**Preface to "Symmetry in Mathematical Analysis and Application"**

'Mathematics servants of Sciences, Mathematics queens of Sciences.' This is the rough translation of a statement in Latin, describing the role of mathematics in the scientific community. At the core of mathematics, mathematical analysis in the past centuries has provided applications in different disciplines that are essential for accessing modern knowledge, in both practical and theoretical aspects. In addition to these applications, mathematics possesses a wonderful beauty: fundamental formulas present deep links in symmetry which go beyond technical expressions.

This Special Issue of *Symmetry* consists of six articles devoted to models in medicine, biology, ecology and other disciplines, all expressed in terms of mathematical analysis, showing the effectiveness of mathematics in different aspects of modern life. Other contributions in pure mathematics also give evidence for the role of Symmetry in these theoretical aspects.

In this preface, the six articles in the Special Issue will be addressed, and a detailed presentation of the different topics will be provided. Here, then, we will give an idea of some of the relevant achievements in the present volume.

In medicine, biology and ecology, immune system response is studied and related to the risk of cancer. The increase of the nutrition of the prey and destabilizing the predator–prey dynamics are both considered.

In symmetry in mathematics, the classical symmetric means are generalized to weighted Pythagorean means. The eigenvalues of the sequences of matrices are studied, in connection with stability and convergence problems.

Other relevant contributions concern the efficiency of public transport, with particular reference to the reduction of congestion, energy consumption and emissions. Blast waves are also considered, in particular in the relevant case of supersonic speed, as in explosions.

Overall, the volume is an excellent report on the relevance of mathematical analysis in applied sciences, with an emphasis placed on the deep relations with *Symmetry*.

> **Luigi Rodino** *Special Issue Editor*

*Article*
