Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Research & information: general --- Mathematics & science --- 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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Research & information: general --- Mathematics & science --- 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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales.

prestressed concrete cylinder pipe --- external prestressed steel strands --- theoretical study --- wire-breakage --- first-principles calculation --- Heusler compounds --- gapless half metals --- spin gapless semiconductor --- bi-directional functionally graded --- bolotin scheme --- dynamic stability --- elastic foundation --- porosity --- two-axis four-gimbal --- electro-optical pod --- dynamics modeling --- coarse–fine composite --- Carbon-fiber-reinforced plastics (CFRPs) --- fastener --- arc --- Joule heat --- finite element analysis (FEA) --- piezoelectric effect --- bimodular model --- functionally-graded materials --- cantilever --- vibration --- functional reinforcement --- graphene nanoplatelets --- higher-order shear deformable laminated beams --- nanocomposites --- nonlinear free vibration --- sandwich beams --- fractional calculus --- Riemann-Liouville fractional derivative --- viscoelasticity --- pipe flow --- fractional Maxwell model --- fractional Zener model --- fractional Burgers model --- Riemann–Liouville fractional derivative --- fractional Kelvin–Voigt model --- fractional Poynting–Thomson model --- curved sandwich nanobeams --- nonlocal strain gradient theory --- quasi-3D higher-order shear theory --- thermal-buckling --- FG-GPL --- GDQ --- heat transfer equation --- higher-order shear deformation theory --- buckling --- FE-GDQ --- functionally graded materials --- 3D elasticity --- 3D shell model --- steady-state hygro-elastic analysis --- Fick moisture diffusion equation --- moisture content profile --- layer-wise approach --- n/a --- coarse-fine composite --- fractional Kelvin-Voigt model --- fractional Poynting-Thomson model

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Lipschitz condition --- heston model --- rectangular matrices --- computational efficiency --- Hull–White --- order of convergence --- signal and image processing --- dynamics --- divided difference operator --- engineering applications --- smooth and nonsmooth operators --- Newton-HSS method --- higher order method --- Moore–Penrose --- asymptotic error constant --- multiple roots --- higher order --- efficiency index --- multiple-root finder --- computational efficiency index --- Potra–Pták method --- nonlinear equations --- system of nonlinear equations --- purely imaginary extraneous fixed point --- attractor basin --- point projection --- fixed point theorem --- convex constraints --- weight function --- radius of convergence --- Frédholm integral equation --- semi-local convergence --- nonlinear HSS-like method --- convexity --- accretive operators --- Newton-type methods --- multipoint iterations --- banach space --- Kantorovich hypothesis --- variational inequality problem --- Newton method --- semilocal convergence --- least square problem --- Fréchet derivative --- Newton’s method --- iterative process --- Newton-like method --- Banach space --- sixteenth-order optimal convergence --- nonlinear systems --- Chebyshev–Halley-type --- Jarratt method --- iteration scheme --- Newton’s iterative method --- basins of attraction --- drazin inverse --- option pricing --- higher order of convergence --- non-linear equation --- numerical experiment --- signal processing --- optimal methods --- rate of convergence --- n-dimensional Euclidean space --- non-differentiable operator --- projection method --- Newton’s second order method --- intersection --- planar algebraic curve --- Hilbert space --- conjugate gradient method --- sixteenth order convergence method --- Padé approximation --- optimal iterative methods --- error bound --- high order --- Fredholm integral equation --- global convergence --- iterative method --- integral equation --- ?-continuity condition --- systems of nonlinear equations --- generalized inverse --- local convergence --- iterative methods --- multi-valued quasi-nonexpasive mappings --- R-order --- finite difference (FD) --- nonlinear operator equation --- basin of attraction --- PDE --- King’s family --- Steffensen’s method --- nonlinear monotone equations --- Picard-HSS method --- nonlinear models --- the improved curvature circle algorithm --- split variational inclusion problem --- computational order of convergence --- with memory --- multipoint iterative methods --- Kung–Traub conjecture --- multiple zeros --- fourth order iterative methods --- parametric curve --- optimal order --- nonlinear equation

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book contains seven reviews and four research articles on the various modern approaches to the problem of quark confinement in quantum chromodynamics (QCD). These approaches include microscopic models of the Yang–Mills vacuum, which are based on the condensation of magnetic monopoles and center vortices, as well as the models of the confining quark-antiquark string. Possible applications of these models to the analysis of the novel superinsulating state, which emerges in such condensed-matter systems as Josephson junction arrays, are further discussed in one of the reviews. Two reviews from this collection discuss the approaches towards the analytic construction of effective confining theories, at the classical level and within the center-vortex model of the Yang–Mills vacuum. Other aspects of non-perturbative physics addressed by this collection include a possible connection between the localization of low-lying Dirac eigenmodes with the deconfinement and the chiral QCD phase transitions, as well as the role of topology in baryon-rich matter. Last but not least, a novel model of dark matter, based on ultralight axion particles, whose masses are arising due to distinct SU(2) Yang–Mills scales and the Planck mass, is suggested and developed in one of the contributed articles.

Research & information: general --- quantum chromodynamics --- confinement --- center vortex model --- vacuum structure --- cooling --- Lattice Gauge Theories --- Effective String Theories --- localization --- QCD --- lattice gauge theory --- finite temperature --- galaxy rotation curves --- low surface brightness --- dark matter --- dark energy --- ultralight axion particles --- cores --- halos --- mass-density --- profiles --- pure Yang–Mills theory --- monopoles --- topological interactions --- ensembles and effective fields --- topological solitons --- higher order theories --- gauge theory --- effective field theory --- magnetic flux symmetry --- chiral symmetry --- monopole --- lattice QCD --- spontaneous symmetry breaking --- Abelian projection --- magnetic catalysis --- magnetic disorder --- confinement models --- center vortices --- magnetic monopoles --- quark condensate --- topology --- lattice field theory --- dense matter --- phase transitions --- n/a --- pure Yang-Mills theory