This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation.

The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed.

The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications.

It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.

Inhalt

1 Classification of Low Dimensional 3-Lie Superalgebras: V. Abramov and P. Lätt.- 2 Semi-Commutative Galois Extension and Reduced Quantum Plane: V. Abramov and Md. Raknuzzaman.- 3 Valued Custom Skew Fields with Generalised PBW Property from Power Series Construction: L. Hellström.- 4 Computing Burchnall-Chaundy Polynomials with Determinants: J. Richter and S. Silvestrov.- 5 Centralizers and Pseudo-Degree Functions: J. Richter.- 6 Asymptotic Expansions for Moment Functionals of Perturbed Discrete Time Semi-Markov Processes: M. Petersson.- 7 Asymptotics for Quasi-Stationary Distributions of Perturbed Discrete Time Semi-Markov Processes: M. Petersson.- 8 PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph: Ch. Engström and S. Silvestrov.- 9 PageRank, Connecting a Line of Nodes with a Complete Graph: Ch. Engström and S. Silvestrov.- 10 Output Rate Variation Problem: Some Heuristic Paradigms and Dynamic Programming: G.B. Thapa and S. Silvestrov.- 11Lp-Boundedness of Two Singular Integral Operators of Convolution Type: J. Musonda and S. Kaijser.- 12 Crossed Product Algebras for Piece-Wise Constant Functions: A.B. Tumwesigye et al.- 13 Linear Classification of Data with Support Vector Machines and Generalized Support Vector Machines: Xiaomin Qi et al.- 14 Linear and Nonlinear Classifiers of Data with Support Vector Machines and Generalized Support Vector Machines: X. Qi et al.- 15 Common Fixed Points of Weakly Commuting Multivalued Mappings on a Domain of Sets Endowed with Directed Graph: S. Silvestrov and T. Nazir.- 16 Common Fixed Point Results for Family of Generalized Multivalued F-contraction Mappings in Ordered Metric Spaces: T. Nazir and S. Silvestrov.