LEADER 04108nam 2200661 450 001 9910463953703321 005 20200520144314.0 024 7 $a10.1515/9781400866618 035 $a(CKB)2670000000608122 035 $a(EBL)1929549 035 $a(OCoLC)908080604 035 $a(SSID)ssj0001530093 035 $a(PQKBManifestationID)12644359 035 $a(PQKBTitleCode)TC0001530093 035 $a(PQKBWorkID)11530557 035 $a(PQKB)10153402 035 $a(MiAaPQ)EBC1929549 035 $a(StDuBDS)EDZ0001756485 035 $a(DE-B1597)459971 035 $a(OCoLC)979630235 035 $a(DE-B1597)9781400866618 035 $a(Au-PeEL)EBL1929549 035 $a(CaPaEBR)ebr11040168 035 $a(CaONFJC)MIL762949 035 $a(EXLCZ)992670000000608122 100 $a20150415h20152015 uy 0 101 0 $aeng 135 $aur|u---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aAction-minimizing methods in Hamiltonian dynamics $ean introduction to Aubry-Mather theory /$fAlfonso Sorrentino 205 $aPilot project,eBook available to selected US libraries only 210 1$aPrinceton, [New Jersey] ;$aOxford, [England] :$cPrinceton University Press,$d2015. 210 4$dİ2015 215 $a1 online resource (129 p.) 225 0 $aMathematical Notes ;$v50 300 $aDescription based upon print version of record. 311 0 $a0-691-16450-9 311 0 $a1-4008-6661-8 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tPreface --$tChapter One. Tonelli Lagrangians and Hamiltonians on Compact Manifolds --$tChapter Two. From KAM Theory to Aubry-Mather Theory --$tChapter Three. Action-Minimizing Invariant Measures for Tonelli Lagrangians --$tChapter Four. Action-Minimizing Curves for Tonelli Lagrangians --$tChapter Five. The Hamilton-Jacobi Equation and Weak KAM Theory --$tAppendices --$tAppendix A. On the Existence of Invariant Lagrangian Graphs --$tAppendix B. Schwartzman Asymptotic Cycle and Dynamics --$tBibliography --$tIndex 330 $aJohn Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic.Starting with the mathematical background from which Mather's theory was born, Alfonso Sorrentino first focuses on the core questions the theory aims to answer-notably the destiny of broken invariant KAM tori and the onset of chaos-and describes how it can be viewed as a natural counterpart of KAM theory. He achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. Sorrentino then describes the whole theory and its subsequent developments and applications in their full generality.Shedding new light on John Mather's revolutionary ideas, this book is certain to become a foundational text in the modern study of Hamiltonian systems. 410 0$aMathematical notes (Princeton University Press) ;$v50. 606 $aHamiltonian systems 606 $aHamilton-Jacobi equations 608 $aElectronic books. 615 0$aHamiltonian systems. 615 0$aHamilton-Jacobi equations. 676 $a514.74 700 $aSorrentino$b Alfonso$01050882 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910463953703321 996 $aAction-minimizing methods in Hamiltonian dynamics$92480988 997 $aUNINA LEADER 05384nam 2200697Ia 450 001 9911020143503321 005 20200520144314.0 010 $a9786612688096 010 $a9781282688094 010 $a128268809X 010 $a9783527628124 010 $a3527628126 010 $a9783527628131 010 $a3527628134 035 $a(CKB)1000000000790388 035 $a(EBL)481435 035 $a(OCoLC)495194020 035 $a(SSID)ssj0000340522 035 $a(PQKBManifestationID)11215314 035 $a(PQKBTitleCode)TC0000340522 035 $a(PQKBWorkID)10387053 035 $a(PQKB)10850009 035 $a(MiAaPQ)EBC481435 035 $a(PPN)243204418 035 $a(Perlego)2764934 035 $a(EXLCZ)991000000000790388 100 $a20010321d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMolecular modeling of inorganic compounds /$fPeter Comba, Trevor W. Hambley 205 $a2nd, completely rev. and enl. ed. 210 $aWeinheim ;$aNew York $cWiley-VCH$dc2001 215 $a1 online resource (346 p.) 300 $aDescription based upon print version of record. 311 08$a9783527317998 311 08$a3527317996 320 $aIncludes bibliographical references (p. [309]-320) and index. 