Kooperativer Bibliotheksverbund

UID:

Umfang: 1 online resource (457 pages)

ISBN: 9783319175454

Anmerkung: Intro -- Foreword -- Preface -- Acknowledgments -- Contents -- Acronyms -- Part I Reminiscences: Rolf Hagedorn and Relativistic Heavy Ion Research -- 1 Spotlight on Rolf Hagedorn -- 1.1 Working with Hagedorn -- Meeting Hagedorn -- A Short Story About Hagedorn Temperature -- Hot Nuclear Matter in the Statistical Bootstrap Model -- Higher Level Computer Language -- Relativistic Heavy Ion Collisions -- Strangeness and the Discovery of Quark-Gluon Plasma -- Retirement -- 1.2 The Righteous Man -- Helping Those in Need -- Le Chambon: A Short Story Outside the Physics Context -- 1.3 Rolf Hagedorn: Biographical Information -- Rolf Hagedorn Curriculum Vitae 1954 -- CERN Appointment -- CERN Obituary: Rolf Hagedorn 1919-2003 -- 2 Rolf Hagedorn: The Years Leading to TH -- 2.1 CERN Theory Division in 1960s -- 2.2 Hagedorn's Path to and at CERN -- The War Years -- At Göttingen -- At CERN -- 2.3 Appreciation -- 3 Music and Science: Tribute to Rolf Hagedorn -- 3.1 Personal Remarks -- Visit to India -- Art and Music -- 3.2 Contribution to Research -- Thermal Particle Production -- Limiting Temperature -- Statistical Bootstrap Model -- 3.3 Active Retirement -- 4 On Hagedorn -- 4.1 In Times Past -- 4.2 Wide Field of Interests -- 4.3 Retrospective -- 5 Hungarian Perspective -- 5.1 Influence Spreads to Hungary -- 5.2 Memories by István Montvay -- 5.3 Tamás Biró Grows up with Hagedorn -- 5.4 Hagedorn Remembered -- 6 The Tale of the Hagedorn Temperature -- 6.1 Particle Production -- 6.2 The Statistical Bootstrap Model -- 6.3 Quark-Gluon Plasma -- 7 The Legacy of Rolf Hagedorn: Statistical Bootstrap and Ultimate Temperature -- 7.1 Rolf Hagedorn -- 7.2 The Statistical Bootstrap -- 7.3 The Limiting Temperature of Hadronic Matter -- 7.4 Resonance Gas and QCD Thermodynamics -- 7.5 Resonance Gas and Heavy Ion Collisions. , 7.6 Particle Yields and Canonical Charge Conservation -- 7.7 Concluding Remarks -- References -- 8 The Hagedorn Spectrum and the Dual Resonance Model: An Old Love Affair -- Preamble -- 8.1 A Surprise That Should Not Have Been One -- 8.2 From TH to the String -- 8.3 Crisis, Reinterpretations -- 8.4 Many Years Later … -- Conclusion -- 9 Hadronic Matter: The Moscow Perspective -- 9.1 The Beginning -- Cosmic Rays and Landau -- Multiperipheral Collisions -- 9.2 Hot Hadron Matter -- Photons and Leptons -- Quark-Gluon Plasma -- Cherenkov Radiation -- Correlations and Fluctuations -- Charm -- 9.3 Open Questions -- Appreciation -- References -- 10 Hagedorn Model of Critical Behavior: Comparison of Lattice and SBM Calculations -- 10.1 Rolf Hagedorn: Some Personal Impressions -- 10.2 Critical Behavior of Hadronic Matter -- Critical Curve from the Lattice Calculations -- Critical Curve from the Statistical Bootstrap Model -- Comparison of SBM and Lattice-QCD -- 10.3 Conclusions -- References -- 11 Hagedorn's Hadron Mass Spectrum andthe Onset of Deconfinement -- 11.1 Hadron Mass Spectrum and the Hagedorn Temperature -- 11.2 Discovery of the Onset of Deconfinement -- References -- 12 Begin of the Search for the Quark-Gluon Plasma -- 12.1 The Beginning -- Bevalac and ISR -- SPS and RHIC Programs Take Shape -- 12.2 Quark-Gluon Plasma Discovered -- New Instrumentation -- Experiments -- 13 The Path to Heavy Ions at LHC and Beyond -- 13.1 Work at the Bevalac -- 13.2 …and at the SPS -- 13.3 How Heavy Ions Got into LHC and the ALICE Was Born -- 13.4 Future Facilities -- 13.5 Epilogue -- 14 A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature -- 14.1 From Hagedorn to Quark-Gluon Plasma -- Deconfinement of Quarks and Gluons -- Lattice QCD Results -- Hot Nuclear Matter -- 14.2 Path to Discovery of the QGP -- QGP Observables -- SPS Results. , Experiments at RHIC -- Experiments at LHC -- Beam Energy Scan at RHIC -- Next Steps -- 14.3 Outlook and Conclusions -- References -- 15 Reminscenses of Rolf Hagedorn -- 15.1 Many Years Ago -- 15.2 The Heavy Ion Era at CERN Begins -- 15.3 Experiments WA85-WA94-WA97-NA57 -- 15.4 The Other Hagedorn -- References -- Part II The Hagedorn Temperature -- 16 Boiling Primordial Matter: 1968 -- 16.1 The Large and the Small in the Universe -- The New Situation: Multiparticle Production in High Energy Physics -- Black Body Radiation -- 16.2 Highest Temperature = The Boiling Pointof Primordial Matter? -- 16.3 Is the Question About the ``Final Building Block''Meaningless? -- Possible Consequences in the Large? -- 17 The Long Way to the Statistical Bootstrap Model: 1994 -- 17.1 Introduction -- 17.2 From 1936 to 1965 -- Fireballs -- Multiple Production: Heisenberg (1936) -- Dulles-Walker Variables (1954) -- `Constant' Mean Transverse Momentum (1956) -- The Two-Centre Model (1958) -- Conclusion: Fireballs with Limited < -- p> -- Exist -- Statistical and Thermodynamical Methods -- Bohr's Compound Nucleus (1936) -- The Weisskopf Evaporation Model (1937) -- Koppe's Attempt and the Fermi Statistical Model (1948/1950) -- Beth-Uhlenbeck, Belenkij (1937/1956) -- The CERN Statistical Model (1958-1962) -- The Decisive Turn of the Screw: Large-Angle Elastic Scattering -- Statistical Model Description of Large-Angle Elastic Scattering -- Thermal Description -- Exponential or Not? -- Asymptotics of Momentum Space -- Interpretation: Distinguishable Particles and Pomeranchuk's Ansatz -- 17.3 The Statistical Bootstrap Model (SBM) -- A Few Well-Known Formulae -- Introducing the Statistical Bootstrap Hypothesis -- The Solution -- Further Developments -- 17.4 Some Further Remarks -- The Difficulty in Killing an Exponential Spectrum -- What is the Value of T0?. , Where Is Landau, Where Are the Californian Bootstrappers? -- 17.5 Conclusion -- Post Scriptum -- References -- 18 About `Distinguishable Particles' -- 18.1 Withdrawn Manuscript -- 18.2 Note by Rolf Hagedorn of 27 October 1964 -- 18.3 From Distinguishable Hadrons to SBM -- 18.4 Hagedorn Temperature as a General Physics Concept -- 19 Thermodynamics of Distinguishable Particles: A Key to High-Energy Strong Interactions? -- 19.1 Introduction -- 19.2 Statistical Thermodynamics of Distinguishable Particles -- 19.3 The Interpretation of the Model -- 19.4 Speculations on a More Realistic Model -- Angular Distribution and Multiplicity -- The Case of Nonzero Mass -- A Speculation on the Mass Spectrum of `Fireballs' -- Elastic and Exchange Scattering -- A Logical Difficulty of the Model -- 19.5 Summary and Conclusions -- Appendix 1 -- Appendix 2 -- References -- 20 On the Hadronic Mass Spectrum -- References -- 21 On the Hadronic Mass Spectrum: 2014 -- 21.1 Data and Hadron Mass Spectrum -- Fits of Hadron Mass Spectrum -- The Value of the Power Index `a' -- 21.2 Quarks and QCD -- Lattice-QCD Trace Anomaly Constraint -- Quark Bags and the Hadron Mass Spectrum -- References -- 22 SBM Guide to the Literature as of June 1972 -- References -- 23 Thermodynamics of Hot Nuclear Matter: 1978 in the Statistical Bootstrap Model -- 23.1 Introduction -- Plan of the Paper -- 23.2 The Statistical Bootstrap Method in Particle and Nuclear Physics -- The Statistical Bootstrap Model in Particle Physics -- Solution of the Bootstrap Equation -- The Nuclear Matter Bootstrap Equation -- The Mass Spectrum for Nuclear Matter -- Laplace and L-Transforms of the Mass Spectrum -- 23.3 Thermodynamics -- The Partition Functions of the One-Component Ideal Gas -- The Strongly Interacting Pion Gas -- Physics Near T0 -- Thermodynamics of Clustered Matter -- Partition Function of Nuclear Matter. , 23.4 Properties of Nuclear Matter in the Bootstrap Model -- The Different Phases -- Baryon Density in the Gaseous Phase -- Baryon Energy in the Gaseous Phase -- 23.5 Summary -- References -- 24 On a Possible Phase Transition Between Hadron Matter and Quark-Gluon Matter: 1981 -- 24.1 Introduction -- 24.2 The Grand Canonical Pressure Partition Function -- Introduction -- How Shall We Use Π(β,ξ,λ)? -- 24.3 The Hadron Gas -- Introduction -- Digression: The Pointlike Hadron Gas -- The Real Hadron Gas -- Interpretation -- The Usual Thermodynamic Limit with Fixed V→∞ -- Hot Hadron Matter: No Fixed Volume -- 24.4 Conclusions -- References -- 25 How We Got to QCD Matter from the Hadron Side: 1984 -- 25.1 Introduction -- 25.2 Pre-bootstrap -- 25.3 Early Bootstrap -- The Bootstrap Idea -- Consequences -- Difficulties -- Early Developments -- Microcanonical Bootstrap -- Exact Analytical Solutions of the BE -- The Bootstrap Function -- The State of Affairs up to 1978 -- 25.4 The Phase Transition: Hadron Matter-Quark Matter -- Hadron Volumes -- References -- Part III Melting Hadrons, Boiling Quarks Heavy Ion Path to Quark-Gluon Plasma -- 26 How to Deal withRelativistic Heavy Ion Collisions -- 26.1 Introduction -- 26.2 Collective Motions -- Useful Variables -- Momentum Distributions -- Determination of the Weight Function F(λ,γ0) -- Violations of the Postulates 1 and 2 -- (a) Transverse Collective Motions -- (b) Violation of Postulate 2 -- 26.3 Statistical Bootstrap Thermodynamics -- The Partition Function -- Interaction -- The Bootstrap Hypothesis -- The Singularity of the Partition Function: Baryon Conservation -- The Partition Function for Real (Extended) Particles -- Properties of the Real Hadron Gas -- Behaviour Near the Critical Curve -- 26.4 Is There Equilibrium in the Relativistic Heavy Ion Collision? -- The Way to Equilibrium -- Expansion and Cooling. , 26.5 Conclusions.

