Recent zbMATH articles in MSC 97 https://zbmath.org/atom/cc/97 2021-11-25T18:46:10.358925Z Werkzeug Book review of: S. Alexander et al., An invitation to Alexandrov geometry. CAT(0) spaces. https://zbmath.org/1472.00021 2021-11-25T18:46:10.358925Z "Kunzinger, M." https://zbmath.org/authors/?q=ai:kunzinger.michael Review of [Zbl 1433.53065]. An introduction to partial differential equations (with Maple). A concise course https://zbmath.org/1472.35001 2021-11-25T18:46:10.358925Z "Li, Zhilin" https://zbmath.org/authors/?q=ai:li.zhilin "Norris, Larry" https://zbmath.org/authors/?q=ai:norris.larry-k Publisher's description: The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations. The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm-Liouville eigenvalue problems and series solutions. The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area. Optimal control model of immunotherapy for autoimmune diseases https://zbmath.org/1472.82031 2021-11-25T18:46:10.358925Z "Costa, M. Fernanda P." https://zbmath.org/authors/?q=ai:costa.m-fernanda-p "Ramos, M. P." https://zbmath.org/authors/?q=ai:ramos.m-p-machado "Ribeiro, C." https://zbmath.org/authors/?q=ai:ribeiro.cassio-b|ribeiro.conceicao|ribeiro.claudio-d|ribeiro.cristina|ribeiro.c-c-h|ribeiro.carlos-h-c|ribeiro.celso-carneiro|ribeiro.cassilda|ribeiro.carlos-f-m|ribeiro.clovis-a|ribeiro.carlos-augusto-david|ribeiro.claudia "Soares, A. J." https://zbmath.org/authors/?q=ai:soares.ana-jacinta Summary: In this work, we develop a new mathematical model to evaluate the impact of drug therapies on autoimmunity disease. We describe the immune system interactions at the cellular level, using the kinetic theory approach, by considering self-antigen presenting cells, self-reactive T cells, immunosuppressive cells, and Interleukin-2 (IL-2) cytokines. The drug therapy consists of an intake of Interleukin-2 cytokines which boosts the effect of immunosuppressive cells on the autoimmune reaction. We also derive the macroscopic model relative to the kinetic system and study the wellposedness of the Cauchy problem for the corresponding system of equations. We formulate an optimal control problem relative to the model so that the quantity of both the self-reactive T cells that are produced in the body and the Interleukin-2 cytokines that are administrated is simultaneously minimized. Moreover, we perform some numerical tests in view of investigating optimal treatment strategies and the results reveal that the optimal control approach provides good-quality approximate solutions and shows to be a valuable procedure in identifying optimal treatment strategies. Data envelopment analysis with fuzzy complex numbers with an empirical case on power plants of Iran https://zbmath.org/1472.90066 2021-11-25T18:46:10.358925Z "Esfandiari, Mahmood" https://zbmath.org/authors/?q=ai:esfandiari.mahmood "Saati, Saber" https://zbmath.org/authors/?q=ai:saati.saber Summary: Using Data Envelopment Analysis (DEA) in complex environment is an idea that has recently presented for measuring the relative efficiencies of a set of Decision Making Units (DMUs) with complex inputs and outputs. The values of the input and output data in real-world problems appear sometimes as fuzzy complex number. For dealing with these types of data in DEA, we need to design a new model. This paper proposes a DEA model with triangular fuzzy complex numbers and solve it by using the concept of the data size and the $$\alpha$$-level approach. This method transforms DEA model with fuzzy complex data to a linear programing problem with crisp data. In the following, a ranking model is also developed using the above approach to rank the efficient DMUs. The proposed method is presented for the first time by the authors and there is no similar method. Finally, we present a case study in the generators of the steam power plants to demonstrate the applicability of the proposed methods in the power industry. Evaluating the potential trade-off between students' satisfaction and school performance using evolutionary multiobjective optimization https://zbmath.org/1472.90123 2021-11-25T18:46:10.358925Z "Marcenaro-Gutiérrez, Oscar D." https://zbmath.org/authors/?q=ai:marcenaro-gutierrez.oscar-d "González-Gallardo, Sandra" https://zbmath.org/authors/?q=ai:gonzalez-gallardo.sandra "Luque, Mariano" https://zbmath.org/authors/?q=ai:luque.mariano Summary: In this article, we carry out a combined econometric and multiobjective analysis using data from a representative sample of Andalusian schools. In particular, four econometric models are estimated in which the students' academic performance (scores in math and reading, and percentage of students reaching a certain threshold in both subjects, respectively) are regressed against the satisfaction of students with different aspects of the teaching-learning process. From these estimates, four objective functions are defined which have been simultaneously maximized, subject to a set of constraints obtained by analyzing dependencies between explanatory variables. This multiobjective programming model is intended to optimize the students' academic performance as a function of the students' satisfaction. To solve this problem we use a decomposition-based evolutionary multiobjective algorithm called Global WASF-GA with different scalarizing functions which allows generating an approximation of the Pareto optimal front. In general, the results show the importance of promoting respect and closer interaction between students and teachers, as a way to increase the average performance of the students and the proportion of high performance students.