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- ItemMonitoring Thermal and Non-Thermal Treatments during Processing of Muscle Foods : A Comprehensive Review of Recent Technological Advances(Basel : MDPI, 2020) Hassoun, Abdo; Ojha, Shikha; Tiwari, Brijesh; Rustad, Turid; Nilsen, Heidi; Heia, Karsten; Cozzolino, Daniel; Bekhit, Alaa El-Din; Biancolillo, Alessandra; Wold, Jens PetterMuscle food products play a vital role in human nutrition due to their sensory quality and high nutritional value. One well-known challenge of such products is the high perishability and limited shelf life unless suitable preservation or processing techniques are applied. Thermal processing is one of the well-established treatments that has been most commonly used in order to prepare food and ensure its safety. However, the application of inappropriate or severe thermal treatments may lead to undesirable changes in the sensory and nutritional quality of heat-processed products, and especially so for foods that are sensitive to thermal treatments, such as fish and meat and their products. In recent years, novel thermal treatments (e.g., ohmic heating, microwave) and non-thermal processing (e.g., high pressure, cold plasma) have emerged and proved to cause less damage to the quality of treated products than do conventional techniques. Several traditional assessment approaches have been extensively applied in order to evaluate and monitor changes in quality resulting from the use of thermal and non-thermal processing methods. Recent advances, nonetheless, have shown tremendous potential of various emerging analytical methods. Among these, spectroscopic techniques have received considerable attention due to many favorable features compared to conventional analysis methods. This review paper will provide an updated overview of both processing (thermal and non-thermal) and analytical techniques (traditional methods and spectroscopic ones). The opportunities and limitations will be discussed and possible directions for future research studies and applications will be suggested.
- ItemZopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2021) Lechner, GandalfDie Yang–Baxter-Gleichung ist eine faszinierende Gleichung, die in vielen Gebieten der Physik und der Mathematik auftritt und die am besten diagrammatisch dargestellt wird. Dieser Snapshot schlägt einen weiten Bogen vom Zöpfeflechten über die Yang–Baxter- Gleichung bis hin zur aktuellen Forschung zu Systemen von unendlichdimensionalen Algebren, die wir „Unterfaktoren“ nennen.
- ItemQuantum symmetry(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Weber, MoritzIn mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from spaces to quantum spaces, from groups to quantum groups, and from symmetry to quantum symmetry, following an analytical approach.
- ItemC∗ -algebras: structure and classification(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2021) Kerr, DavidThe theory of C∗C∗-algebras traces its origins back to the development of quantum mechanics and it has evolved into a large and highly active field of mathematics. Much of the progress over the last couple of decades has been driven by an ambitious program of classification launched by George A. Elliott in the 1980s, and just recently this project has succeeded in achieving one of its central goals in an unexpectedly dramatic fashion. This Snapshot aims to recount some of the fundamental ideas at play.
- ItemRotating needles, vibrating strings, and Fourier summation(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Zahl, JoshuaWe give a brief survey of the connection between seemingly unrelated problems such as sets in the plane containing lines pointing in many directions, vibrating strings and drum heads, and a classical problem from Fourier analysis.
- ItemQuantum symmetry(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Caspers, MartijnThe symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized notion of symmetry. It is an abstract way of characterizing the symmetry of a much richer class of mathematical and physical objects. In this snapshot we explain how quantum symmetry emerges as matrix symmetries using a famous example: Mermin’s magic square. It shows that quantum symmetries can solve problems that lie beyond the reach of classical symmetries, showing that quantum symmetries play a central role in modern mathematics.
- ItemDeterminacy versus indeterminacy(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Berg, ChristianCan a continuous function on an interval be uniquely determined if we know all the integrals of the function against the natural powers of the variable? Following Weierstrass and Stieltjes, we show that the answer is yes if the interval is finite, and no if the interval is infinite.
- ItemEmergence in biology and social sciences(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Hoffmann, Franca; Merino-Aceituno, SaraMathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf venation, opinion dynamics, and network formation, to name a few. In this article, we explore how mathematics is able to traverse scales, and in particular its application in modelling collective motion of bacteria driven by chemical signalling.