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Applied functional analysis has an extensive history. In the last century, this field has often been used in physical sciences, such as wave and heat phenomena. In recent decades, with the development of nonlinear functional analysis, this field has been used to model a variety of engineering, medical, and computer sciences. Two of the most significant issues in this area are modeling and optimization. Thus, we consider some recently published works on fixed point, variational inequalities, and optimization problems. These works could lead readers to obtain new novelties and familiarize them with some applications of this area.

vector variational-like inequalities --- vector optimization problems --- limiting (p,r)-α-(η,θ)-invexity --- Lipschitz continuity --- Fan-KKM theorem --- set-valued optimization problems --- higher-order weak adjacent epiderivatives --- higher-order mond-weir type dual --- benson proper efficiency --- fractional calculus --- ψ-fractional integrals --- fractional differential equations --- contraction --- hybrid contractions --- volterra fractional integral equations --- fixed point --- inertial-like subgradient-like extragradient method with line-search process --- pseudomonotone variational inequality problem --- asymptotically nonexpansive mapping --- strictly pseudocontractive mapping --- sequentially weak continuity --- method with line-search process --- pseudomonotone variational inequality --- strictly pseudocontractive mappings --- common fixed point --- hyperspace --- informal open sets --- informal norms --- null set --- open balls --- modified implicit iterative methods with perturbed mapping --- pseudocontractive mapping --- strongly pseudocontractive mapping --- nonexpansive mapping --- weakly continuous duality mapping --- set optimization --- set relations --- nonlinear scalarizing functional --- algebraic interior --- vector closure --- conjugate gradient method --- steepest descent method --- hybrid projection --- shrinking projection --- inertial Mann --- strongly convergence --- strict pseudo-contraction --- variational inequality problem --- inclusion problem --- signal processing

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Fuzzy Logic is a good model for the human ability to compute words. It is based on the theory of fuzzy set. A fuzzy set is different from a classical set because it breaks the Law of the Excluded Middle. In fact, an item may belong to a fuzzy set and its complement at the same time and with the same or different degree of membership. The degree of membership of an item in a fuzzy set can be any real number included between 0 and 1. This property enables us to deal with all those statements of which truths are a matter of degree. Fuzzy logic plays a relevant role in the field of Artificial Intelligence because it enables decision-making in complex situations, where there are many intertwined variables involved. Traditionally, fuzzy logic is implemented through software on a computer or, even better, through analog electronic circuits. Recently, the idea of using molecules and chemical reactions to process fuzzy logic has been promoted. In fact, the molecular word is fuzzy in its essence. The overlapping of quantum states, on the one hand, and the conformational heterogeneity of large molecules, on the other, enable context-specific functions to emerge in response to changing environmental conditions. Moreover, analog input–output relationships, involving not only electrical but also other physical and chemical variables can be exploited to build fuzzy logic systems. The development of “fuzzy chemical systems” is tracing a new path in the field of artificial intelligence. This new path shows that artificially intelligent systems can be implemented not only through software and electronic circuits but also through solutions of properly chosen chemical compounds. The design of chemical artificial intelligent systems and chemical robots promises to have a significant impact on science, medicine, economy, security, and wellbeing. Therefore, it is my great pleasure to announce a Special Issue of Molecules entitled “The Fuzziness in Molecular, Supramolecular, and Systems Chemistry.” All researchers who experience the Fuzziness of the molecular world or use Fuzzy logic to understand Chemical Complex Systems will be interested in this book.

Research & information: general --- Biology, life sciences --- fuzzy logic --- complexity --- chemical artificial intelligence --- human nervous system --- fuzzy proteins --- conformations --- photochromic compounds --- qubit --- protein dynamics --- conformational heterogeneity --- promiscuity --- fuzzy complexes --- higher-order structures --- protein evolution --- fuzzy set theory --- artificial intelligence --- GCN4 mimetic --- peptides-DNA --- E:Z photoisomerization --- conformational fuzziness --- photoelectrochemistry --- wide bandgap semiconductor --- artificial neuron --- in materio computing --- neuromorphic computing --- intrinsically disordered protein --- intrinsically disordered protein region --- liquid-liquid phase transition --- protein-protein interaction --- protein-nucleic acid interaction --- proteinaceous membrane-less organelle --- fuzzy complex. --- d-TST --- activation energy --- Transitivity plot --- solution kinetic --- Maxwell-Boltzmann path --- Euler's formula for the exponential --- activation --- transitivity --- transport phenomena --- moonlighting proteins --- intrinsically disordered proteins --- metamorphic proteins --- morpheeins

