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Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more. The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters.

Fractals. --- Fractal analysis.

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A couple of decades have passed since the advent of electromagnetic metamaterials. Although the research on artificial microwave materials dates back to the middle of the 20th century, the most prominent development in the electromagnetics of artificial media has happened in the new millennium. In the last decade, the electromagnetics of one-, two-, and three-dimensional metamaterials acquired robust characterization and design tools. Novel fabrication techniques have been developed. Many exotic effects involving metamaterials and metasurfaces, which initially belonged in a scientist’s lab, are now well understood by practicing engineers. Therefore, it is the right time for the metamaterial concepts to become a designer’s tools of choice in the landscape of electronics, microwaves, and photonics. Answering such a demand, the book “Engineering Metamaterials” focuses on the theory and applications of electromagnetic metamaterials, metasurfaces, and metamaterial transmission lines as the building blocks of present-day and future electronic, photonic, and microwave devices.

evanescent field tunneling --- metamaterials --- mu-negative material --- epsilon-negative material --- split-ring-resonators --- waveguides --- spoof surface plasmon polariton (SSPP) --- metal hole arrays (MHA) --- electromagnetic distortion --- two-dimensional imaging --- common-mode noise --- corrugated ground plane --- differential signaling --- electromagnetic bandgap --- metamaterial --- stepped impedance --- metasurfaces --- linear to circular polarization converter --- dual-band polarization converters --- transmission-based polarization conversion --- dual-band --- fractals --- microwave absorbers --- UHF-RFID --- left-handed line --- sensors --- phase shift --- terahertz metamaterials --- graphene --- encoder --- active control --- n/a

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Symmetry is one of the most important notions in natural science; it lies at the heart of fundamental laws of nature and serves as an important tool for understanding the properties of complex systems, both classical and quantum. Another trend, which has in recent years undergone intensive development, is mesoscopic physics. This branch of physics also combines classical and quantum ideas and methods. Two main directions can be distinguished in mesoscopic physics. One is the study of finite quantum systems of mesoscopic sizes. Such systems, which are between the atomic and macroscopic scales, exhibit a variety of novel phenomena and find numerous applications in creating modern electronic and spintronic devices. At the same time, the behavior of large systems can be influenced by mesoscopic effects, which provides another direction within the framework of mesoscopic physics. The aim of the present book is to emphasize the phenomena that lie at the crossroads between the concept of symmetry and mesoscopic physics.

Bose systems --- asymptotic symmetry breaking --- Bose–Einstein condensation --- particle fluctuations --- stability of Bose systems --- fractals --- small-angle scattering --- form factor --- structural properties --- dimension spectra --- pair distance distribution function --- stochastic dynamics --- symmetry breaking --- field-theoretic renormalization group --- Bose–Einstein condensates --- density --- position variance --- momentum variance --- angular-momentum variance --- harmonic-interaction model --- MCTDHB --- particle-hole symmetry --- metal–insulator transition --- random gap model --- Monte Carlo simulations --- structure factor --- quantum droplet --- binary Bose–Einstein condensate --- modulational instability --- graphene --- ripple --- transport --- symmetry --- quantum dot --- Kramers degeneracy --- spin-orbit interaction --- tight-binding approach --- Bose-Einstein condensates --- Josephson oscillations --- spontaneous symmetry breaking --- Thomas-Fermi approximation --- dynamical chaos --- ground states --- perturbation theory

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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.

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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Our Special Issue we publish at a turning point, which we have not dealt with since World War II. The interconnected long-term global shocks such as the coronavirus pandemic, the war in Ukraine, and catastrophic climate change have imposed significant humanitary, socio-economic, political, and environmental restrictions on the globalization process and all aspects of economic and social life including the existence of individual people. The planet is trapped—the current situation seems to be the prelude to an apocalypse whose long-term effects we will have for decades. Therefore, it urgently requires a concept of the planet's survival to be built—only on this basis can the conditions for its development be created. The Special Issue gives evidence of the state of econophysics before the current situation. Therefore, it can provide excellent econophysics or an inter-and cross-disciplinary starting point of a rational approach to a new era.

energy --- economic growth --- output elasticities --- entropy production --- emissions --- optimization --- speculative attacks --- currency crisis --- neural networks --- deep learning --- Quantum-Inspired Neural Network --- traveling salesman problem --- simulated annealing technique --- kinetic exchange model --- Gini index --- Kolkata index --- minority game --- Kolkata Paise Restaurant problem --- time series analysis --- cross-correlations --- power law classification scheme --- network analysis --- globalisation --- entropy --- portfolio optimization --- regularization --- renormalization --- econophysics --- highway freight transportation --- radiation model --- transportation network --- network diversity --- power law --- economic development --- decision-making --- bounded rationality --- complexity economics --- information-theory --- maximum entropy principle --- quantal response statistical equilibrium --- correlation coefficient --- detrended cross-correlation analysis --- COVID-19 --- mobility indices --- random geometry --- risk measurement --- disordered systems --- replica theory --- return distributions --- power-law tails --- stretched exponentials --- q-Gaussians --- financial markets --- financial complexity --- collective intelligence --- emergent property --- stock correlation --- lexical evolution of econophysics --- text as data --- correspondence analysis --- long-range memory --- 1/f noise --- absolute value estimator --- anomalous diffusion --- ARFIMA --- first-passage times --- fractional Lèvy stable motion --- Higuchi’s method --- mean squared displacement --- multiplicative point process --- correlation filtering --- minimal spanning tree --- planar maximally filtered graph --- topological data analysis --- SGX --- TAIEX --- complex systems --- ecological economics --- urban–regional economics --- income distribution --- financial market dynamics --- income tax --- tax deduction --- income redistribution --- government transfer --- government dependency --- poverty line --- basic income guarantee --- effective tax rate --- balanced budget --- elastic tax --- Cantor set --- fractals --- homeomorphism --- detrended fluctuation analysis --- Hurst exponent --- continuous time random walk --- intertrade times --- volatility clustering --- local transfer entropy --- long-short-term-memory --- Bitcoin --- cryptocurrencies --- multiscale analysis --- detrended cross-correlations --- covariance matrices --- copulas --- high-frequency trading --- market stability --- agent-based models --- structural entropy --- Economic Freedom of the World index --- Index of Economic Freedom --- rank-size law technique --- power law behaviour --- exponential behaviour --- multiscale partition function --- multifractal analysis --- company market --- export readiness --- internationalization --- options pricing --- mortality --- companies --- start-up --- FTSE100 --- Gompertz --- MinMax --- survival probability distribution --- high-frequency trader --- multivariate Hawkes process --- forex market --- wealth distribution --- kinetic models --- wealth inequalities --- compartmental epidemic modelling --- vaccination campaign --- flash crash --- systemic risk --- financial networks --- high frequency trading --- market microstructure --- phase transition --- criticality --- dynamics of complex networks --- cascading failure --- network science --- economic complexity --- relatedness --- products and services --- planar graph --- partial correlation --- discounting --- bond pricing --- real interest rates --- calendar anomalies --- day-of-the-week effect --- market indices --- multifractal detrended fluctuation analysis --- n/a --- fractional Lèvy stable motion --- Higuchi's method --- urban-regional economics