Weitere Ausg.: Print version: Rafelski, Johann Melting Hadrons, Boiling Quarks - from Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN Cham : Springer International Publishing AG,c2015 ISBN 9783319175447

Sprache: Englisch

Fachgebiete: Physik

Schlagwort(e): Electronic books. ; Festschrift ; Electronic books. ; Electronic books.

URL: Click to View

URL: Volltext  (kostenfrei)

URL: kostenfrei

URL: ProQuest Ebook Central

URL: ProQuest Ebook Central

URL: Full Text

URL: http://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9783319175454

URL: Click here to view book

URL: lizenzpflichtig

UID:

Umfang: XII, 544 p. , online resource.

ISBN: 9783540386131

Serie: Lecture Notes in Mathematics, 851

Anmerkung: “To begin at the beginning: …” -- Stochastic integrals: Basic theory -- Stochastic integration and discontinuous martingales -- Martingales, the Malliavin calculus and Hörmander's theorem -- On a representation of local martingale additive functionals of symmetric diffusions -- Set-parametered martingales and multiple stochastic integration -- Generalized ornstein — Uhlenbeck processes as limits of interacting systems -- Weak and strong solutions of stochastic differential equations: Existence and stability -- On the decomposition of solutions of stochastic differential equations -- A differential geometric formalism for the ito calculus -- Homogenization and stochastic parallel displacement -- Bessel processes and infinitely divisible laws -- Euclidean quantum mechanics and stochastic integrals -- The malliavin calculus and its applications -- The probability functionals (Onsager-machlup functions) of diffusion processes -- Ito and girsanov formulae for two parameter processes -- Lp-inequalities for two-parameter martingales -- Dirichlet processes -- Brownian motion, negative curvature, and harmonic maps -- Local behaviour of hilbert space valued stochastic integrals and the continuity of mild solutions of stochastic evolution equations -- Some markov processes and markov fields in quantum theory, group theory, hydrodynamics and C*-algebras.

In: Springer eBooks

Weitere Ausg.: Printed edition: ISBN 9783540106906

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Konferenzschrift ; Konferenzschrift

DOI: 10.1007/BFb0088719

URL: http://dx.doi.org/10.1007/BFb0088719

URL: Volltext

URL: Volltext  (lizenzpflichtig)

URL: Volltext  (Deutschlandweit zugänglich)

URL: Cover

UID:

Umfang: 1 online resource (62 pages)

Serie: Policy research working papers.

Inhalt: The paper provides basic guidelines and tools for simulating subsidy reforms with Stata using a single cross-section survey. Simulations are discussed under a partial equilibrium and medium-term framework using a marginal approach. The paper distinguishes between single priced products, such as fuel or bread, and multiple priced products, such as household utilities. Part I provides basic instructions for carrying out subsidy analyses. Part II outlines economic theory and formulae for the two types of products considered. Part III illustrates the use of the Stata codes, which are downloadable from the Internet.

Sprache: Englisch

DOI: 10.1596/1813-9450-6148

URL: Volltext  (Deutschlandweit zugänglich)

URL: Volltext  (kostenfrei)

UID:

Umfang: 1 online resource (411 pages) : , illustrations (some color), photographs

