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The development of special and general relativity has relied significantly on ideas of symmetry. Similarly, modern efforts to test these theories have often sought either violations or extensions of the symmetries seen, and symmetry is regularly used a tool in seeking new applications. In this Special Issue of symmetry, we explore some contemporary research related to symmetry in special and general relativity.
Lorentz symmetry  rotation invariance  StandardModel Extension  Noether’s theorem  Weyl method  Palais principle of symmetric criticality  solutions to Einstein’s equations  magnetic monopole  pulsar timing  StandardModel Extension  binary pulsars  Lorentz and CPT violation  StandardModel Extension  Dirac fermions  Dirac neutrinos  Majorana neutrinos  determinants of block matrices  lorentz violation  CPT violation  penning trap  quantum mechanics  antimatter  interferometry  gravitational waves  Lorentz violation  standardmodel extension  geodesic deviation  Lorentz violation  standard model extension  CPT violation
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This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the socalled hard sciences—specifically mathematics—without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these.
crowd dynamics  scaling  kinetic models  safety  learning dynamics  kinetic theory  complex systems  multiscale modeling  cell movement  haptotaxis  kinetic theory  opinion dynamics  symmetric interactions  kinetic equations  integrodifferential equations  conformist society  individualistic society  Efficient frontier  kinetic theory  CVaR  vehicular traffic  short and longrange interactions  kinetic theory  Crowd dynamics  kinetic models  stress conditions  boundary conditions  safety  kinetic theory  living systems  social dynamics  active particles  learning  social dynamics  pattern formation
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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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This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.
Metric dimension  basis  resolving set  gear graph  generalized gear graph  Devaney chaos  hypercyclicity  topological transitivity  topologically mixing  disjointness  connectivity  topological indices  cuprite  atom bond connectivity index  Zagreb indices  geometric arithmetic index  general Randi? index  titanium difluoride  direct product of graphs  geodesics  Gromov hyperbolicity  bipartite graphs  alphaboron nanotube  resolving set  metric basis  metric dimension  distinguishing number  functigraph  complete graph  graph operators  gromov hyperbolicity  geodesics  topological indices  polycyclic aromatic hydrocarbons  resolving set  domination  secure resolving set and secure resolving domination  harmonic index  harmonic polynomial  inverse degree index  products of graphs  algorithm  general randi? index  atombond connectivity ABC index  geometricarithmetic GA index  HexDerived Cage networks  dominating set  binary locatingdomination number  rotationallysymmetric convex polytopes  ILP models
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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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The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and transSasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both wellknown geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.
Euclidean submanifold  position vector field  concurrent vector field  concircular vector field  rectifying submanifold  Tsubmanifolds  constant ratio submanifolds  Ricci soliton  Kähler–Einstein metrics  compact complex surfaces  pinching of the curvatures  statistical manifolds  Hessian manifolds  Hessian sectional curvature  scalar curvature  Ricci curvature  Minkowski plane  Minkowskian length  Minkowskian angle  Minkowskian pseudoangle  L2harmonic forms  Hodge–Laplacian  manifold with singularity  L2Stokes theorem  capacity  kth generalized Tanaka–Webster connection  nonflat complex space form  real hypersurface  lie derivative  shape operator  conical surface  developable surface  generalized 1type Gauss map  cylindrical hypersurface  inextensible flow  lightlike surface  ruled surface  Darboux frame  CBochner tensor  generalized normalized ?Casorati curvature  Sasakian manifold  slant  invariant  antiinvariant  transSasakian 3manifold  Reeb flow symmetry  Ricci operator  Sasakian statistical manifold  conjugate connection  Casorati curvature  framed rectifying curves  singular points  framed helices  centrodes  circular rectifying curves  statistical structure  affine hypersurface  affine sphere  conjugate symmetric statistical structure  sectional ?curvature  complete connection  symplectic curves  circular helices  symplectic curvatures  Frenet frame
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Engineering mathematics is a branch of applied mathematics where mathematical methods and techniques are implemented for solving problems related to the engineering and industry. It also represents a multidisciplinary approach where theoretical and practical aspects are deeply merged with the aim at obtaining optimized solutions. In line with that, the present Special Issue, 'Engineering Mathematics in Ship Design', is focused, in particular, with the use of this sort of engineering science in the design of ships and vessels. Articles are welcome when applied science or computation science in ship design represent the core of the discussion.
roll motion  roll damping  CFD  harmonic excitation  singlestepped planing hulls  symmetric 2D + T theory  hydrodynamic forces  towing tank tests  piezoelectric sensor  damaged sensor  impact traction  LeadZirconiumTitanium (PZT)  fracture mechanics  marine industry  water entry  hydroelasticity  cavitation  FSI  SPH  slamming  plate  stiffeners  constructal design  finite element method  deflection  numerical simulation  stiffened plate  constitutive model  finite element  fluidstructure interaction  ship design  stateoftheart  fixed pitch propeller  controllable pitch propeller  lowspeed Diesel engine  selection  optimisation  modelling  coanda effect  turbulence model  computational fluid dynamic  finite volume method  H.O.M.E.R. nozzle  numerical model  SHIPMOVE  MMG Model  external forces  marine transport  environmental management system  balanced scorecard  ISO 14001  ISO 9126  ISO 14598  AHP method  MCDM method  n/a
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Modern dynamics was established many centuries ago by Galileo and Newton before the beginning of the industrial era. Presently, we are in the presence of the fourth industrial revolution, and mechanical systems are increasingly being integrated with electronic, electrical, and fluidic systems. This trend is present not only in the industrial environment, which will soon be characterized by the cyberphysical systems of industry 4.0, but also in other environments like mobility, health and bioengineering, food and natural resources, safety, and sustainable living. In this context, purely mechanical systems with quasistatic behavior will become less common and the stateoftheart will soon be represented by integrated mechanical systems, which need accurate dynamic models to predict their behavior. Therefore, mechanical system dynamics are going to play an increasingly central role. Significant research efforts are needed to improve the identification of the mechanical properties of systems in order to develop models that take nonlinearity into account, and to develop efficient simulation tools. This Special Issue aims at disseminating the latest research achievements, findings, and ideas in mechanical systems dynamics, with particular emphasis on applications that are strongly integrated with other systems and require a multiphysical approach.