327 $aMolecular Modeling of Inorganic Compounds; Contents; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; Part I: Theory; 1 Introduction; 1.1 Molecular Modeling; 1.2 Historical Background; 2 Molecular Modeling Methods in Brief; 2.1 Molecular Mechanics; 2.2 Quantum Mechanics; 2.2.1 Hartree-Fock Calculations; 2.2.2 Semi-Empirical Approaches; 2.2.3 Density Functional Theory; 2.2.4 Methods and Basis Sets; 2.3 Other Methods; 2.3.1 Conformational Searching; 2.3.1.1 Stochastic Methods; 2.3.1.2 Molecular Dynamics; 2.3.2 Database Searching; 2.3.3 Cluster Analysis 327 $a2.3.4 Free Energy Perturbation2.3.5 QSAR; 3 Parameterization, Approximations and Limitations of Molecular Mechanics; 3.1 Concepts; 3.2 Potential Energy Functions; 3.2.1 Bond Length Deformation; 3.2.2 Valence Angle Deformation; 3.2.3 Torsion Angle Deformation; 3.2.4 Cross-Terms; 3.2.5 van der Waals Interactions; 3.2.6 Electrostatic Interactions; 3.2.7 Hydrogen Bonding Interactions; 3.2.8 Out-of-Plane Deformation; 3.3 Force-Field Parameters; 3.3.1 Bond Length Deformation; 3.3.2 Valence Angle Deformation; 3.3.3 Torsion Angle Deformation; 3.3.4 Out-of-Plane Deformation 327 $a3.3.5 Non-Bonded Interactions3.3.6 Electrostatic Interactions; 3.3.7 Hydrogen-Bonding Interactions; 3.4 Spectroscopic Force Fields; 3.5 Model and Reality; 3.6 Electronic Effects; 3.7 The Environment; 3.8 Entropy Effects; 3.9 Summary; 4 Computation; 4.1 Input and Output; 4.2 Energy Minimization; 4.2.1 The Simplex Method; 4.2.2 Gradient Methods; 4.2.3 Conjugate-Gradient Methods; 4.2.4 The Newton-Raphson Method; 4.2.5 Least-Squares Methods; 4.3 Constraints and Restraints; 5 The Multiple Minima Problem; 5.1 Deterministic Methods; 5.2 Stochastic Methods; 5.3 Molecular Dynamics 327 $a5.4 Practical Considerations5.5 Making Use of Experimental Data; 6 Conclusions; Part II: Applications; 7 Structural Aspects; 7.1 Accuracy of Structure Prediction; 7.2 Molecular Visualization; 7.3 Isomer Analysis; 7.4 Analysis of Structural Trends; 7.5 Prediction of Complex Polymerization; 7.6 Unraveling Crystallographic Disorder; 7.7 Enhanced Structure Determination; 7.8 Comparison with Solution Properties; 8 Stereoselectivities; 8.1 Conformational Analysis; 8.2 Enantioselectivities; 8.2.1 Racemate Separation; 8.2.2 Stereoselective Synthesis; 8.2.3 Prediction of Enantioinduction 327 $a8.3 Structure Evaluation8.4 Mechanistic Information; 9 Metal Ion Selectivity; 9.1 Chelate Ring Size; 9.2 Macrocycle Hole Size; 9.3 Preorganization; 9.4 Quantitative Correlations Between Strain and Stability Differences; 9.5 Conclusions; 10 Spectroscopy; 10.1 Vibrational Spectroscopy; 10.2 Electronic Spectroscopy; 10.3 EPR Spectroscopy; 10.4 NMR Spectroscopy; 10.5 QM-Based Methods; 11 Electron Transfer; 11.1 Redox Potentials; 11.2 Electron-Transfer Rates; 12 Electronic Effects; 12.1 d-Orbital Directionality; 12.2 The trans Influence; 12.3 Jahn-Teller Distortions; 13 Bioinorganic Chemistry 327 $a13.1 Complexes of Amino Acids and Peptides 330 $aAfter the second edition introduced first density functional theory aspects, this third edition expands on this topic and offers unique practice in molecular mechanics calculations and DFT. In addition, the tutorial with its interactive exercises has been completely revised and uses the very latest software, a full version of which is enclosed on CD, allowing readers to carry out their own initial experiments with forcefield calculations in organometal and complex chemistry. 606 $aInorganic compounds$xMathematical models 606 $aChemical models 615 0$aInorganic compounds$xMathematical models. 615 0$aChemical models. 676 $a541.22015118 700 $aComba$b Peter$0621773 701 $aHambley$b Trevor W$01837966 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020143503321 996 $aMolecular modeling of inorganic compounds$94416837 997 $aUNINA