ISBN: 0-12-811148-8

Anmerkung: Includes index. , Front Cover -- Serum Pharmacochemistry of Traditional Chinese Medicine -- Serum Pharmacochemistry of Traditional Chinese Medicine: Technologies, Strategies and Applications -- Copyright -- Contents -- List of Contributors -- Preface -- 1 - Traditional Chinese Medicine: Current State, Challenges, and Applications -- 1. CURRENT STATE -- 2. APPLICATION OF TCM -- 3. THE COMING ERA OF PRECISION MEDICINE: WHAT CAN WE LEARN FROM CHINESE MEDICINE? -- 4. THE CHALLENGES OF TCM -- 5. FUTURE PERSPECTIVE -- REFERENCES -- 2 - Serum Pharmacochemistry of Traditional Chinese Medicine: Historical Development and Strategies -- 1. HISTORICAL DEVELOPMENT OF SERUM PHARMACOCHEMISTRY OF TRADITIONAL CHINESE MEDICINE -- 2. THEORETICAL FOUNDATION AND RESEARCH CATEGORY OF SPT -- 3. SPT TECHNIQUES -- 4. APPLICATION AND FUTURE PERSPECTIVES OF SPT -- 5. CONCLUSION -- REFERENCES -- 3 - Integrated Serum Pharmacochemistry of TCM and Metabolomics Strategies for Innovative Drug Discovery -- 1. INTRODUCTION -- 2. METABOLOMICS IN EFFICACY EVALUATION OF FORMULAE -- 3. INTEGRATED SERUM PHARMACOCHEMISTRY OF TCM WITH METABOLOMICS -- 4. CONCLUSION -- REFERENCES -- 4 - UPLC/MS and Its Potential in Traditional Chinese Medicine Development -- 1. INTRODUCTION -- 2. POTENTIAL POWER OF UHPLC-MS -- 3. UHPLC-MS APPROACH IN TCM -- 4. IDENTIFICATION OF CHEMICAL CONSTITUENTS IN TCM SAMPLES -- 5. QUALITATIVE AND QUANTITATIVE ANALYSIS OF TCM -- 6. PHARMACOKINETICS -- 7. UHPLC-MS-BASED METABOLITE IDENTIFICATION -- 8. METABOLOMICS APPLICATION -- 9. QUALITY CONTROL OF TCM -- 10. PHARMACOLOGICAL STUDIES -- 11. CONCLUSIONS AND FUTURE PERSPECTIVE -- REFERENCES -- 5 - Analytical Characterization of Yin-Chen-Hao-Tang by Serum Pharmacochemistry of TCM -- 1. INTRODUCTION -- 2. EXPERIMENTAL -- 2.1 CHEMICALS AND MATERIALS -- 2.2 ANIMALS -- 2.3 PREPARATION OF YINCHENHAO TANG SAMPLES FOR LC/MS ANALYSIS. , 2.4 Q-TOF/MS ANALYSIS -- 2.5 DATA PROCESSING -- 3. RESULTS AND DISCUSSIONS -- 3.1 OPTIMIZATION OF MS CONDITIONS -- 3.2 UPLC-UV-Q-TOF/MS ANALYSIS OF YCHT SAMPLES IN VITRO -- 3.3 UPLC-UV-Q-TOF ANALYSIS OF PLASMA SAMPLE AFTER ORAL YCHT -- 4. CONCLUSION -- 6 - Pharmacokinetic Strategy for Screening the Effective Components From YCHT -- 1. INTRODUCTION -- 2. EXPERIMENTAL -- 2.1 CHEMICALS AND MATERIALS -- 2.2 INSTRUMENT AND ANALYTICAL CONDITIONS -- 2.3 PHARMACOKINETIC ANALYSIS IN VIVO -- 2.3.1 Animals -- 2.3.2 Preparation of YCHT Samples -- 2.3.3 Pharmacokinetic Experiments -- 2.3.4 Compartmental Analysis -- 2.4 PATTERN-RECOGNITION ANALYSIS -- 3. RESULTS -- 4. DISCUSSION -- 5. CONCLUSION -- REFERENCES -- 7 - Synergism Effects of Active Ingredients From YCHT -- 1. INTRODUCTION -- 2. MATERIALS AND METHODS -- 2.1 MATERIALS AND REAGENTS -- 2.2 CHROMATOGRAPHIC CONDITION -- 2.3 ANIMAL HANDLING -- 2.4 SAMPLES PREPARATION -- 2.5 METHOD VALIDATION -- 2.6 PHARMACOKINETICS -- 2.7 BIOCHEMICAL ANALYSIS -- 2.8 STATISTICAL ANALYSIS -- 3. RESULTS -- 3.1 METHOD VALIDATION OF PHARMACOKINETICS -- 3.2 THERAPEUTIC EFFICACY OF COC AS INDICATED BY A RAT HI MODEL -- 3.3 COC CAUSES SYNERGISTIC EFFECTS ON PHARMACOKINETICS -- 4. DISCUSSION -- 5. CONCLUSION -- 8 - Serum Pharmacochemistry of TCM for Screening the Active Ingredients From Wen-Xin Formulae -- 1. INTRODUCTION -- 2. EXPERIMENTAL -- 2.1 PREPARATION OF WEN-XIN-FORMULA SAMPLES FOR LC-MS/MS ANALYSIS -- 2.2 ANIMAL EXPERIMENTS -- 2.3 PREPARATION OF SERUM SAMPLES -- 2.4 CHROMATOGRAPHY ANALYSIS CONDITION -- 2.5 MASS SPECTROMETRY EXPERIMENTS -- 2.6 DATA PROCESSING -- 3. RESULTS AND DISCUSSION -- 3.1 OPTIMIZATION OF LC AND MS CONDITIONS -- 3.2 UPLC-ESI-Q-TOF-MS ANALYSIS OF WEN-XIN-FORMULA IN VITRO -- 3.3 CHARACTERIZATION OF CHEMICAL CONSTITUENTS FROM WEN-XIN-FORMULA IN VIVO. , 3.4 METABOLYNX ANALYSIS OF PROTOTYPE AND METABOLITES OF WEN-XIN-FORMULA -- 4. CONCLUSION -- REFERENCES -- 9 - Characterization and Pharmacokinetic Study of Multiple Constituents From Shengmai San -- 1. INTRODUCTION -- 2. EXPERIMENTAL -- 2.1 PREPARATION OF SMS SAMPLES -- 2.2 PREPARATION OF PLASMA SAMPLES -- 2.3 PHARMACOKINETIC STUDY -- 2.4 UPLC-Q-TOF-HDMS ANALYSIS -- 2.4.1 Liquid Chromatography Conditions -- 2.4.2 Mass Spectrometry Detection -- 2.5 DATA ANALYSIS -- 2.6 METHOD VALIDATION AND DATA ANALYSIS OF PHARMACOKINETICS -- 3. RESULTS AND DISCUSSION -- 3.1 ANALYTICAL CONSIDERATION FOR UPLC-Q-TOF-HDMS -- 3.2 OPTIMIZATION OF SAMPLE PREPARATION -- 3.3 IDENTIFICATION OF CONSTITUENTS OF SMS IN VIVO BY UPLC-Q-TOF-HDMS -- 3.4 STRUCTURAL CHARACTERIZATION OF PROPOSED BIOACTIVE COMPONENTS -- 3.5 APPLICATION OF METABOLYNX TO ANALYSIS COMPOUNDS IN VIVO -- 3.6 VALIDATION OF PHARMACOKINETIC METHOD -- 3.7 PHARMACOKINETIC