LEADER 04459nam 2200577 450 001 9910822597303321 005 20220823074619.0 010 $a0-8218-8535-9 035 $a(CKB)3240000000070086 035 $a(EBL)3113337 035 $a(SSID)ssj0000601382 035 $a(PQKBManifestationID)11361987 035 $a(PQKBTitleCode)TC0000601382 035 $a(PQKBWorkID)10566369 035 $a(PQKB)10960870 035 $a(MiAaPQ)EBC3113337 035 $a(RPAM)17113804 035 $a(PPN)197102069 035 $a(EXLCZ)993240000000070086 100 $a20120110h20122012 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAlgebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics $eJairo Charris Seminar 2010, Universidad Sergio Arboleda, Santa Marta, Colombia /$fPrimitivo B. Acosta-Huma?nez [and three others], editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society ;$a[Madrid] :$cInstituto de Matematicas y sus Aplicaciones,$d[2012] 210 4$dİ2012 215 $a1 online resource (226 p.) 225 1 $aContemporary mathematics,$v563$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-7584-1 320 $aIncludes bibliographical references. 327 $aPreface -- Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials -- 1. Introduction -- 2. Background -- 3. Integrability of equation (1) by Picard-Vessiot -- 4. Spectral/quadrature duality. An integration procedure -- 5. The I??-functons -- 6. Integration as a linearly exponential I??-extension -- 7. Integrability and differential closedness -- 8. Definition of through Liouvillian extension -- 9. Non-finite-gap integrable counterexamples -- 10. Concluding remarks -- References -- Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty -- 1. Introduction -- 2. A brief outline of supersymmetric quantum mechanics -- 3. EOP's associated with broken supersymmetry -- 4. Relation with higher order Darboux transformation -- 5. Information-theoretic lengths for the partner potential of linear harmonic oscillator via supersymmetry -- 6. Moment of the quantum mechanical states associated with the partner of harmonic oscillator via supersymmetry -- 7. Discussion: -- References -- On orthogonal polynomials spanning a non-standard flag -- 1. Introduction -- 2. Preliminaries -- 3. Codimension 1 flags -- 4. Higher codimension flags -- Acknowledgements -- References -- On the Supersymmetric Spectra of two Planar Integrable Quantum Systems -- 1. Introduction -- 2. =2 supersymmetric planar quantum systems -- 3. The planar quantum Kepler/Coulomb problem and supersymmetry -- 4. The planar quantum Euler/Coulomb problem and supersymmetry -- 5. Two center collapse in one center -- 6. Further comments -- Acknowledgements -- References -- Solvable rational extension of translationally shape invariant potentials -- Introduction -- 1. Solvable rational extensions of the harmonic oscillator -- 2. Second category potentials -- 3. Conclusion -- Acknowledgments -- References -- The pentagram map: geometry, algebra, integrability -- 1. Introduction: The pentagram map -- 2. Complete integrability of the pentagram map on the space _{ } -- 3. Relation to the Boussinesq equation -- 4. The space _{ } and 2-frieze patterns -- Acknowledgments -- References -- Jet Bundles, symmetries, Darboux transforms -- Elliptic beta integrals and solvable models of statistical mechanics. 410 0$aContemporary mathematics (American Mathematical Society).$v563$x0271-4132 606 $aDifferential algebra$vCongresses 606 $aDarboux transformations$vCongresses 606 $aQuantum theory$xMathematics$vCongresses 615 0$aDifferential algebra 615 0$aDarboux transformations 615 0$aQuantum theory$xMathematics 676 $a512/.56 686 $a12H05$a33E30$a81Q60$a81Q80$a82B23$a33E99$2msc 702 $aAcosta Humanez$b Primitivo B. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910822597303321 996 $aAlgebraic aspects of Darboux transformations, quantum integrable systems, and supersymmetric quantum mechanics$9241049 997 $aUNINA LEADER 03612nam 22006735 450 001 996309060403316 005 20231110212445.0 024 7 $a10.1515/9783110562545 035 $a(CKB)4100000002260369 035 $a(DE-B1597)487705 035 $a(OCoLC)1024006445 035 $a(DE-B1597)9783110562545 035 $a(MiAaPQ)EBC5511088 035 $a(Au-PeEL)EBL5511088 035 $a(EXLCZ)994100000002260369 100 $a20190615d2017 fg 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProbability and Statistics $eA Course for Physicists and Engineers /$fArak M. Mathai, Hans J. Haubold 210 1$aBerlin ;$aBoston : $cDe Gruyter, $d[2017] 210 4$dİ2018 215 $a1 online resource (604 p.) 225 0 $aDe Gruyter Textbook 311 $a3-11-056253-7 311 $a3-11-056254-5 327 $tFrontmatter -- $tIntroduction / $rMathai, A. M. / Haubold, Hans J. -- $tPreface / $rMathai, A. M. / Haubold, Hans J. -- $tAcknowledgement -- $tContents -- $tList of Tables -- $tList of Symbols -- $t1. Random phenomena -- $t2. Probability -- $t3. Random variables -- $t4. Expected values -- $t5. Commonly used discrete distributions -- $t6. Commonly used density functions -- $t7. Joint distributions -- $t8. Some multivariate distributions -- $t9. Collection of random variables -- $t10. Sampling distributions -- $t11. Estimation -- $t12. Interval estimation -- $t13. Tests of statistical hypotheses -- $t14. Model building and regression -- $t15. Design of experiments and analysis of variance -- $t16. Questions and answers -- $tTables of percentage points -- $tReferences -- $tIndex 330 $aThis book offers an introduction to concepts of probability theory, probability distributions relevant in the applied sciences, as well as basics of sampling distributions, estimation and hypothesis testing. As a companion for classes for engineers and scientists, the book also covers applied topics such as model building and experiment design. ContentsRandom phenomenaProbabilityRandom variablesExpected valuesCommonly used discrete distributionsCommonly used density functionsJoint distributionsSome multivariate distributionsCollection of random variablesSampling distributionsEstimationInterval estimationTests of statistical hypothesesModel building and regressionDesign of experiments and analysis of varianceQuestions and answers 410 3$aDe Gruyter Textbook 606 $aEngineering$xStatistical methods$vTextbooks 606 $aProbabilities$vTextbooks 606 $aModellbildung 606 $aStatistik 606 $aVersuchsplanung 606 $aWahrscheinlichkeitsrechnung 606 $3(DE-601)106075764$3(DE-588)4079013-7$aWahrscheinlichkeitstheorie$2gnd 606 $3(DE-601)106152955$3(DE-588)4056995-0$aStatistik$2gnd 606 $aMATHEMATICS / Probability & Statistics / General$2bisacsh 615 0$aEngineering$xStatistical methods 615 0$aProbabilities 615 4$aModellbildung. 615 4$aStatistik. 615 4$aVersuchsplanung. 615 4$aWahrscheinlichkeitsrechnung. 615 7$aWahrscheinlichkeitstheorie 615 7$aStatistik 615 7$aMATHEMATICS / Probability & Statistics / General. 676 $a519.2 686 $aSK 800$2rvk 700 $aMathai$b Arak M., $0868596 702 $aHaubold$b Hans J., 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a996309060403316 996 $aProbability and Statistics$91938987 997 $aUNISA