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Fuzzy Logic is a good model for the human ability to compute words. It is based on the theory of fuzzy set. A fuzzy set is different from a classical set because it breaks the Law of the Excluded Middle. In fact, an item may belong to a fuzzy set and its complement at the same time and with the same or different degree of membership. The degree of membership of an item in a fuzzy set can be any real number included between 0 and 1. This property enables us to deal with all those statements of which truths are a matter of degree. Fuzzy logic plays a relevant role in the field of Artificial Intelligence because it enables decision-making in complex situations, where there are many intertwined variables involved. Traditionally, fuzzy logic is implemented through software on a computer or, even better, through analog electronic circuits. Recently, the idea of using molecules and chemical reactions to process fuzzy logic has been promoted. In fact, the molecular word is fuzzy in its essence. The overlapping of quantum states, on the one hand, and the conformational heterogeneity of large molecules, on the other, enable context-specific functions to emerge in response to changing environmental conditions. Moreover, analog input–output relationships, involving not only electrical but also other physical and chemical variables can be exploited to build fuzzy logic systems. The development of “fuzzy chemical systems” is tracing a new path in the field of artificial intelligence. This new path shows that artificially intelligent systems can be implemented not only through software and electronic circuits but also through solutions of properly chosen chemical compounds. The design of chemical artificial intelligent systems and chemical robots promises to have a significant impact on science, medicine, economy, security, and wellbeing. Therefore, it is my great pleasure to announce a Special Issue of Molecules entitled “The Fuzziness in Molecular, Supramolecular, and Systems Chemistry.” All researchers who experience the Fuzziness of the molecular world or use Fuzzy logic to understand Chemical Complex Systems will be interested in this book.

fuzzy logic --- complexity --- chemical artificial intelligence --- human nervous system --- fuzzy proteins --- conformations --- photochromic compounds --- qubit --- protein dynamics --- conformational heterogeneity --- promiscuity --- fuzzy complexes --- higher-order structures --- protein evolution --- fuzzy set theory --- artificial intelligence --- GCN4 mimetic --- peptides–DNA --- E:Z photoisomerization --- conformational fuzziness --- photoelectrochemistry --- wide bandgap semiconductor --- artificial neuron --- in materio computing --- neuromorphic computing --- intrinsically disordered protein --- intrinsically disordered protein region --- liquid–liquid phase transition --- protein–protein interaction --- protein–nucleic acid interaction --- proteinaceous membrane-less organelle --- fuzzy complex. --- d-TST --- activation energy --- Transitivity plot --- solution kinetic --- Maxwell–Boltzmann path --- Euler’s formula for the exponential --- activation --- transitivity --- transport phenomena --- moonlighting proteins --- intrinsically disordered proteins --- metamorphic proteins --- morpheeins --- n/a --- peptides-DNA --- liquid-liquid phase transition --- protein-protein interaction --- protein-nucleic acid interaction --- Maxwell-Boltzmann path --- Euler's formula for the exponential

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We are immersed in the so-called digital energy network, continuously introducing new technological advances for a better way of life. Numerous emerging words are in the spotlight, namely: Internet of Things (IoT), Big Data, Smart Cities, Smart Grid, Industry 4.0, etc. To achieve this formidable goal, systems should work more efficiently, and this fact inevitably leads to power quality (PQ) assurance. Apart from its economic losses, a bad PQ implies serious risks for machines, and consequently for people. Many researchers are endeavoring to develop new analysis techniques, instruments, measurement methods, and new indices and norms that match and fulfil the requirements regarding the current operation of the electrical network. This book offers a compilation of the some recent advances in this field. The chapters range from computing issues to technological implementations, going through event detection strategies and new indices and measurement methods that contribute significantly to the advancement of PQ analysis. Experiments have been developed within the frames of research units and projects, and deal with real data from industry and public buildings. Human beings have an unavoidable commitment with sustainability, which implies adapting PQ monitoring techniques to our dynamic world, defining a digital and smart concept of quality for electricity.