ANALYSIS -- 4. CONCLUSION -- REFERENCES -- 10 - Multivariate Data Processing Tools to Screen the Active Ingredients From Kai-Xin-San -- 1. INTRODUCTION -- 2. MATERIAL AND METHODS -- 2.1 PREPARATION OF KAI-XIN-SAN SAMPLES -- 2.2 ANIMALS HANDLING -- 2.3 PREPARATION OF PLASMA SAMPLES IN VIVO -- 2.4 ULTRAHIGH PERFORMANCE LIQUID CHROMATOGRAPHY CONDITION -- 2.5 MASS SPECTROMETRY CONDITION -- 2.6 MULTIVARIATE DATA PROCESSING APPROACH -- 2.7 METABOLYNX PROCESSING APPROACH FOR METABOLITES ANALYSIS -- 3. RESULTS AND DISCUSSION -- 3.1 RAPID DISCOVERY AND GLOBAL CHARACTERIZATION OF MULTIPLE CONSTITUENTS FROM KAI-XIN-SAN -- 3.2 OPTIMIZATION OF CHROMATOGRAPHIC AND MASS SPECTROMETRY CONDITIONS -- 3.3 MULTIVARIATE STATISTICAL ANALYSIS -- 3.4 METABOLITES IDENTIFIED USING THE METABOLYNX TOOL -- 4. CONCLUSION -- REFERENCES -- 11 - Serum Pharmacochemistry of TCM for Determining the Active Ingredients of Shuanghuanglian Formulae -- 1. INTRODUCTION. , 2. MATERIAL AND METHODS -- 2.1 PREPARATION OF SHUANGHUANGLIAN FORMULAE SAMPLES FOR LIQUID CHROMATOGRAPHY-MASS SPECTROMETRY ANALYSIS -- 2.2 PREPARATION OF SERUM SAMPLES -- 2.3 HIGH-RESOLUTION LIQUID CHROMATOGRAPHY-MASS SPECTROMETRY ANALYSIS -- 2.4 IMPLEMENTATION OF THE BACKGROUND-SUBTRACTION ALGORITHM -- 2.5 MULTIPLE-DATA PROCESSING APPROACH -- 3. RESULTS -- 3.1 UPLC-MS CHARACTERIZATION OF CHEMICAL CONSTITUENTS FROM SHUANGHUANGLIAN FORMULAE -- 3.2 BACKGROUND-SUBTRACTION ALGORITHM -- 3.3 MULTIVARIATE STATISTICAL ANALYSIS FOR IN VIVO IDENTIFICATION OF SHUANGHUANGLIAN FORMULAE -- 3.4 CHARACTERIZATION ANALYSIS OF PROTOTYPE CONSTITUENTS AND METABOLITES OF SHUANGHUANGLIAN FORMULAE -- 4. DISCUSSION -- 5. CONCLUSION -- REFERENCES -- 12 - Pharmacokinetic-Pharmacodynamic Study of Zhi Zhu Wan -- 1. INTRODUCTION -- 2. EXPERIMENTAL -- 2.1 CHEMICALS AND REAGENTS -- 2.2 UPLC-MS/MS ANALYSIS -- 2.2.1 Liquid Chromatography Conditions -- 2.2.2 Mass Spectrometry Detection -- 2.3 ANIMAL HANDLING -- 2.4 ESTABLISHMENT OF DETERMINING METHOD FOR HESPERETIN AND NARINGENIN -- 2.4.1 Plasma Sample Preparation -- 2.4.2 Method Validation -- 2.5 PHARMACOKINETICS -- 2.6 PHARMACODYNAMICS STUDY -- 2.6.1 Isolated Mice Intestine -- 2.6.2 Effects on Mouse Small Intestinal Propulsion -- 2.7 DATA ANALYSIS -- 3. RESULTS -- 3.1 VALIDATION OF UPLC-MS/MS METHODS -- 3.2 PHARMACOKINETIC STUDY -- 3.3 PHARMACODYNAMIC STUDY -- 4. DISCUSSION -- 5. CONCLUSION -- REFERENCES -- 13 - Identification of the Absorbed Components of Shaoyao-Gancao Decoction -- 1. INTRODUCTION -- 2. MATERIALS AND METHODS -- 2.1 PREPARATION OF SHAOYAO-GANCAO DECOCTION SAMPLES -- 2.2 ANIMAL EXPERIMENTS -- 2.3 PREPARATION OF SERUM SAMPLES -- 2.4 CHROMATOGRAPHIC ANALYSIS SYSTEM -- 2.5 MASS SPECTROMETRY CONDITIONS -- 2.6 DATA PROCESSING -- 3. RESULTS AND DISCUSSION. , 3.1 UPLC-MS CHARACTERIZATION OF CHEMICAL CONSTITUENTS FROM SHAOYAO-GANCAO DECOCTION -- 3.2 CHARACTERIZATION OF IN VIVO CONSTITUENTS FROM SHAOYAO-GANCAO DECOCTION -- a, Radix Glycyrrhizae -- b, Radix Paeoniae Alba -- Api, apiose -- Glc, β-d-glucose -- GluA, glucuronic acid -- MW, Molecular weight -- Xyl, ... -- 3.3 METABOLYNX DETECTION OF THE ABSORBED COMPONENTS -- 3.4 DETECTION AND IDENTIFICATION OF CONJUGATED METABOLITES IN RAT PLASMA -- 4. CONCLUSIONS -- REFERENCES -- 14 - Rapid Analysis of Multiple Constituents of Suanzaoren Decoction by UPLC-MS -- 1. INTRODUCTION -- 2. EXPERIMENTAL -- 2.1 SAMPLE PREPARATION -- 2.2 CHROMATOGRAPHY AND MASS SPECTROMETRY CONDITIONS -- 2.3 ESTABLISHMENT OF AN IN-HOUSE MOLECULAR FORMULA DATABASE -- 3. RESULTS AND DISCUSSION -- 3.1 OPTIMIZATION OF UPLC AND MS CONDITIONS -- 3.2 UPLC-ESI-Q-TOF-MS ANALYSIS OF SZRD -- 4. CONCLUSION -- 15 - UPLC-MS Analysis of the Chemical Constituents of Liuwei Dihuang Wan -- 1. INTRODUCTION -- 2. MATERIAL AND METHODS -- 2.1. PREPARATION OF LDW SAMPLES FOR LC-MS ANALYSIS -- 2.2. CHROMATOGRAPHIC SEPARATION -- 2.3 MASS SPECTROMETRY -- 2.4 DATA PROCESSING -- 3. RESULTS AND DISCUSSION -- 4. CONCLUSION -- REFERENCE -- 16 - Multivariate Data Analysis for Rapid Identification of Chemical Constituents of Simiao Wan -- 1. INTRODUCTION -- 2. MATERIAL AND METHODS -- 2.1 PREPARATION OF SW SAMPLES FOR LC-MS ANALYSIS -- 2.2 UHPLC CONDITION -- 2.3 HIGH-RESOLUTION MS -- 2.4 DATA PROCESSING -- 3. RESULTS AND DISCUSSION -- 3.1 OPTIMIZATION OF UHPLC-ESI-Q-TOF-MS CONDITIONS -- 3.2 UHPLC-ESI-Q-TOF-MS ANALYSIS OF SW -- 3.3 MS/MS CHARACTERIZATION OF CHEMICAL CONSTITUENTS FROM SW -- 4. CONCLUSION -- 17 - Time-Course Study of Multicomponents After Oral Administration of Stemonae Radix -- 1. INTRODUCTION -- 2. EXPERIMENTAL -- 2.1 SAMPLE PREPARATION OF STEMONAE RADIX -- 2.2 LIQUID CHROMATOGRAPHY CONDITIONS. , 2.3 MASS SPECTROMETRY DETECTION.

