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Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems.

History of engineering & technology --- Khovanov homology --- braid link --- Jones polynomial --- drone deployment --- drone port --- traveling salesman --- facility location problem --- molecular arrays --- constrained optimization --- equivariant bifurcation theory --- generalized Lane–Emden systems --- Noether-like operator --- conservation laws --- barycentric coordinate system --- coordinate system --- hexagonal grid --- triangular grid --- tri-hexagonal grid --- transformations --- test for outliers --- order statistics --- extreme values --- confidence intervals --- Monte-Carlo simulation --- nonlinear equations --- systems --- derivative-free methods --- fast algorithms --- computational efficiency --- neutrosophic soft sets --- inconsistent information --- prospect theory --- stochastic multi-criteria group decision making --- lie symmetries --- invariants --- shallow water --- similarity solutions --- optimal system --- equal volume projection --- hierarchical grid --- iterative function --- multiple root --- composite method --- derivative-free method --- optimal convergence --- full-scale fire experiment --- compartment fire --- permutation entropy --- two length permutation entropy --- time series analysis --- parametric Jensen-Shannon statistical complexity --- symmetric duality --- alpha-power skew-t distribution --- skew-t distribution --- power-t distribution --- asymmetry --- Fisher information matrix --- maximum likelihood estimation --- iteration --- fixed points --- fractals --- Khovanov homology --- braid link --- Jones polynomial --- drone deployment --- drone port --- traveling salesman --- facility location problem --- molecular arrays --- constrained optimization --- equivariant bifurcation theory --- generalized Lane–Emden systems --- Noether-like operator --- conservation laws --- barycentric coordinate system --- coordinate system --- hexagonal grid --- triangular grid --- tri-hexagonal grid --- transformations --- test for outliers --- order statistics --- extreme values --- confidence intervals --- Monte-Carlo simulation --- nonlinear equations --- systems --- derivative-free methods --- fast algorithms --- computational efficiency --- neutrosophic soft sets --- inconsistent information --- prospect theory --- stochastic multi-criteria group decision making --- lie symmetries --- invariants --- shallow water --- similarity solutions --- optimal system --- equal volume projection --- hierarchical grid --- iterative function --- multiple root --- composite method --- derivative-free method --- optimal convergence --- full-scale fire experiment --- compartment fire --- permutation entropy --- two length permutation entropy --- time series analysis --- parametric Jensen-Shannon statistical complexity --- symmetric duality --- alpha-power skew-t distribution --- skew-t distribution --- power-t distribution --- asymmetry --- Fisher information matrix --- maximum likelihood estimation --- iteration --- fixed points --- fractals