modulation --- FPGA --- flicker --- DC power quality indices --- limited resources hardware --- low cost monitor --- dynamic phasor estimation --- harmonics --- RMS voltage estimation --- islanding operation --- embedded system --- signal waveform compression --- big data --- digital signal processing --- data scalability --- data compression --- wind-grid distribution --- voltage fluctuations --- smart grid (SG) applications --- power event detection --- modelling --- voltage ripple --- power quality monitoring --- higher-order statistics (HOS) --- power distribution systems --- power quality disturbances --- reconfigurable computing --- operation analysis --- sensor node --- power quality (PQ) --- distribution networks --- wireless sensor network --- reliability --- power system measurements --- embedded microcontroller --- phasor measurement units --- IoT --- soft computing --- smart grids --- power quality monitor --- induction machines --- sensors and instruments for PQ --- Kalman filters --- low-voltage DC networks --- convolution neural network --- spectral kurtosis --- municipal distribution network --- statistical signal processing --- detection --- power quality disturbance --- smart grid --- energizing warning --- dense-mesh topology --- low computational cost --- fourth-order statistics --- PQ indices and thresholds --- machine learning --- voltage sags --- power quality --- computational solutions for advanced metering infrastructure (AMI) --- constant amplitude trend --- phasor measurement --- improved principal component analysis --- long-term

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Symmetry and complexity are studied by a selection of outstanding papers ranging from pure Mathematics and Physics to Computer Science and Engineering applications. In this Special Issue, the authors give a short but intensive description of the many applications of the basic structure of symmetry and complexity in many fields. Some interesting results were given in the Hydrodynamic Analysis of 3-D Hydrofoil and Marine Propeller and in the SAT Problems. The Study on Hypergraph Representations of Complex Fuzzy Information shows the importance of methods based on symmetry and complexity. A deep study of Information Technology Services in Public Organizations has been given in this issue, together with some interesting papers dealing with Adaptive Block Truncation Coding Based on an Edge-Based Quantization, SIR Model in a Patchy Environment, and the Evolution of Conformity Dynamics in Complex Social Networks. Another interesting paper provides some new insights into the Novel Computational Technique for Impulsive Fractional Differential Equations. In this collection, An Intelligent Approach for Handling Complexity by Migrating from Conventional Databases to Big Data shows the importance of such topics related to complexity.

History of engineering & technology --- big data --- complexity --- NoSQL databases --- Oracle NoSQL --- data migration --- B-spline scheme --- dihedral hydrofoil --- hydrodynamics --- marine propeller --- propeller wake --- sweptback hydrofoil --- surface panel method --- fractional derivative --- Adomian method --- computational technique --- conformity --- evolutionary dynamics --- ring network --- small-world network --- scale-free network --- epidemic model --- irreducible matrix --- Metzler matrix --- disease transition and transmission matrices --- decentralized control --- disease-free and endemic equilibrium points --- Moore–Penrose pseudoinverse --- next generation matrix --- patchy environment --- vaccination controls --- numerical inverse Laplace transform --- orthonormalized Bernstein polynomials --- operational matrices --- fractional differential equations --- BTC --- edge-based quantization --- reversible data hiding --- histogram shifting technique --- directional hölder regularity --- anisotropic hölder regularity --- directional scaling function --- anisotropic scaling function --- directional multifractal formalism --- wavelet bases --- sierpinski cascade functions --- fractional brownian sheets --- nonlinear equations --- multiple roots --- higher order methods --- attraction basins --- service identification --- IT service --- IT services catalog --- IT services portfolio --- multiobjective --- symmetric duality --- second-order --- nondifferentiable --- fractional programming --- support function --- Gf-bonvexity/Gf-pseudobonvexity --- complex q-rung orthopair fuzzy set --- complex q-rung orthopair fuzzy graphs --- complex q-rung orthopair fuzzy hypergraphs --- transversals --- SAT problem --- membrane computing --- P system --- splitting rule