Weitere Ausg.: ISBN 0-12-811147-X

Sprache: Englisch

UID:

Umfang: 1 online resource (382 pages) : , illustrations

ISBN: 0-12-812745-7

Anmerkung: Front Cover -- Systems Biology and its Application in TCM Formulas Research -- Copyright -- Contents -- Contributors -- Introduction -- Section 1: Ideas and Methods for the Modern Research of TCM Formulas -- Chapter 1: Strategy for Modern Research of Traditional Chinese Medicine Formulae -- 1.1. Current Research on TCM Formulae -- 1.2. Principles for the Study of TCM Formulae -- 1.2.1. Holism and Reductionism -- 1.2.2. Macro- and Microstudies -- 1.2.3. In Vitro and in vivo Studies -- 1.3. Modern TCM Formulae Research -- 1.3.1. Research on Therapeutic Materials Basis -- 1.3.2. Modern Pharmacology -- 1.3.2.1. Top-Down: Holistic Pharmacology and Active Components Screening -- 1.3.2.2. Bottom-Up: Pharmacological Evaluation of Key Active Components and Multicomponent Compatibility -- 1.3.3. Systems Biology -- 1.3.3.1. Genomics -- 1.3.3.2. Proteomics -- 1.3.3.3. Metabolomics -- 1.3.3.4. Epigenomics -- 1.3.3.5. Metagenomics -- 1.4. Network Biology and TCM Network Pharmacology -- References -- Chapter 2: Theories and Methods for the Evaluation of the Pharmacodynamic Material Basis of Traditional Chinese Medicine -- 2.1. The Development of Research on the Pharmacodynamic Material Basis of TCM -- 2.2. New Methods for the Study of the Pharmacodynamic Material Basis of TCM -- 2.2.1. Combined Chemical Technologies for the Study of TCM -- 2.2.2. Serum Pharmacology and Serum Pharmacochemistry Method -- 2.2.3. Analysis of Spectrum-Effect Relationships -- 2.2.4. HTS of Multiple Targets -- 2.2.5. Molecular Biological Chromatography Technique -- 2.2.6. Metabolism Method -- 2.2.7. System Biology Method -- References -- Chapter 3: Application of Systems Biology in the Research of TCM Formulae -- Abstract -- Keywords -- 3.1. Omics in Systems Biology -- 3.1.1. Genomics -- 3.1.1.1. Pharmacogenomics -- 3.1.1.2. Metagenomics -- 3.1.1.3. Epigenomics. , 3.1.2. Transcriptomics -- 3.1.3. Proteomics -- 3.1.3.1. Phosphoproteomics -- 3.1.3.2. Glycoproteomics -- 3.1.3.3. Chemoproteomics -- 3.1.4. Metabolomics -- 3.1.4.1. Pharmacometabolomics -- 3.1.4.2. Lipidomics -- 3.1.5. Other "Omics" Technologies -- 3.1.5.1. Phenomics -- 3.1.5.2. Immunomics -- 3.1.5.3. Metallomics -- 3.1.5.4. Cytomics -- 3.1.5.5. Ionomics -- 3.1.5.6. Interactomics -- 3.2. Application of Systems Biology in the Research of TCM Formulae -- 3.2.1. Action Mechanisms of TCM Formulae -- 3.2.2. The Concept of a Syndrome in TCM -- 3.2.3. Active Component Compatibility (or Synergy) in TCM Formulae -- 3.2.4. Pharmacokinetic Studies of TCM Formulae -- 3.2.5. Discovery and Development of TCM-Based New Drugs -- References -- Chapter 4: Network Pharmacology in the Study of TCM Formulae -- 4.1. Identification of Therapeutically Effective TCM Compounds -- 4.2. Identification of the Targets of Active TCM Compounds -- 4.2.1. Proteomic Technologies -- 4.2.2. Computational Predictions -- 4.2.3. Database Searching -- 4.3. Identification of Disease-Associated Genes and Construction of Disease-Related Networks -- 4.3.1. Identification of Disease-Associated Genes -- 4.3.2. Construction of Disease Networks -- 4.4. Identification of TCM Formulae-Regulated Signaling Pathways and the Evaluation of the TCM Formulae on Disease-Relate ... -- 4.4.1. Identification of Drug Target-Rich Pathways -- 4.4.2. Construction of Subnetworks Influenced by Drugs and Evaluation of the Effects of TCM Formulae -- 4.4.2.1. Heuristic Algorithm -- 4.4.2.2. Steiner Minimum Tree Algorithm -- 4.4.2.3. Network Proximity Scoring Algorithm -- 4.5. Case Studies -- 4.5.1. Case Study 1: Antidepressant Activity of St. John's Wort -- 4.5.2. Case Study 2: The Effect of Realgar-Indigo Naturalis Formula on Acute Promyelocytic Leukemia -- 4.6. Perspectives -- References. , Chapter 5: Application of Intestinal Flora in the Study of TCM Formulae -- 5.1. Classification of Intestinal Flora -- 5.2. The Relationship Between Intestinal Dysbacteriosis and Disease -- 5.3. Influence of Intestinal Bacterial Metabolism on Effective TCM Ingredients -- 5.3.1. Enhanced Absorption and Elevated Efficacy of Intestinal Flora Metabolism on TCM Ingredients -- 5.3.2. Attenuated or Increased Toxicity of Intestinal Flora on TCM Ingredients -- 5.3.3. Confirmation of the Rationality of TCM Synergy and Compatibility -- 5.4. Modulation of the Intestinal Flora by TCM -- 5.4.1. Regulation of Intestinal Flora Composition by TCM -- 5.4.1.1. Effects of a Single Herb or Single Extract on Intestinal Flora Composition -- 5.4.1.2. Effects of TCM Formulae on Intestinal Flora Composition -- 5.4.2. Protecting the Intestinal Mucosa Barrier Function and Preventing the Intestinal Bacteria Translocation Penetration -- 5.4.2.1. Single TCM Herbs -- 5.4.2.2. TCM Formulae -- 5.4.2.3. Other TCM Preparations -- References -- Chapter 6: Application of Connectivity Map (CMAP) Database to Research on Traditional Chinese Medicines (TCMs) -- 6.1. Establishing the CMAP Database -- 6.1.1. Molecules Treating Cell Lines -- 6.1.2. The CMAP Concept -- 6.2. Application in TCM -- 6.2.1. Application in Components of TCM -- 6.2.2. Application in TCM Formulae -- 6.3. Perspectives -- References -- Section 2: Case Study on Shexiang Baoxin Pill -- Chapter 7: The Study of the Material Basis of the Shexiang Baoxin Pill -- 7.1. Identification of Nonvolatile Constituents in the TCM-Formula Shexiang Baoxin Pill by LC Coupled With DAD-ESI-MS-MS -- 7.1.1. Experimental -- 7.1.1.1. Materials and Chemicals -- 7.1.1.2. Preparation of Samples -- 7.1.1.3. LC-DAD-MS System -- 7.1.2. Results and Discussion -- 7.1.2.1. LC-DAD Analysis of SBP -- 7.1.2.2. ESI-MS(2) Analysis of Authentic Compounds. , 7.1.2.3. LC-DAD-MS-MS Analysis of SBP -- 7.1.3. Conclusion -- 7.2. The Study on Volatile Components in the Shexiang Baoxin Pill -- 7.2.1. Instrumentation and Materials -- 7.2.1.1. Instrumentation -- 7.2.1.2. Reagents -- 7.2.1.3. Chemicals -- 7.2.2. Method and Results -- 7.2.2.1. Preparation of the Standard Solution -- 7.2.2.2. Preparation of Sample Solution -- 7.2.2.3. Chromatographic Conditions -- 7.2.2.4. Identification of SBP -- 7.2.3. Conclusions -- References -- Chapter 8: Study on the Serum Pharmacochemistry of the Shexiang Baoxin Pill -- 8.1. Analysis of the Nonvolatile Constituents in Rat Plasma After Oral Administration of the Baoxin Pill by HPLC-ESI-MS/MS -- 8.1.1. Experimental -- 8.1.1.1. Chemicals and Reagents -- 8.1.1.2. Instrumentation and Conditions -- 8.1.1.3. Animals, Drug Administration, and Blood Sampling -- 8.1.1.4. Sample Preparation -- 8.1.2. Results and Discussion -- 8.1.2.1. LC-ESI-MS/MS Analysis of Shexiang Baoxin Pill Extracts and Plasma Samples -- 8.1.2.2. Method Validation -- 8.1.2.3. Identification of Prototype Components in Rat Plasma -- 8.1.2.4. Identification of Metabolites in Rat Plasma -- 8.1.3. Conclusion -- 8.2. Analysis of the Volatile Constituents in Rat Plasma After Oral Administration of the Shexiang Baoxin Pill by GC-MS -- 8.2.1. Instrument and Reagent -- 8.2.1.1. Mass Spectrometer -- 8.2.1.2. Reagent -- 8.2.1.3. Animal -- 8.2.1.4. Shexiang Baoxin Pill Analysis and Sample Preparation -- 8.2.1.5. Separate Condition -- 8.2.1.6. Mass Condition -- 8.2.2. Results and Discussion -- 8.2.3. Conclusion -- References -- Chapter 9: The Quality Study of the Shexiang Baoxin Pill -- 9.1. The Quality Study of Bovis Calculus in the SBP -- 9.1.1. Experimental -- 9.1.1.1. Reagents and Materials -- 9.1.1.2. Chromatographic System -- 9.1.1.3. Analytical Conditions -- 9.1.1.4. Sample Preparation -- 9.1.1.5. Calibration Curves. , 9.1.2. Results and Discussion -- 9.1.2.1. Chromatographic Analysis -- 9.1.2.2. Validation -- 9.1.2.3. Sample Analysis -- 9.1.3. Conclusions -- 9.2. The Quality Standard of the SBP -- 9.2.1. The Quality Standard of Nonvolatile Components in the SBP -- 9.2.1.1. Experimental -- Reagents and Materials -- Chromatographic System -- Analytical Conditions -- Sample Preparation -- 9.2.1.2. Results and Discussion -- Chemical Fingerprint of SBP -- Sample Analysis and Quality Evaluation -- 9.2.1.3. Conclusions -- 9.2.2. The Quality Standard of Volatile Components in the SBP -- 9.2.2.1. Experimental -- Instruments -- Reagents and Materials -- GC Analysis -- Sample Preparation -- 9.2.2.2. Results and Discussion -- Chemical Fingerprinting Analysis -- Validation -- 9.2.2.3. Conclusions -- References -- Chapter 10: Pharmacokinetic Study of the Shexiang Baoxin Pill -- 10.1. Pharmacokinetic Study of Five Ginsenosides Following Single and Multiple Oral Administrations of The Shexiang Baoxi ... -- 10.1.1. Experimental -- 10.1.1.1. Chemicals and Reagents -- 10.1.1.2. Animals -- 10.1.1.3. Preparation of the SBP Extract and the Determination of Five Ginsenosides in the Extract -- 10.1.1.4. Preparation of Calibration Standards and Quality Control (QC) Samples -- 10.1.1.5. Instruments and LC-MS/MS Conditions -- 10.1.1.6. Sample Preparation -- 10.1.1.7. Method Validation -- 10.1.1.8. PK Study -- Experimental Design for Animals -- PK Calculation and Statistics -- 10.1.2. Results and Discussion -- 10.1.2.1. Method Development -- 10.1.2.2. Method Validation -- 10.1.2.3. PK Study -- Single Dosing -- Mutiple Dosing -- 10.1.3. Conclusions -- 10.2. Pharmacokinetics and Tissue Distribution of Five Bufadienolides From the SBP in Mice -- 10.2.1. Experimental -- 10.2.1.1. Chemicals and Reagents -- 10.2.1.2. Animals -- 10.2.1.3. Instruments and Conditions -- Liquid Chromatography. , Mass Spectrometric Conditions.

Weitere Ausg.: ISBN 0-12-812744-9

Sprache: Englisch

UID:

Umfang: 1 online resource (708 pages) : , illustrations (some color), tables

Ausgabe: Second edition.