dynamics  mesh stiffness  forced response  timevariant parameters  Method of Multiple TimeScales  cyclicsymmetric systems dynamics  lumped parameters model  quadruped robots  highspeed locomotion  leg trajectory planning  trot gait  motion capture sensor  lowspeed stability  balancing  motorcycle dynamics  rider control  unsteady flow control  vortex dynamics  separation flow  DetachedEddy Simulation  natural motion  natural dynamics  energy saving  robotic system  trajectory planning  optimization  landing gear  emergency extension  reliability sensitivity analysis  driving mechanism  mixture of models  damper force  pitch angle  seeder dynamics  simulation model  reaching law  sliding mode control (SMC)  groundbased laser communication turntable  chatterfree  quasisliding mode domain (QSMD)  underplatform damper  bladed disc’s rotation  compositive motion  relative displacement  dynamical characteristic  variable compression ratio  adjustable hydraulic volume  mathematical model  dynamic characteristics  simulation  switched reluctance motor  vibration prediction  multiphysics modelling  personal mobility vehicle  active tilting  inner wheel lifting  obstacle avoidance  energy efficiency  n/a
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In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the socalled generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.
wave equation  spherically symmetric spacetimes  lie symmetries  roots  optimal systems  invariant solutions  n/a  Noether symmetry approach  FLRW spacetime  action integral  variational principle  first integral  modified theories of gravity  GaussBonnet cosmology  Noether’s theorem  action integral  generalized symmetry  first integral  invariant  nonlocal transformation  boundary term  conservation laws  analytic mechanics  Noether’s theorem  generalized symmetry  energymomentum tensor  Lagrange anchor  viscoelasticity  KelvinVoigt equation  Lie symmetries  optimal system  groupinvariant solutions  conservation laws  multiplier method  continuous symmetry  symmetry reduction  integrable nonlocal partial differential equations  symmetries  conservation laws  Noether operator identity  quasiNoether systems  quasiLagrangians  Lie symmetry  conservation law  double dispersion equation  Boussinesq equation  systems of ODEs  Noether operators  Noether symmetries  first integrals  partial differential equations  approximate symmetry and solutions
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In 1978, Fred Hoyle proposed that interstellar comets carrying several viruses landed on Earth as part of the panspermia hypotheses. With respect to life, the origin of homochirality on Earth has been the greatest mystery because life cannot exist without molecular asymmetry. Many scientists have proposed several possible hypotheses to answer this longstanding LD question. Previously, Martin Gardner raised the question about mirror symmetry and broken mirror symmetry in terms of the homochirality question in his monographs (1964 and 1990). Possible scenarios for the LD issue can be categorized into (i) Earth and exoterrestrial origins, (ii) bychance and necessity mechanisms, and (iii) mirrorsymmetrical and nonmirrorsymmetrical forces as physical and chemical origins. These scenarios should involve further great amplification mechanisms, enabling a pure L or Dworld.
chirogenesis  enantiomorphism  nepheline  magmatic flow  etch figures  origin of life  biological homochirality  deracemization  superhighvelocity impact  plasma reactor  absolute asymmetric synthesis  amino acids  origin of life  amino acid handedness  nucleus–molecular coupling  chirality  circularly polarized luminescence  circular dichroism  symmetry breaking  parity violation  weak neutral current  tunneling  Z0 boson  homochirality  precision measurement  homochirality  circularly polarized light  asymmetric reaction  polymer  ?strand  hidden chirality  twofold helix  multipoint approximation  tiltchirality  high dimensional chirality  spin polarized electrons  homochirality  magnetism  prebiotic  environmental chirality  C1 and C2symmetric catalysts  chiral field (memory)  racemic field  Viedma ripening effect  Wallach’s rule  heat capacity  metalorganic framework  triethylenediamine (DABCO) molecules  racemate  Salam hypothesis  homochirality  parity violation  neutrinos  gravitation  enantiomer selfdisproportionation  SDE  achiral stationary phase  homochiral and heterochiral aggregates  chiral separation  chirality  genesis of life chirality  asymmetric autocatalysis  homochirality  chirality  asymmetric synthesis  Soai reaction  biological homochirality  enantioselective reaction  autocatalysis  origin of life  replicators  bioorganic homochirality  circularly polarized photon  spinpolarized lepton  parity violation in the weak interaction  symmetry breaking  assemblies  supramolecular chirality  homochirality  selfassembly  vortex  lipid  supramolecular assembly  symmetry breaking  homochirality
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