LEADER 10601nam 2200613 450 001 996495171703316 005 20230606145851.0 010 $a3-031-06170-5 035 $a(MiAaPQ)EBC7105452 035 $a(Au-PeEL)EBL7105452 035 $a(CKB)24978727900041 035 $a(PPN)265857988 035 $a(EXLCZ)9924978727900041 100 $a20230307d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInfinite dimensional analysis, quantum probability and applications $eQP41 Conference, Al Ain, UAE, March 28-April 1, 2021 /$fLuigi Accardi, Farrukh Mukhamedov, and Ahmed Al Rawashdeh 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2022] 210 4$d©2022 215 $a1 online resource (369 pages) 225 1 $aSpringer Proceedings in Mathematics & Statistics 311 08$aPrint version: Accardi, Luigi Infinite Dimensional Analysis, Quantum Probability and Applications Cham : Springer International Publishing AG,c2022 9783031061691 327 $aIntro -- Organization -- Preface -- Contents -- Part I Quantum Probability Methods -- The Non-linear and Quadratic Quantization Programs -- 1 Introduction -- 1.1 Quadratic Quantization -- 2 Some Properties of *-Lie Algebras -- 2.1 The Complex d-Dimensional Heisenberg Algebra: heis1,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) -- 2.2 The Complex d-Dimensional Quadratic Heisenberg Algebra heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) -- 3 The Symplectic Approach to Homogeneous Quadratic Boson Fields -- 3.1 The *-Lie Algebra of Homogeneous Quadratic Boson Fields -- 3.2 Identification of the *-Lie Algebra of Homogeneous Quadratic Boson Fields with heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) -- 3.3 Central Decomposition of heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900): heis2,d,cls(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) -- 4 The Complex Symplectic *-Lie Algebra sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) -- 4.1 The Involution on sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) : sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) -- 4.2 *-Isomorphism Between heis2,d, cls(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and sp(2d,0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) -- 4.3 The Isomorphism Between heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and sp(2d, 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) : Direct Proof -- 5 Real Lie Sub-algebras of heis2,d(0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and spskew,(2d,0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900). 327 $a5.1 Real *-Lie Algebra-Isomorphism Between spskew,(2d,0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900 0=Ctoheight0.900) and sp-(2d,IR) -- 6 Vacuum Averages -- 7 Lie Groups Associated with the Symplectic Algebra -- 7.1 The Siegel Unit Disk -- 7.2 The Metaplectic Group -- 7.3 The Abstract Symplectic Algebra and Its Lie Groups -- 8 The Problems of Diagonalizability and Vacuum Factorizability -- 8.1 Diagonalizability and Factorizability of Quadratic Fields -- 8.2 Diagonalizability Implies Vacuum-Factorizability -- References -- A Pedagogical Note on the Computation of Relative Entropy of Two n-Mode Gaussian States -- 1 Introduction -- 2 Preliminary Concepts on Gaussian States -- 3 Williamson's Theorem Applied to n-Mode Gaussian Covariance Matrix -- 4 Structure Theorem for n-Mode Gaussian States -- 5 Relative Entropy S(?vertvert?) of Two Gaussian States -- 6 Petz-Rényi Relative Entropy S?(?vertvert?), 0< -- ?< -- 1 of Two Gaussian States -- References -- Quantum Operators of the Semicircle Distributions -- 1 Introduction -- 2 Background -- 3 Position-(0-Momentum) Decomposition of the Semicircle Distributions -- References -- Quantum Probability for Modeling Cognition, Decision Making, and Artificial Intelligence -- 1 Introduction -- 2 Classical Versus Quantum Probability -- 2.1 Interference of Probabilities -- 2.2 Bayesian Versus Non-Bayesian Inference -- 3 Quantum-Like Paradigm -- 4 Paradoxes of CP Decision Theory and Their QP Resolution -- 5 Quantum Scheme of Decision Making -- 6 Interference in Decision Making -- 6.1 Savage Sure Thing Principle as the Rationality Axiom -- 6.2 Is CP-Irrationality Just QP-Rationality? -- 6.3 Logic and Rationality -- 6.4 Social Laser -- 7 Quantum-Like AI -- References -- Part II Quantum Information Methods -- Note on Complexity of Communication Processes -- 1 Introduction -- 2 Quantum Channels. 