, such as existence, uniqueness, ...

Modern technologies allow for the collection of large biological datasets that can be utilised for diverse health-related applications. However, to extract useful information from such data, computational methods are needed. ...

In this thesis, we study additive problems using the transference principle and the Hardy-Littlewood circle method. The problems studied are related to Waring's prolem and Goldbach's conjecture. Waring's problem states ...

In this thesis we study the distribution of prime numbers by considering approximations to fundamental open conjectures about them. The conjectures in question are the so-called Landau’s problems, named after Edmund Landau ...

The Post Correspondence Problem was introduced by Emil Post in 1946. The problem considers pairs of lists of sequences of symbols, or words, where each word has its place on the list determined by its index. The Post ...

The study of intrinsic metrics is an interesting area of research in the geometric function theory, which is a subfield of mathematical analysis. The topics of research include quasiregular mappings, conformal capacity and ...

In biomedical research, applied machine learning and bioinformatics are the essential disciplines heavily involved in translating data-driven findings into medical practice. This task is especially accomplished by developing ...

The classical setting in optimal stopping and optimal control theory assumes that the agent controlling the system can operate continuously in time. In optimal stopping this setting is highly stylized for many applications, ...

In this thesis we study questions on the distribution of primes and multiplicative orders modulo prime numbers. The problems are attacked using methods from analytic and algebraic number theory. In the first article, ...