ISBN: 9780081022573 , 0081022573 , 9780081022566 , 0081022565

Anmerkung: Front Cover -- Principles of Electron Optics -- Copyright Page -- Contents -- Preface to the Second Edition -- Preface to the First Edition (Extracts) -- Acknowledgments -- 1 Introduction -- 1.1 Organization of the Subject -- 1.2 History -- I. Classical Mechanics -- 2 Relativistic Kinematics -- 2.1 The Lorentz Equation and General Considerations -- 2.2 Conservation of Energy -- 2.3 The Acceleration Potential -- 2.4 Definition of Coordinate Systems -- 2.5 Conservation of Axial Angular Momentum -- 3 Different Forms of Trajectory Equations -- 3.1 Parametric Representation in Terms of the Arc-Length -- 3.2 Relativistic Proper-Time Representation -- 3.3 The Cartesian Representation -- 3.4 Scaling Rules -- 4 Variational Principles -- 4.1 The Lagrange Formalism -- 4.2 General Rotationally Symmetric Systems -- 4.3 The Canonical Formalism -- 4.4 The Time-Independent Form of the Variational Principle -- 4.5 Static Rotationally Symmetric Systems -- 5 Hamiltonian Optics -- 5.1 Introduction of the Characteristic Function -- 5.2 The Hamilton-Jacobi Equation -- 5.3 The Analogy With Light Optics -- 5.4 The Influence of Vector Potentials -- 5.5 Gauge Transformations -- 5.6 Poincaré's Integral Invariant -- 5.7 The Problem of Uniqueness -- 5.8 Lie Algebra -- 5.9 Summary -- II. Calculation of Static Fields -- 6 Basic Concepts and Equations -- 6.1 General Considerations -- 6.2 Field Equations -- 6.3 Variational Principles -- 6.4 Rotationally Symmetric Fields -- 6.5 Planar Fields -- 7 Series Expansions -- 7.1 Azimuthal Fourier Series Expansions -- 7.1.1 Scalar Potentials -- 7.1.2 Vector Potentials -- 7.2 Radial Series Expansions -- 7.2.1 Scalar Potentials -- 7.2.2 Vector Potentials -- 7.2.3 Explicit Representations -- 7.3 Rotationally Symmetric Fields -- 7.3.1 Electrostatic Fields -- 7.3.2 Magnetic Fields -- 7.4 Multipole Fields -- 7.5 Planar Fields. , 7.6 Fourier-Bessel Series Expansions -- 8 Boundary-Value Problems -- 8.1 Boundary-Value Problems in Electrostatics -- 8.2 Boundary Conditions in Magnetostatics -- 8.3 Examples of Boundary-Value Problems in Magnetostatics -- 8.3.1 Devices with Superconducting Yokes -- 8.3.2 Conventional Round Magnetic Lenses -- 8.3.3 Unconventional Round Magnetic Lenses -- 8.3.4 Toroidal Magnetic Deflection Systems -- 9 Integral Equations -- 9.1 Integral Equations for Scalar Potentials -- 9.1.1 General Theory -- 9.1.2 Dirichlet Problems -- 9.1.3 Neumann Problems -- 9.2 Problems with Interface Conditions -- 9.3 Reduction of the Dimensions -- 9.3.1 Dirichlet Problems -- 9.3.2 Interface Conditions -- 9.3.3 Planar Fields -- 9.4 Important Special Cases -- 9.4.1 Rotationally Symmetric Scalar Potentials -- 9.4.2 Rotationally Symmetric Vector Potentials -- 9.4.3 Unconventional Magnetic Lenses -- 9.4.4 Magnetic Deflection Coils -- 9.4.5 Multipole Systems -- 9.4.6 Small Perturbations of the Rotational Symmetry -- 9.5 Résumé -- 10 The Boundary-Element Method -- 10.1 Evaluation of the Fourier Integral Kernels -- 10.1.1 Introduction of Moduli -- 10.1.2 Radial Series Expansions -- 10.1.3 Recurrence Relations -- 10.1.4 Analytic Differentiation -- 10.2 Numerical Solution of One-Dimensional Integral Equations -- 10.2.1 Conventional Solution Techniques -- 10.2.2 The Charge Simulation Method -- 10.2.3 Combination with Interpolation Kernels -- 10.2.3.1 General formalism -- 10.2.3.2 Marginal positions -- 10.2.3.3 General properties -- 10.2.3.4 Solution of integral equations -- 10.2.3.5 Application to field calculations -- 10.2.4 Evaluation of Improper Integrals -- 10.3 Superposition of Aperture Fields -- 10.3.1 Electric Field of a Single Aperture -- 10.3.2 Superposition Procedure -- 10.3.3 Combination with the BEM -- 10.3.4 Extrapolation of the Number of Segments. , 10.4 Three-Dimensional Dirichlet Problems -- 10.5 Examples of Applications of the Boundary-Element Method -- 11 The Finite-Difference Method (FDM) -- 11.1 The Choice of Grid -- 11.2 The Taylor Series Method -- 11.3 The Integration Method -- 11.4 Nine-Point Formulae -- 11.5 The Finite-Difference Method in Three Dimensions -- 11.6 Other Aspects of the Method -- 11.6.1 Expanding Spherical-Mesh Grid -- 11.6.2 Extrapolation on Multiple Grids -- 11.6.3 Combination with the BEM -- 11.7 Iterative Solution Techniques -- 12 The Finite-Element Method (FEM) -- 12.1 Formulation for Round Magnetic Lenses -- 12.2 Formulation for Self-adjoint Elliptic Equations -- 12.3 Solution of the Finite-Element Equations -- 12.4 Improvement of the Finite-Element Method -- 12.4.1 Introduction -- 12.4.2 Alternative Formulations -- 12.4.3 First- and Second-Order Finite-Element Methods (FOFEM and SOFEM) -- 12.5 Comparison and Combination of Different Methods -- 12.6 Deflection Units and Multipoles -- 12.7 Related Work -- 13 Field-Interpolation Techniques -- 13.1 One-Dimensional Differentiation and Interpolation -- 13.1.1 Hermite Interpolation -- 13.1.2 Cubic Splines -- 13.1.3 Differentiation Using Difference Schemes -- 13.1.4 Evaluation of Radial Series Expansions -- 13.2 Two-Dimensional Interpolation -- 13.2.1 Hermite Interpolation -- 13.2.2 The Use of Derivatives of Higher Order -- 13.3 Interpolation and the Finite-Element Method -- III. The Paraxial Approximation -- 14 Introduction to Paraxial Equations -- 15 Systems with an Axis of Rotational Symmetry -- 15.1 Derivation of the Paraxial Ray Equations from the General Ray Equations -- 15.1.1 Physical Significance of the Coordinate Rotation -- 15.2 Variational Derivation of the Paraxial Equations -- 15.3 Forms of the Paraxial Equations and General Properties of their Solutions -- 15.3.1 Reduced Coordinates. , 15.3.2 Stigmatic Image Formation -- 15.3.3 The Wronskian -- 15.4 The Abbe Sine Condition and Herschel's Condition -- 15.5 Some Other Transformations -- 16 Gaussian Optics of Rotationally Symmetric Systems: Asymptotic Image Formation -- 16.1 Real and Asymptotic Image Formation -- 16.2 Asymptotic Cardinal Elements and Transfer Matrices -- 16.3 Gaussian Optics as a Projective Transformation (Collineation) -- 16.4 Use of the Angle Characteristic to Establish the Gaussian Optical Quantities -- 16.5 The Existence of Asymptotes -- 17 Gaussian Optics of Rotationally Symmetric Systems: Real Cardinal Elements -- 17.1 Real Cardinal Elements for High Magnification and High Demagnification -- 17.2 Osculating Cardinal Elements -- 17.3 Inversion of the Principal Planes -- 17.4 Approximate Formulae for the Cardinal Elements: The Thin-Lens Approximation and the Weak-Lens Approximation -- Magnetic Lenses -- Electrostatic Lenses -- 18 Electron Mirrors -- 18.1 Introduction -- 18.2 The Modified Temporal Representation -- 18.3 The Cartesian Representation -- 18.4 A Quadratic Transformation -- 19 Quadrupole Lenses -- 19.1 Paraxial Equations for Quadrupoles -- 19.2 Transaxial Lenses -- 20 Cylindrical Lenses -- IV. Aberrations -- 21 Introduction to Aberration Theory -- 22 Perturbation Theory: General Formalism -- 23 The Relation Between Permitted Types of Aberration and System Symmetry -- 23.1 Introduction -- 23.2 N=1 -- 23.2.1 N=1. Systems with a Plane of Symmetry -- 23.3 N=2 -- 23.3.1 N=2. Systems Possessing a Plane of Symmetry -- 23.4 N=3 -- 23.5 N=4 -- 23.6 N=5 and 6 -- 23.7 Systems with an Axis of Rotational Symmetry -- 23.8 Note on the Classification of Aberrations -- 23.8.1 Terms Independent of xo, yo (p=q=0): Aperture Aberrations -- 23.8.2 Terms Independent of xa, ya (r=s=0): Distortions -- 23.8.3 Intermediate Terms -- 23.8.4 Phase Shifts. , 23.8.5 Parasitic Aberrations -- 24 The Geometrical Aberrations of Round Lenses -- 24.1 Introduction -- 24.2 Derivation of the Real Aberration Coefficients -- 24.2.1 The Trajectory Method -- 24.2.2 The Eikonal Method -- 24.3 Spherical Aberration (Terms in xa and ya only) -- 24.3.1 Electrostatic case (B=0, ϕ ≠ const) -- General Relativistic Expression -- General Nonrelativistic Expression -- 24.3.2 Magnetic case (ϕ=const, B≠0) -- General Relativistic Case -- 24.3.3 Scherzer's Theorem -- 24.3.4 Thin-Lens Approximation -- 24.4 Coma (Terms Linear in xo, yo) -- 24.4.1 Thin-Lens Formulae -- 24.5 Astigmatism and Field Curvature (Terms Linear in xa, ya) -- 24.5.1 Thin-Lens Formulae -- 24.6 Distortion (Terms in xo and yo only) -- 24.6.1 Thin-Lens Formulae -- 24.7 The Variation of the Aberration Coefficients with Aperture Position -- 24.8 Reduced Coordinates -- 24.9 Seman's Transformation of the Characteristic Function -- 24.10 Fifth-Order Aberrations -- 24.10.1 Isotropic Aberration Coefficients -- 24.10.2 Anisotropic Aberration Coefficients -- 25 Asymptotic Aberration Coefficients -- 25.1 Spherical Aberration -- 25.2 Coma -- 25.3 Astigmatism and Field Curvature -- 25.4 Distortion -- 25.5 Aberration Matrices and the Integrals ij -- 25.6 Dependence on Object Position or Magnification -- 25.7 Dependence on Aperture Position -- 25.8 Thin-Lens Approximations -- 26 Chromatic Aberrations -- 26.1 Real Chromatic Aberrations -- 26.2 Asymptotic Chromatic Aberrations -- 26.3 Higher Order Chromatic Aberration Coefficients -- 26.3.1 Third-Order (Fourth-Rank) Aberrations -- 26.3.1.1 Isotropic Aberrations -- 26.3.1.2 Anisotropic Aberrations -- 26.3.1.3 Definitions -- 26.3.2 Third-Rank Aberrations -- 27 Aberration Matrices and the Aberrations of Lens Combinations -- 28 The Aberrations of Mirrors and Cathode Lenses -- 28.1 The Modified Temporal Theory. , 28.2 The Cartesian Theory.

