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Mathematical ecology is an area of applied mathematics concerned with the application of mathematical concepts, tools and techniques, usually in the form of mathematical models, to problems arising in population dynamics, ecology and evolution. This Special Issue is designed to provide a snapshot of the state of the art in mathematical ecology. Topics of interest are (in no particular order) biological invasions, biological control, ecological pattern formation, ecologically relevant multiscale models, food webs, individual movement and dispersal, ecoepidemiology, evolutionary ecology, agroecosystems, regime shifts and early warning signals, synchronization and chaos. The list is inclusive rather than exclusive, and a few other relevant topics will also be considered.
biological invasions  biological control  pattern formation  ecoepidemiology  chaos  mathematical genealogy  random walks  Levy walks  individual animal movement  immune response  environmental stochasticity  fragmented environment  preypredator  competition  nonlocal consumption  food web  dispersal  ecosystem engineers  biodiversity
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This book presents the current views of leading physicists on the bizarre property of quantum theory: nonlocality. Einstein viewed this theory as “spooky action at a distance” which, together with randomness, resulted in him being unable to accept quantum theory. The contributions in the book describe, in detail, the bizarre aspects of nonlocality, such as Einstein–Podolsky–Rosen steering and quantum teleportation—a phenomenon which cannot be explained in the framework of classical physics, due its foundations in quantum entanglement. The contributions describe the role of nonlocality in the rapidly developing field of quantum information. Nonlocal quantum effects in various systems, from solidstate quantum devices to organic molecules in proteins, are discussed. The most surprising papers in this book challenge the concept of the nonlocality of Nature, and look for possible modifications, extensions, and new formulations—from retrocausality to novel types of multipleworld theories. These attempts have not yet been fully successful, but they provide hope for modifying quantum theory according to Einstein’s vision.
quantum nonlocality  quantum mechanics  Stern–Gerlach experiment  quantum measurement  pre and postselected systems  retrocausal channel  channel capacity  channel entropy  axioms for quantum theory  PR box  nonlocal correlations  classical limit  retrocausality  quantum correlations  quantum bounds  nonlocality  tsallis entropy  ion channels  selectivity filter  quantum mechanics  nonlinear Schrödinger model  biological quantum decoherence  nonlocality  parity measurements  entanglement  pigeonhole principle  controlledNOT  semiconductor nanodevices  quantum transport  densitymatrix formalism  Wignerfunction simulations  nonlocal dissipation models  steering  entropic uncertainty relation  general entropies  Bell’s theorem  Einstein–Podolsky–Rosen argument  local hidden variables  local realism  nosignalling  parallel lives  local polytope  quantum nonlocality  communication complexity  optimization  KS Box  PR Box  Noncontextuality inequality  discretevariable states  continuousvariable states  quantum teleportation of unknown qubit  hybrid entanglement  collapse of the quantum state  quantum nonlocality  communication complexity  quantum nonlocality  Bell test  deviceindependent  pvalue  hypothesis testing  nonsignaling  EPR steering  quantum correlation  nonlocality  entanglement  uncertainty relations  nonlocality  entanglement  quantum
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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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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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