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Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.
Mathematical (or Higher Transcendental) Functions and Their Applications  Fractional Calculus and Its Applications  qSeries and qPolynomials  Analytic Number Theory  Special Functions of Mathematical Physics and Applied Mathematics  Geometric Function Theory of Complex Analysis
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This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 2527, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the lightmatter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into postquantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize postquantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on postquantum cryptography.
Mathematical and Computational Engineering  Data Structures and Information Theory  Quantum Computing  Systems and Data Security  Mathematical and Computational Engineering Applications  Data and Information Security  Cryptography for Quantum Computers  Postquantum Cryptography  Number Theory  Representation Theory  Quantum Physics  Security Modelling  Open Access  Maths for engineers  Algorithms & data structures  Information theory  Mathematical theory of computation  Computer security  Network security
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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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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeperlevel"" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de BroglieBohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeperlevel questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and nonclassical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.
quantum foundations  nonlocality  retrocausality  Bell’s theorem  Bohmian mechanics  quantum theory  surrealistic trajectories  Bell inequality  quantum mechanics  generalized Lagrangian paths  covariant quantum gravity  emergent spacetime  Gaussianlike solutions  entropy and time evolution  resonances in quantum systems  the Friedrichs model  complex entropy.  Bell’s theorem  the causal arrow of time  retrocausality  superdeterminism  toymodels  quantum ontology  subquantum dynamics  microconstituents  emergent spacetime  emergent quantum gravity  entropic gravity  black hole thermodynamics  SternGerlach  trajectories  spin  Bell theorem  fractal geometry  padic metric  singular limit  gravity  conspiracy  free will  number theory  quantum potential  Feynman paths  weak values  Bohm theory  nohiddenvariables theorems  observables  measurement problem  Bohmian mechanics  primitive ontology  Retrocausation  weak values  Stochastic Electrodynamics  quantum mechanics  decoherence  interpretations  pilotwave theory  Bohmian mechanics  Born rule statistics  measurement problem  quantum thermodynamics  strong coupling  operator thermodynamic functions  quantum theory  de Broglie–Bohm theory  contextuality  atomsurface scattering  bohmian mechanics  matterwave optics  diffraction  vortical dynamics  Schrödinger equation  de Broglie–Bohm theory  nonequilibrium thermodynamics  zeropoint field  de Broglie–Bohm interpretation of quantum mechanics  pilot wave  interiorboundary condition  ultraviolet divergence  quantum field theory  Aharonov–Bohm effect  physical ontology  nomology  interpretation  gauge freedom  Canonical Presentation  relational space  relational interpretation of quantum mechanics  measurement problem  nonlocality  discrete calculus  iterant  commutator  diffusion constant  LeviCivita connection  curvature tensor  constraints  Kilmister equation  Bianchi identity  stochastic differential equations  Monte Carlo simulations  Burgers equation  Langevin equation  fractional velocity  interpretations of quantum mechanics  David Bohm  mind–body problem  quantum holism  fundamental irreversibility  spacetime fluctuations  spontaneous state reduction  Poincaré recurrence  symplectic camel  quantum mechanics  Hamiltonian  molecule interference  matterwaves  metrology  magnetic deflectometry  photochemistry  past of the photon  Mach–Zehnder interferometer  Dove prism  photon trajectory  weak measurement  transition probability amplitude  atomic metastable states  Bell’s theorem  Bohmian mechanics  nonlocality  many interacting worlds  wavefunction nodes  bouncing oil droplets  stochastic quantum dynamics  de Broglie–Bohm theory  quantum nonequilibrium  Htheorem  ergodicity  ontological quantum mechanics  objective nonsignaling constraint  quantum inaccessibility  epistemic agent  emergent quantum state  selfreferential dynamics  dynamical chaos  computational irreducibility  undecidable dynamics  Turing incomputability  quantum ontology  nonlocality  timesymmetry  retrocausality  quantum causality  conscious agent  emergent quantum mechanics  Bohmian mechanics  de BroglieBohm theory
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