327 $a2.1 Quantum Communication Processes -- 3 Entropy and Mutual Entropy for General Quantum Systems -- 4 Compound States -- 5 Conclusion -- References -- Trace Decreasing Quantum Dynamical Maps: Divisibility and Entanglement Dynamics -- 1 Introduction -- 2 Trace Distance Approach to Non-Markovianity -- 3 System-Ancilla Entanglement Dynamics -- 4 Generalized Erasure Dynamics -- 5 Conclusions -- References -- Compound State, Its Conditionality and Quantum Mutual Information -- 1 Introduction -- 2 Quantum Compound States and CP Maps -- 2.1 Preliminaries -- 2.2 Duality Between Quantum States and Linear Maps, and Their Classification -- 2.3 Quantum Compound State Versus Classical Joint Probability -- 3 Quantum Mutual Information on Quantum Bayes Formula -- 3.1 Compound State via Choi-Jamio?kowski Isomorphism -- 3.2 Quantum Mutual Information via Quantum Channel ?ast -- 4 Conclusions -- References -- Block Markov Chains on Trees -- 1 Introduction -- 2 Rooted Trees -- 3 Some Reminders on Markov Fields -- 4 Structure of Block Markov Chains on Trees -- 5 Connection with MCs and MRFs -- 6 One-Dimensional BMC -- 7 Counter-Example -- 8 Conclusion -- References -- Part III Quantum Dynamical Systems -- Hilbert von Neumann Modules Versus Concrete von Neumann Modules -- 1 Von Neumann Modules: Comparison -- 2 Self-duality -- 3 Von Neumann Correspondences, Connes Correspondences, and Their Tensor Products -- References -- Absorption and Fixed Points for Semigroups of Quantum Channels -- 1 Introduction -- 2 Preliminaries on Semigroups of Quantum Channels -- 3 Absorption Operators to Describe Fixed Points -- 4 Reducibility of Recurrent Semigroups -- References -- Characterization of Gaussian Quantum Markov Semigroups -- 1 Introduction -- 2 Gaussian States -- 3 Gaussian Maps -- 4 Gaussian Quantum Markov Semigroups -- References -- A Mean-Field Laser Quantum Master Equation. 327 $a1 Introduction -- 2 The Quantum Master Equation -- 3 Quantum Hopf Bifurcation -- 3.1 Long-Time Behaviour -- 4 Conclusions and Outlook -- References -- Unique Ergodicity and Weakly Monotone Fock Space -- 1 Introduction -- 2 Preliminaries -- 3 Weakly Monotone Fock Space -- 4 Shift-Invariant States on Weakly Monotone upper C Superscript asteriskC*-Algebra -- References -- Part IV Infinite Dimensional Analysis -- Solutions of Infinite Dimensional Partial Differential Equations -- 1 Introduction and Background -- 1.1 Young Functions -- 1.2 Functional Spaces -- 1.3 Formal Power Series Spaces -- 1.4 Taylor Map -- 1.5 Laplace Transform -- 2 Convolution Calculus -- 2.1 Convolution of Two Distributions -- 2.2 White Noise Gel'fand Triple -- 2.3 Convolution Functionals -- 3 Initial-Valued Evolution Equation -- 3.1 Main Theorem -- 4 Gross Laplacian -- 4.1 Gross Laplacian as a Convolution Operator -- 5 Concluding Remarks -- 5.1 Interpretation of the Solutions of the Evolution Equation -- 5.2 Heat Equation Associated to the Gross Laplacian -- References -- On Some Properties of Solution Sets of Discontinuous Quantum Stochastic Differential Inclusions -- 1 Introduction -- 2 Notations and Fundamental Structures -- 3 Preliminary Results and Assumptions -- 4 Main Result -- References -- Fractional Operators from Vanishing Morrey to Vanishing Campanato Spaces in the Variable Exponent Setting on Quasi-metric Measure Spaces -- 1 Introduction -- 2 Preliminaries -- 2.1 Quasi-metric Measure Spaces -- 2.2 Variable Exponent Spaces -- 3 Boundedness Result -- References -- Part V Operator Algebras -- Characterization of Certain Traces on von Neumann Algebras -- 1 Introduction -- 2 Definitions and Notation -- 3 Trace Characterization on upper C Superscript asteriskC*-Algebras -- References -- Actions of *-Morphisms on Certain Projections of C*-Matrix Algebras -- 1 Introduction. 327 $a2 Preliminaries -- 3 Actions of *-Morphisms on Pi,j(a) -- References -- Part VI Stochastic Operators -- Compatible Linear Lypunov Function for Infinite Dimensional Volterra Quadratic Stochastic Operators -- 1 Introduction -- 2 Main Results -- References -- Bijectivity of a Class of Lotka-Volterra Operators Defined on 2D-Simplex -- 1 Introduction -- 2 Preliminaries -- 3 Main Result -- 4 Conclusion -- References -- Dynamics of Stochastic Cesaro Operators -- 1 Introduction -- 2 Nonlinear Stochastic Operators Generated by Linear Ones -- 3 Riesz Stochastic Operators -- 4 Cesaro Operators -- References -- The Dynamics of a Volterra Cubic Operator -- 1 Introduction -- 2 Preliminaries -- 3 Main Results -- References -- The Dynamics of Superposition of Non-Volterra Quadratic Stochastic Operators on upper S squaredS2 -- 1 Introduction -- 2 Preliminaries -- 3 Superposition of Operators -- 4 Notes and Comments -- References -- A Quadratic Worm Propagation Model -- 1 Introduction -- 2 Preliminaries -- 3 Discrete Time SIR-models -- References -- Author Index. 