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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.
Fubini polynomials  wtorsion Fubini polynomials  fermionic padic integrals  symmetric identities  Chebyshev polynomials  sums of finite products  hypergeometric function  Fubini polynomials  Euler numbers  symmetric identities  elementary method  computational formula  two variable qBerstein polynomial  two variable qBerstein operator  qEuler number  qEuler polynomial  Fubini polynomials  Euler numbers  congruence  elementary method  qBernoulli numbers  qBernoulli polynomials  two variable qBernstein polynomials  two variable qBernstein operators  padic integral on ?p  the degenerate gamma function  the modified degenerate gamma function  the degenerate Laplace transform  the modified degenerate Laplace transform  Fibonacci  Lucas  linear form in logarithms  continued fraction  reduction method  sums of finite products of Chebyshev polynomials of the third and fourth kinds  Hermite  generalized Laguerre  Legendre  Gegenbauer  Jacobi  thirdorder character  classical Gauss sums  rational polynomials  analytic method  recursive formula  fermionic padic qintegral on ?p  qEuler polynomials  qChanghee polynomials  symmetry group  Apostoltype Frobenius–Euler polynomials  threevariable Hermite polynomials  symmetric identities  explicit relations  operational connection  qVolkenborn integral on ?p  Bernoulli numbers and polynomials  generalized Bernoulli polynomials and numbers of arbitrary complex order  generalized Bernoulli polynomials and numbers attached to a Dirichlet character ?  Changhee polynomials  Changhee polynomials of type two  fermionic padic integral on ?p  Chebyshev polynomials of the first, second, third, and fourth kinds  sums of finite products  representation  catalan numbers  elementary and combinatorial methods  recursive sequence  convolution sums  wellposedness  stability  acoustic wave equation  perfectly matched layer  Fibonacci polynomials  Lucas polynomials  trivariate Fibonacci polynomials  trivariate Lucas polynomials  generating functions  central incomplete Bell polynomials  central complete Bell polynomials  central complete Bell numbers  Legendre polynomials  Laguerre polynomials  generalized Laguerre polynomials  Gegenbauer polynomials  hypergeometric functions 1F1 and 2F1  Euler polynomials  Bernoulli polynomials  elementary method  identity  congruence  new sequence  Catalan numbers  elementary and combinatorial methods  congruence  conjecture  fluctuation theorem  thermodynamics of information  stochastic thermodynamics  mutual information  nonequilibrium free energy  entropy production
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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Currently, the use of computational fluid dynamics (CFD) solutions is considered as the stateoftheart in the modeling of unsteady nonlinear flow physics and offers an early and improved understanding of air vehicle aerodynamics and stability and control characteristics. This Special Issue covers recent computational efforts on simulation of aerospace vehicles including fighter aircraft, rotorcraft, propeller driven vehicles, unmanned vehicle, projectiles, and air drop configurations. The complex flow physics of these configurations pose significant challenges in CFD modeling. Some of these challenges include prediction of vortical flows and shock waves, rapid maneuvering aircraft with fast moving control surfaces, and interactions between propellers and wing, fluid and structure, boundary layer and shock waves. Additional topic of interest in this Special Issue is the use of CFD tools in aircraft design and flight mechanics. The problem with these applications is the computational cost involved, particularly if this is viewed as a bruteforce calculation of vehicle’s aerodynamics through its flight envelope. To make progress in routinely using of CFD in aircraft design, methods based on sampling, model updating and system identification should be considered.
wake  bluff body  square cylinder  DDES  URANS  turbulence model  large eddy simulation  Taylor–Green vortex  numerical dissipation  modified equation analysis  truncation error  MUSCL  dynamic Smagorinsky subgridscale model  kinetic energy dissipation  computational fluid dynamics (CFD)  microfluidics  numerical methods  gasdynamics  shockchannel  microelectromechanical systems (MEMS)  discontinuous Galerkin finite element method (DG–FEM)  fluid mechanics  characteristicsbased scheme  multidirectional  Riemann solver  Godunov method  bifurcation  wind tunnel  neural networks  modeling  unsteady aerodynamic characteristics  high angles of attack  hypersonic  wake  chemistry  slenderbody  angle of attack  detection  afterbody  Sduct diffuser  flow distortion  flow control  vortex generators  aeroelasticity  reducedorder model  flutter  wind gust responses  computational fluid dynamics  convolution integral  sharpedge gust  reduced order aerodynamic model  geometry  meshing  aerodynamics  CPACS  MDO  VLM  Euler  CFD  variable fidelity  multifidelity  aerodynamic performance  formation  VLM  RANS  hybrid reducedorder model  quasianalytical  aeroelasticity  flexible wings  subsonic  wing–propeller aerodynamic interaction  pfactor  installed propeller  overset grid approach
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In order to measure and quantify the complex behavior of realworld systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and nonuniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineeringoriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and antisynchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.
multitime scale fractional stochastic differential equations  fractional Brownian motion  fractional stochastic partial differential equation  analytical solution  nonautonomous (autonomous) dynamical system  topological entropy  (asymptotical) focal entropy point  disturbation  mdimensional manifold  geometric nonlinearity  Bernoulli–Euler beam  colored noise  noise induced transitions  true chaos  Lyapunov exponents  wavelets  Lyapunov exponents  Wolf method  Rosenstein method  Kantz method  neural network method  method of synchronization  Benettin method  Fourier spectrum  Gauss wavelets  fractional calculus  Adomian decomposition  Mittag–Leffler function  descriptor fractional linear systems  regular pencils  Schur factorization  hyperchaotic system  selfsynchronous stream cipher  permutation entropy  image encryption  wavelet transform  product MValgebra  partition  Tsallis entropy  conditional Tsallis entropy  dynamical system  discrete chaos  discrete fractional calculus  hidden attractors  approximate entropy  stabilization  Information transfer  continuous flow  discrete mapping  Lorenz system  Chua’s system  deterministic chaos  random number generator  unbounded chaos  bounded chaos  phaselocked loop  Gaussian white noise  n/a
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