This Ph.D. thesis consists of an introduction and 7 papers where we investigate the requirements for finding integer or rational solutions to a selection of Diophantine equations leading to problems connected to power means and homogenization. In Paper 1 we present a modern view of classic number theory in a historic context. In Paper 2 we introduce the Crossed Ladders Problem and present a proof ...

To avoid the worst impacts of climate change a rapid green energy transition is required where traditional fossil fuels are replaced by low-carbon alternatives. One attractive route to emissions reduction is blue hydrogen, which has lower CO₂ emissions that traditional hydrogen production. For hydrocarbon exporters, increased blue hydrocarbon production can be achieved in two main ways: ...

<p>The research in this PhD thesis is focused on some problems of general interest in both applied mathematics and engineering sciences. It contains new results, which can be directly used for solving some important structural problems in engineering sciences, but which are also of interest in pure mathematics. The main body of this PhD thesis consists of six papers (Papers A – F). <p>In Paper A ...

In applications for technical problems, Geometric modeling and sensor technology are key in both scientific and industrial development. Simulations and visualization techniques are the next step after defining geometry models and data types. This thesis attempts to combine different aspects of geometric modeling and sensor technology as well as to facilitate simulation and visualization. It includes ...

Real-time viscosity and density measurements give insight into the status of many chemical and biochemical processes and allow for automated controls. In many applications, sensors that enable the real-time measurements of fluid properties use resonant elements. Such sensors measure induced changes in the element’s resonance frequency and damping that can be related to the fluid properties. These ...

With the increased focus on sustainable development and circular economy, as never before, the value recovery and re-creation from the End-of-Use and End-of-Life products has been paid considerable attention by the whole society. Reverse logistics is believed as one of the most effective and promising means for the value recovery of the End-of-Use and End-of-Life products, which is the process for ...

<p>This PhD thesis focuses on the investigation of approximation properties of Cesàro means of the Vilenkin-Fourier series. In particular, we obtain some new inequalities related to the rate of <i>L^p</i> approximation by Cesàro means of the Vilenkin-Fourier series of functions from <i>L^p</i>. These inequalities imply sufficient conditions for the convergence of Cesàro means of ...

The study in this PhD thesis aims at development of certain mathematical methods used in applications, in particular, in the study of regularity properties of solutions in various mathematical models described by Partial Differential Equations (PDEs). To this end, we study various operators of harmonic analysis in certain function spaces, since solutions to many PDEs may be expressed in terms of ...