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The authors present one of the most important contributions of statistics to the discussion of causality, through the model of potential responses proposed by Rubin, and its interface with the epidemiological method. Of particular interest are the scientific and statistical solutions explored, in addition to the underlying premises of homogeneity and stability. The work establishes a dialogue with epidemiology in which the identities of each discipline are valued and protected. The interdisciplinary spirit makes this work important not only for epidemiologists and biostatisticians, but also for other public health professionals who aim to expand their view on the issue of causality.
Epidemiology. --- Causality (Physics) --- Causality --- Heisenberg uncertainty principle --- Nuclear physics --- Physics --- Quantum theory --- Diseases --- Public health --- Philosophy --- Modelos epidemiológicos --- Inferência --- Causalidade
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The present volume collects the contributions selected for publication in the Special Issue entitled "Microlocal and Time-Frequency Analysis" of the journal Mathematics, edited by Elena Cordero and S. Ivan Trapasso over 2020 and 2021.
pseudodifferential operators --- Gevrey regularity --- sharp Gårding inequality --- p-evolution equations --- ultradifferentiable functions --- ultradistributions --- extended Gevrey regularity --- boundary values of analytic functions --- wave front sets --- Rio Papaloapan Bridge --- vibration signals --- damage identification --- wavelet energy accumulation method --- admissibility condition --- the continuous wavelet transform --- inversion formula --- semi-discrete wavelet transform --- tight frames --- covriance matrix --- polar duality --- uncertainty principle --- reconstruction problem --- BBM equation --- ill-posedness --- Fourier amalgam spaces --- Wiener amalgam spaces --- Fourier–Lebesgue spaces --- modulation spaces --- bounded measures --- convolution --- homogeneous Banach spaces --- integrated group representation --- Segal algebra --- Wiener amalgam space --- bounded uniform partition of unity --- locally compact groups
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The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties.
entanglement indicators --- generalized uncertainty principle --- Tsallis entropy --- linear entropy --- quantum-classical relationship --- Wigner–Yanase–Dyson skew information --- deep learning --- spinors in quantum and classical physics --- quantum mechanics --- entropy --- original Bell inequality --- Bohmian dynamics --- qudit states --- square integrable --- uncertainty relation --- quantum bound --- uncertainty relations --- foundations of quantum mechanics --- Born probability rule --- Rényi entropy --- energy quantization --- quantum foundations --- Born rule --- measure of classicality --- minimal observable length --- quantum information --- Kochen–Specker theorem --- neuromorphic computing --- bell inequalities --- successive measurements --- Gleason theorem --- continuous variables --- quantum memory --- perfect correlation/anticorrelation --- quantum trajectory --- quantum computing --- high performance computing --- Quantum Hamilton-Jacobi Formalism --- quantum uncertainty
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The importance and usefulness of subjects and topics involving integral transformations and operational calculus are becoming widely recognized, not only in the mathematical sciences but also in the physical, biological, engineering and statistical sciences. This book contains invited reviews and expository and original research articles dealing with and presenting state-of-the-art accounts of the recent advances in these important and potentially useful subjects.
Research & information: general --- Mathematics & science --- approximation operators --- differences of operators --- Szász–Mirakyan–Baskakov operators --- Durrmeyer type operators --- Bernstein polynomials --- modulus of continuity --- starlike functions --- subordination --- q-Differential operator --- k-Fibonacci numbers --- Lorentz invariant complex measures --- Minkowski space --- spectral decomposition --- measure convolution --- measure product --- Feynman propagator --- q-difference operator --- Janowski function --- meromorphic multivalent function --- distortion theorem --- partial sum --- closure theorem --- analytic functions --- multivalent (or p-valent) functions --- differential subordination --- q-derivative (or q-difference) operator --- Dunkel type integral inequality --- Schur-convexity --- majorization theory --- arithmetic mean-geometric mean (AM-GM) inequality --- Lerch function --- quadruple integral --- contour integral --- logarithmic function --- preinvex fuzzy mappings --- strongly preinvex fuzzy mappings --- strongly invex fuzzy mappings --- strongly fuzzy monotonicity --- strongly fuzzy mixed variational-like inequalities --- Fourier integral theorem --- double integral --- exponential function --- Catalan’s constant --- Aprey’s constant --- non-separable linear canonical wavelet --- symplectic matrix --- non-separable linear canonical transform --- uncertainty principle --- Fox–Wright function --- generalized hypergeometric function --- Mittag–Leffler function
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The first quantum revolution started in the early 20th century and gave us new rules that govern physical reality. Accordingly, many devices that changed dramatically our lifestyle, such as transistors, medical scanners and lasers, appeared in the market. This was the origin of quantum technology, which allows us to organize and control the components of a complex system governed by the laws of quantum physics. This is in sharp contrast to conventional technology, which can only be understood within the framework of classical mechanics. We are now in the middle of a second quantum revolution. Although quantum mechanics is nowadays a mature discipline, quantum engineering as a technology is now emerging in its own right. We are about to manipulate and sense individual particles, measuring and exploiting their quantum properties. This is bringing major technical advances in many different areas, including computing, sensors, simulations, cryptography and telecommunications. The present collection of selected papers is a clear demonstration of the tremendous vitality of the field. The issue is composed of contributions from world leading researchers in quantum optics and quantum information, and presents viewpoints, both theoretical and experimental, on a variety of modern problems.
entangled states --- two atoms --- two-modes --- cavity QED setup --- entanglement --- interference phenomenon --- superposition of quantum states --- quantum tomograms --- quantum optics --- nonclassicality --- quantum resource theories --- non-Gaussianity --- photon-number-resolving detectors --- multiport devices --- Fock states --- quantum tomography --- photon losses --- relativistic dynamics --- no-interaction theorem --- world line condition --- circular gauge --- Landau gauge --- arbitrary linear gauge --- stepwise variation --- center-of-orbit coordinates --- relative coordinates --- elliptic and hyperbolic solenoids --- angular momentum --- magnetic moment --- squeezing --- mutually unbiased bases --- group representations --- graphs --- quantum information --- E = mc2 from Heisenberg’s uncertainty relations --- one symmetry for quantum mechanics and special relativity --- coherent states --- harmonic oscillator --- SU(2) coherent states --- 2D coherent states --- resolution of the identity --- uncertainty principle --- isotropic harmonic oscillator --- anisotropic harmonic oscillator --- Sudarshan --- apology --- non-hermitian operators --- real spectrum --- nonlinear algebras --- nonclassical states --- bound entanglement --- entanglement witness --- Hilbert–Schmidt measure --- optimization algorithms --- probability representation --- quantizer–dequantizer --- qubit --- quantum suprematism --- n/a --- E = mc2 from Heisenberg's uncertainty relations --- Hilbert-Schmidt measure --- quantizer-dequantizer --- Research.
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