Sprache: Englisch

UID:

Umfang: 1 online resource (xvii, 420 pages) : , digital, PDF file(s).

Ausgabe: Second edition.

ISBN: 9781107786134 (ebook)

Serie: Encyclopedia of mathematics and its applications ; volume 155

Inhalt: Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , 1. Background -- The gamma and beta functions -- Hypergeometric series -- Orthogonal polynomials of one variable -- Classical orthogonal polynomials -- Modified classical polynomials -- Notes -- 2. Orthogonal polynomials in two variables -- Introduction -- Product orthogonal polynomials -- Orthogonal polynomials on the unit disk -- Orthogonal polynomials on the triangle -- Orthogonal polynomials and differential equations -- Generating orthogonal polynomials of two variables -- First family of koornwinder polynomials -- A related family of orthogonal polynomials -- Second family of koornwinder polynomials -- 3. General properties of orthogonal polynomials in several variables -- Notation and preliminaries -- Moment funtionals and orthogonal polynomials -- The three-term relation -- Jacobi matrices and commuting operators -- Further properties of the three-term relation -- Reproducing kernels and fourier orthogonal series -- Common zeros of orthogonal polynomials in several variables -- Gaussian cubature formulae -- Notes -- 4. Orthogonal polynomials on the unit sphere -- Spherical harmonics -- Orthoginal structures on Sd and on Bd -- Orthogonal structures on Bd and on Sd+m-1 -- Orthogonal structure on the simplex -- Van der corput -- Schaake inequality -- 5. Examples of orthogonal polynomials in several variables -- Orthogonal polynomials for simple weight functions -- Classical orthogonal polynomials on the unit ball -- Classical orthogonal polynomials on the simplex -- Orthogonal polynomials via symmetric functions -- Chebyshev polynomials to Type Ad -- Sobolev orthogonal polynomials on the unit ball -- 6. Root systems and coxeter groups -- Introduction and overview -- Root systems -- Invariant polynomials -- Differential-difference operators -- The intertwining operator -- The K-analogue of the exponential -- Invariant differential operators -- 7. Spherical harmonics associated with reflection groups -- h-Harmonic polynomials -- Inner products on polynomials -- Reproducing kernels and the poisson kernel -- Integration of the intertwining operator -- Example: Abelian group Z d/2 -- Example: Dihedral groups -- The dunk1 transform -- 8. Generalized classical orthogonal polynomials -- Generalized classical orthogonal polynomials on the ball -- Generalized classical orthogonal polynomials on the simplex -- Generalized hermite polynomials -- Generalized laguerre polynomials -- 9. Summability of orthogonal expansions -- General results on orthogonal expansions -- Orthogonal expansion on the sphere -- Orthogonal expansion on the ball -- Orthogonal expansion on the simplex -- Orthogonal expansion of Laguerre and Hermite polynomials -- Multiple Jacobi expansion -- 10. Orthogonal polynomials associated with symmetric groups -- Partitions, compositions and orderings -- Commuting self-adjoint operators -- The dual polynomials basis -- Sd-invariant subspaces -- Degree-changing recurrences -- Norm formulae -- Symmetric functions and jack polynomials -- Miscellaneous topics -- 11. Orthogonal polynomials associated with octahedral groups, and applications -- Operators of Type B -- Polynomial eigenfunctions of Type B -- Generalized binomial coefficients -- Hermite polynomials of Type B -- Calogero-Sutherland systems.

Weitere Ausg.: Print version: ISBN 9781107071896

Sprache: Englisch

Fachgebiete: Mathematik

URL: https://doi.org/10.1017/CBO9781107786134

URL: Volltext

URL: Inhaltstext

UID:

Umfang: XII, 498 p. , online resource.

Ausgabe: Fourth Edition.

ISBN: 9780387217062

Serie: Statistics and Computing,

Inhalt: S is a powerful environment for the statistical and graphical analysis of data. It provides the tools to implement many statistical ideas that have been made possible by the widespread availability of workstations having good graphics and computational capabilities. This book is a guide to using S environments to perform statistical analyses and provides both an introduction to the use of S and a course in modern statistical methods. Implementations of S are available commercially in S-PLUS(R) workstations and as the Open Source R for a wide range of computer systems. The aim of this book is to show how to use S as a powerful and graphical data analysis system. Readers are assumed to have a basic grounding in statistics, and so the book is intended for would-be users of S-PLUS or R and both students and researchers using statistics. Throughout, the emphasis is on presenting practical problems and full analyses of real data sets. Many of the methods discussed are state of the art approaches to topics such as linear, nonlinear and smooth regression models, tree-based methods, multivariate analysis, pattern recognition, survival analysis, time series and spatial statistics. Throughout modern techniques such as robust methods, non-parametric smoothing and bootstrapping are used where appropriate. This fourth edition is intended for users of S-PLUS 6.0 or R 1.5.0 or later. A substantial change from the third edition is updating for the current versions of S-PLUS and adding coverage of R. The introductory material has been rewritten to emphasis the import, export and manipulation of data. Increased computational power allows even more computer-intensive methods to be used, and methods such as GLMMs,.