410 0$aSpringer proceedings in mathematics & statistics. 606 $aDimensional analysis 606 $aProbabilities$vCongresses 606 $aAnàlisi dimensional$2thub 606 $aProbabilitats$2thub 606 $aTeoria quàntica$2thub 608 $aCongressos$2thub 608 $aLlibres electrònics$2thub 615 0$aDimensional analysis. 615 0$aProbabilities 615 7$aAnàlisi dimensional 615 7$aProbabilitats 615 7$aTeoria quàntica 676 $a530.8 700 $aAccardi$b Luigi$0464431 702 $aMukhamedov$b Farrukh 702 $aAl Rawashdeh$b Ahmed 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996495171703316 996 $aInfinite dimensional analysis, quantum probability and applications$93056928 997 $aUNISA LEADER 04373nam 22006615 450 001 9910483770303321 005 20240508185522.0 010 $a9789812874412 010 $a9812874410 024 7 $a10.1007/978-981-287-441-2 035 $a(CKB)3710000000415810 035 $a(EBL)2094464 035 $a(SSID)ssj0001501428 035 $a(PQKBManifestationID)11968022 035 $a(PQKBTitleCode)TC0001501428 035 $a(PQKBWorkID)11524809 035 $a(PQKB)11584722 035 $a(DE-He213)978-981-287-441-2 035 $a(MiAaPQ)EBC2094464 035 $a(PPN)186025963 035 $a(EXLCZ)993710000000415810 100 $a20150518d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDevelopment of Science Teachers' TPACK $eEast Asian Practices /$fedited by Ying-Shao Hsu 205 $a1st ed. 2015. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2015. 215 $a1 online resource (165 p.) 300 $aDescription based upon print version of record. 311 08$a9789812874405 311 08$a9812874402 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aPreface -- Part I TPACK in Teaching Practices -- Chapter 1 The development of teachers' professional learning and knowledge -- Chapter 2 The TPACK-P framework for science teachers in a practical teaching context -- Chapter 3 The current status of science teachers' TPACK in Taiwan from interview data -- Part II The Transformative Model of TPACK -- Chapter 4 Rubrics of TPACK-P for teaching science with ICTs -- Chapter 5 -- Applying TPACK-P to a teacher education program -- Part III The Integrative Model of TPACK -- Chapter 6 Developing preservice teachers' sensitivity to the interplay between subject matter, pedagogy and ICTs -- Chapter 7 Examining teachers' TPACK in using e-learning resources in primary science lessons -- Part IV Epilogue -- Chapter 8 The end of the beginning: An epilogue. 330 $aScience is a subject matter that requires learners to explore the world and develop their own abilities on the basis of that exploration. As technology broadens and deepens, science teachers need to expand their Technological Pedagogical Content Knowledge (TPACK), which determines how well they use technology to help students learn science. The book details our efforts to prepare science teachers to teach with the help of technology, examining various aspects of teacher education, professional development, and teaching material preparation. It consists of three parts, which focus on: how TPACK is conceptually constructed within the field of science education, how teacher evaluation and teaching materials are developed and utilized based on the transformative model, and how science teachers are prepared and supported with electronic resources based on the integrative model. The book offers a valuable resource for all those working in science education, as well as those readers who are interested in teacher education. Science teachers will come to know how simulations and animations can pedagogically support student learning. Practices for teachers? TPACK development such as learning-by-design, evaluation and measurement, and teacher communities are also addressed, applied and discussed in the case of science teachers. The individual chapters will provide teacher educators and researchers from all disciplines with new insights into preparing teachers for the Digital Era. 606 $aScience$xStudy and teaching 606 $aTeachers$xTraining of 606 $aTechnical education 606 $aScience Education 606 $aTeaching and Teacher Education 606 $aEngineering and Technology Education 615 0$aScience$xStudy and teaching. 615 0$aTeachers$xTraining of. 615 0$aTechnical education. 615 14$aScience Education. 615 24$aTeaching and Teacher Education. 615 24$aEngineering and Technology Education. 676 $a370 676 $a370711 676 $a507.1 676 $a607.11 702 $aHsu$b Ying-Shao$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910483770303321 996 $aDevelopment of Science Teachers' TPACK$92596794 997 $aUNINA