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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

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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

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Modern financial management is largely about risk management, which is increasingly data-driven. The problem is how to extract information from the data overload. It is here that advanced statistical and machine learning techniques can help. Accordingly, finance, statistics, and data analytics go hand in hand. The purpose of this book is to bring the state-of-art research in these three areas to the fore and especially research that juxtaposes these three.

Index parameter --- estimation --- wrapped stable --- Hill estimator --- characteristic function-based estimator --- asymptotic --- efficiency --- GARCH model --- HARCH model --- PHARCH model --- Griddy-Gibs --- Euro-Dollar --- safe-haven assets --- gold price --- Swiss Franc exchange rate --- oil price --- generalized Birnbaum–Saunders distributions --- ACD models --- Box-Cox transformation --- high-frequency financial data --- goodness-of-fit --- banking competition --- credit risk --- NPLs --- Theil index --- convergence analysis --- interest rates --- yeld curve --- no-arbitrage --- bonds --- B-splines --- time series --- multifractal processes --- fractal scaling --- heavy tails --- long range dependence --- financial models --- Bitcoin --- capital asset pricing model --- estimation of systematic risk --- tests of mean-variance efficiency --- t-distribution --- generalized method of moments --- multifactor asset pricing model --- Lerner index --- stochastic frontiers --- shrinkage estimator --- seemingly unrelated regression model --- multicollinearity --- ridge regression --- financial incentives --- public service motivation --- job performance --- job satisfaction --- intention to leave

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The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.

continuous-time Markov chains --- non-stationary Markovian queueing model --- stability --- perturbation bounds --- forward Kolmogorov system --- threshold processing --- random samples --- long-term dependence --- mean-square risk estimate --- integrals and sums --- rates of convergence --- conditional law of large numbers --- conditional central limit theorem --- stochastic differential observation system --- nonlinear filtering problem --- state-dependent observation noise --- numerical filtering algorithm --- filtering given time-discretized observations --- stable approximation --- approximation accuracy --- Rényi theorem --- Kantorovich distance --- zeta-metrics --- Stein’s method --- stationary renewal distribution --- equilibrium transform --- geometric random sum --- characteristic function --- precipitation --- limit theorems --- statistical test --- generalized negative binomial distribution --- generalized gamma distribution --- asymptotic approximations --- extreme order statistics --- random sample size --- slowly varying --- monotony in the Zygmund sense --- class Γa(g) --- self-neglecting function --- convergence rates --- citation distribution --- Hirsch index --- geometric distribution --- Sibuya distribution --- geometrically stable distribution --- generalized Linnik distribution --- random sum --- transfer theorem --- multivariate normal scale mixtures --- heavy-tailed distributions --- multivariate stable distribution --- multivariate Linnik distribution --- generalized Mittag–Leffler distribution --- multivariate generalized Mittag–Leffler distribution --- stable distribution --- probability density function --- distribution function --- Hankel contours --- multivariate stable processes --- contour integrals --- fractional laplacian --- second order expansions --- high-dimensional --- low sample size --- Laplace distribution --- Student’s t-distribution --- pareto mixture distribution --- multiserver system --- uniform distance --- perfect simulation --- priority system --- marked Markov arrival process --- phase-type distribution --- change of the priority --- dispatching --- heterogeneous servers --- Markov decision process --- policy-iteration algorithm --- mean number of customers --- decomposable semi-regenerative process --- multiple power series distribution --- integral limit theorem --- local limit theorem --- Tauberian lemma --- R-weakly one-sided oscillation of the multiple sequence at infinity along the given multiple sequence --- pension schemes --- balance equation --- gross premium --- premium load --- lump sum --- defined contribution pension schemes --- decrement tables --- robustness --- minimax approach --- stable estimation