Anmerkung: 1 Introduction -- 1.1 A Quick Overview of S -- 1.2 Using S -- 1.3 An Introductory Session -- 1.4 What Next? -- 2 Data Manipulation -- 2.1 Objects -- 2.2 Connections -- 2.3 Data Manipulation -- 2.4 Tables and Cross-Classification -- 3 The S Language -- 3.1 Language Layout -- 3.2 More on S Objects -- 3.3 Arithmetical Expressions -- 3.4 Character Vector Operations -- 3.5 Formatting and Printing -- 3.6 Calling Conventions for Functions -- 3.7 Model Formulae -- 3.8 Control Structures -- 3.9 Array and Matrix Operations -- 3.10 Introduction to Classes and Methods -- 4 Graphics -- 4.1 Graphics Devices -- 4.2 Basic Plotting Functions -- 4.3 Enhancing Plots -- 4.4 Fine Control of Graphics -- 4.5 Trellis Graphics -- 5 Univariate Statistics -- 5.1 Probability Distributions -- 5.2 Generating Random Data -- 5.3 Data Summaries -- 5.4 Classical Univariate Statistics -- 5.5 Robust Summaries -- 5.6 Density Estimation -- 5.7 Bootstrap and Permutation Methods -- 6 Linear Statistical Models -- 6.1 An Analysis of Covariance Example -- 6.2 Model Formulae and Model Matrices -- 6.3 Regression Diagnostics -- 6.4 Safe Prediction -- 6.5 Robust and Resistant Regression -- 6.6 Bootstrapping Linear Models -- 6.7 Factorial Designs and Designed Experiments -- 6.8 An Unbalanced Four-Way Layout -- 6.9 Predicting Computer Performance -- 6.10 Multiple Comparisons -- 7 Generalized Linear Models -- 7.1 Functions for Generalized Linear Modelling -- 7.2 Binomial Data -- 7.3 Poisson and Multinomial Models -- 7.4 A Negative Binomial Family -- 7.5 Over-Dispersion in Binomial and Poisson GLMs -- 8 Non-Linear and Smooth Regression -- 8.1 An Introductory Example -- 8.2 Fitting Non-Linear Regression Models -- 8.3 Non-Linear Fitted Model Objects and Method Functions -- 8.4 Confidence Intervals for Parameters -- 8.5 Profiles -- 8.6 Constrained Non-Linear Regression -- 8.7 One-Dimensional Curve-Fitting -- 8.8 Additive Models -- 8.9 Projection-Pursuit Regression -- 8.10 Neural Networks -- 8.11 Conclusions -- 9 Tree-Based Methods -- 9.1 Partitioning Methods -- 9.2 Implementation in rpart -- 9.3 Implementation in tree -- 10 Random and Mixed Effects -- 10.1 Linear Models -- 10.2 Classic Nested Designs -- 10.3 Non-Linear Mixed Effects Models -- 10.4 Generalized Linear Mixed Models -- 10.5 GEE Models -- 11 Exploratory Multivariate Analysis -- 11.1 Visualization Methods -- 11.2 Cluster Analysis -- 11.3 Factor Analysis -- 11.4 Discrete Multivariate Analysis -- 12 Classification -- 12.1 Discriminant Analysis -- 12.2 Classification Theory -- 12.3 Non-Parametric Rules -- 12.4 Neural Networks -- 12.5 Support Vector Machines -- 12.6 Forensic Glass Example -- 12.7 Calibration Plots -- 13 Survival Analysis -- 13.1 Estimators of Survivor Curves -- 13.2 Parametric Models -- 13.3 Cox Proportional Hazards Model -- 13.4 Further Examples -- 14 Time Series Analysis -- 14.1 Second-Order Summaries -- 14.2 ARIMA Models -- 14.3 Seasonality -- 14.4 Nottingham Temperature Data -- 14.5 Regression with Autocorrelated Errors -- 14.6 Models for Financial Series -- 15 Spatial Statistics -- 15.1 Spatial Interpolation and Smoothing -- 15.2 Kriging -- 15.3 Point Process Analysis -- 16 Optimization -- 16.1 Univariate Functions -- 16.2 Special-Purpose Optimization Functions -- 16.3 General Optimization -- Appendices -- A Implementation-Specific Details -- A.1 Using S-PLUS under Unix / Linux -- A.2 Using S-PLUS under Windows -- A.3 Using R under Unix / Linux -- A.4 Using R under Windows -- A.5 For Emacs Users -- B The S-PLUS GUI -- C Datasets, Software and Libraries -- C.1 Our Software -- C.2 Using Libraries -- References.

In: Springer eBooks

Weitere Ausg.: Printed edition: ISBN 9781441930088

Sprache: Englisch

DOI: 10.1007/978-0-387-21706-2

URL: http://dx.doi.org/10.1007/978-0-387-21706-2

URL: Volltext

URL: Volltext  (lizenzpflichtig)

URL: Cover

UID:

Umfang: 1 online resource (527 p.)

Ausgabe: 2nd Eng. ed.

ISBN: 1-282-28929-2 , 9786612289293 , 0-08-096019-7

Serie: North-Holland mathematical library ; v. 31

Inhalt: Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of G

Anmerkung: Based on the author's Teoria liczb. , Front Cover; Elementary Theory of Numbers; Copyright Page; Contents; Author's Preface; Editor's Preface; Chapter I Divisibility and Indeterminate Equations of First Degree; 1. Divisibility; 2. Least common multiple; 3. Greatest common divisor; 4. Relatively prime numbers; 5. Relation between the greatest common divisor and the least common multiple; 6. Fundamental theorem of arithmetic; 7. Proof of the formulae (al, a2, ..., an+1) = (al,a2, ..., an),an+1) and [a1, a2, ...,an+1] = [[a1, a2, ...,an], an+1]; 8. Rules for calculating the greatest common divisor of two numbers , 9. Representation of rationals as simple continued fractions10. Linear form of the greatest common divisor; 11. Indeterminate equations of m variables and degree 1; 12. Chinese Remainder Theorem; 13. Thue's Theorem; 14. Square-free numbers; Chapter II Diophantlne Analysis of Second and Higher Degrees; 1. Diophantine equations of arbitrary degree and one unknown; 2. Problems concerning Diophantine equations of two or more unknowns; 3. The equation x2 +y2 = z2; 4. Integral solutions of the equation x2+y2 = z2 for which x-y = ±1; 5. Pythagorean triangles of the same area , 6. On squares whose sum and difference are squares7. The equation x4 +y4 = z2; 8. On three squares for which the sum of any two is a square; 9. Congruent numbers; 10. The equation x2 + y2+ z2 = t2; 11. The equation xy = zt; 12. The equation x4 - x2y2 + y4 = z2; 13. The equation x4 + 9x2y2 +27y4 = z2; 14. The equation x3 + y3 = 2z3; 15. The equation x3 + y3 = az3 with a 〉 2; 16. Triangular numbers; 17. The equation x2 - Dy2 = 1; 18. The equations x2 +k = y3 where k is an integer; 19. On some exponential equations and others; Chapter III Prime Numbers , 1. The primes. Factorization of a natural number m into primes2. The Eratosthenes sieve. Tables of prime numbers; 3. The differences between consecutive prime numbers; 4. Goldbach's conjecture; 5. Arithmetical progressions whose terms are prime numbers; 6. Primes in a given arithmetical progression; 7. Trinomial of Euler x2 + x+ 41; 8. The Conjecture H; 9. The function p (x); 10. Proof of Bertrand's Postulate (Theorem of Tchebycheff); 11. Theorem of H. F. Scherk; 12. Theorem of H.-E. Richert; 13. A conjecture on prime numbers; 14. Inequalities for the function p (x) , 15. The prime number theorem and its consequencesChapter IV Number of Divisors and Their Sum; 1. Number of divisors; 2. Sums d(1)+d(2)+ ... +d(n); 3. Numbers d(n) as coefficients of expansions; 4. Sum of divisors; 5. Perfect numbers; 6. Amicable numbers; 7. The sum s'(1)+s""(2)+ .., +s""(n); 8. The numbers s""(n) as coefficients of various expansions; 9. Sums of summands depending on the natural divisors of a natural number n; 10. The Möbius function; 11. The Liouville function ? (n); Chapter V Congruences; 1. Congruences and their simplest properties , 2. Roots of congruences. Complete set of residues , English

Weitere Ausg.: ISBN 0-444-86662-0

Sprache: Englisch

UID:

Umfang: 1 online resource (xii, 224 pages) : , digital, PDF file(s).

ISBN: 9781316424254 (ebook)

Inhalt: Gravitational lensing is a consequence of general relativity, where the gravitational force due to a massive object bends the paths of light originating from distant objects lying behind it. Using very little general relativity and no higher level mathematics, this text presents the basics of gravitational lensing, focusing on the equations needed to understand the phenomena. It then applies them to a diverse set of topics, including multiply imaged objects, time delays, extrasolar planets, microlensing, cluster masses, galaxy shape measurements, cosmic shear, and lensing of the cosmic microwave background. This approach allows undergraduate students and others to get quickly up to speed on the basics and the important issues. The text will be especially relevant as large surveys such as LSST and Euclid begin to dominate the astronomical landscape. Designed for a one semester course, it is accessible to anyone with two years of undergraduate physics background.

Anmerkung: Title from publisher's bibliographic system (viewed on 29 May 2018). , 1. Overview -- 2. Deflection of light -- 3. Multiple images -- 4. Magnification -- 5. Microlensing -- 6. Weak lensing : galaxy shapes -- 7. Mass from shapes -- 8. Cosmic shear -- 9. Lensing of the cosmic microwave background -- Appendix A. Numbers -- Appendix B. Lensing formulae.

Weitere Ausg.: Print version: ISBN 9781107129764

Sprache: Englisch

URL: https://doi.org/10.1017/9781316424254

URL: lizenzpflichtig