# Mathematics and systems engineering

## Mathematics and systems engineering

**Many inventions that we currently take for granted are based on mathematical innovations and models. The aim of the research is to develop and strengthen the theoretical mathematics for the future’s need for new advanced and sustainable products.**

In the field of mathematics and systems engineering we combine depth of scientific research in mathematics, statistics and physics with a strong applied research in areas such as radar technology, remote sensing, traffic research and health technology. Mathematical modeling is the core of these projects.

Our research projects have funding from e.g. the Knowledge Foundation, the European Union, the Swedish Transport Agency, the Crafoord Foundation, the municipality of Karlshamn and the Royal Swedish Academy of Sciences.

Our research is done in collaboration with for example Saab EDS, RUAG Space Agency, FOI, Netport Science Park AB, Sweco, Blekinge County Council, University of Gothenburg, Linnaeus University, University West, Mälardalen University, Universidade Federal de Santa Catarina (Brazil) and Ufa State Aviation Technical University (Russia).

The research in mathematics and systems engineering is mainly conducted at the Department of Mathematics and Natural Sciences.

## Specialisations

• Novel image inversion algorithms based on Doppler measurements for security and climate monitoring

• Methodology for impact assessment of road user charging for heavy vehicles. – A project within the Arena platform

• Tentacle – Capitalising on the TEN-T core network corridors for growth and cohesion.

• One-sided and two-sided nil-ideals in skew group rings.

• Radio occulation inversion methods.

• Modeling and optimization of systems.

# Examples of projects

## Novel image inversion algorithms based on Doppler measurement for security and climate monitoring

Radar and radar-like instruments are increasingly used in our society to make light and weather-independent imagery. The applications are many and they are used e.g. to study climate change and to monitor various conflict areas on your world. In this research project, we improve performance in these systems. In particular, we focus on systems that use Doppler to generate high resolution. The instruments we focus on are Radio Occultation Instruments and Synthetic Apertur Radar and the applications are e.g. to improve weather measurements in the atmosphere and the ability to detect changes occurring on the ground in connection with human activity.

## TENTacle

Regional growth is of great importance in EU transport policy instrument on the major transport axes across Europe i.e. the Trans - European Transport Network (TEN-T). The TENTacle project aims at making proposals for how planning methods and infrastructures can be further improved and developed. This in order for regions outside Europe's main grid corridors to benefit from the growth pulses expected along the corridors. In Sweden, the TEN-T corridor runs between Stockholm and Malmö-Trelleborg, and from Oslo (Norway) through Gothenburg to Malmö-Trelleborg.

### One-sided and two-sided nil ideals in skew group rings

This project is included in the research area “Noncommutative Algebra”. Matrix algebras represent some of the most elementary examples of noncommutative algebras and, for a long time, there has been a good understanding of their algebraic structure. Skew group rings comprise a major form of non-commutative algebra that generalises matrix algebras, among other things.

The algebraic structure of skew group rings is not as fully understood. This project, sponsored by the Crafoord Foundation, aims to investigate the incidence of one-sided and two-sided nil ideals in skew group rings.

**Contact person**: Johan Öinert

### Fuzzy Sets and Systems theory (FSS) and Computational Intelligence (CI) in medical and technical applications

Models inspired by FSS and CI are particularly useful in research to provide answers to medical questions. The research can, for example, be used to estimate life expectancy, and to decide on an appropriate type of operation in patients diagnosed with stomach cancer. The most effective medication was also analysed through the application of decision-making algorithms. Parameter types of functions are currently being developed to express several functions from a single formula. This measure should help develop computer programs that can review the credibility of algorithms in major databases.

**Contact person:** Elisabeth Rakus-Andersson

### Lie group analysis

Lie group analysis is a growing area of mathematics with many applications. Ideas about symmetry and invariance, which are at the core of the Lie theory, permeate all mathematical models in natural and engineering sciences. ALGA is an international research centre with the aim of producing new knowledge and increasing understanding of classical and modern group analysis.

**Contact person**: Nail Ibragimov

### Dynamic systems and encryption

We study discrete dynamic systems for various number-theoretical structures, such as the ring of integers and non-Archimedean solids. The focus is to try to identify periodic points and classify them, and thus acquire a better understanding of the dynamics. In addition to the theory of dynamic systems, the work involves algebra, number theory and combinatorics, among other things. This combination of different areas of mathematics inspires us to try to find applications within cryptology and particularly cryptanalysis. We collaborate with researchers at the Linnaeus University in Sweden.

**Contact person**: Robert Nyqvist

### Didactics of mathematics

Mathematical reasoning and gifted education are the two main branches of research within the didactics of mathematics.

Mathematical reasoning is about the mathematical dialogue between pupils and teachers. It includes the understanding of mathematical formula language compared to natural language, mathematical maps as a way for pupils to work in groups to develop a holistic comprehension of their math skills, and logical graphs showing mathematical relationships in a graphic form.

Research in gifted education involves case studies of the study situation for primary school pupils with exceptional mathematical abilities. It also involves studying the implementation of gifted education on math-intensive upper secondary school programmes. The fundamental starting point of the research is the question of what characterises pupils with exceptional abilities in math, and how teaching can be improved to support the development of these pupils’ abilities.

**Contact person**: Linda Mattsson

### Combinatorial optimisation – for parallel computer systems and codes

Mathematical problems occur in many different contexts. One is when you are trying to get a parallel computer to function as efficiently as possible. If you were to solve these mathematical problems, it would mean that you have very clear boundaries for your computer, allowing it to become optimally efficient.

The same applies to coding theory. When we send text messages between one mobile phone to another, the signals are subjected to interference. However, by using efficient codes, the message can be reconstructed to what was originally sent. In order to optimise this process, you need to solve specific mathematical problems.

**Contact person**: Håkan Lennerstad