Note: Intro -- Mass Metrology -- Preface -- Contents -- Chapter 1: Unit of Mass and Standards of Mass -- Chapter 2: Two-Pan Equal-Arm Balances -- Chapter 3: Single-Pan Mechanical Balances -- Chapter 4: Electronic Balances and Effect of Gravity -- Chapter 5: Strain Gauge Load Cells -- Chapter 6: Various Types of Transducers for Weighing -- Chapter 7: Testing of Electronic Balances -- Chapter 8: Air Density and Buoyancy Correction -- Chapter 9: Weights-Standards of Mass -- Chapter 10: Group Weighing Method -- Chapter 11: Nanotechnology for Detection of Small Mass Difference -- Chapter 12: Redefining the Unit of Mass -- CGPM Draft Resolution 2011 -- Index.

Note: Intro -- Units of Measurement -- 1 Metrology Through Ages -- 1.1 Introduction -- 1.2 History of Metrology in India -- 1.2.1 Legal Metrology -- 1.2.2 Town Planning -- 1.2.3 Length Measurements -- 1.2.4 Time Measurements -- Time Intervals -- Sidereal Metrics -- Smaller Units of Time Used in the Vedas -- Lunar Metrics -- Tropical Metrics -- Reckoning of Time Among Other Entities -- Counting of Time -- Time Scale in Seconds -- 1.2.5 Units of Time and Angle -- 1.2.6 Mass Measurement -- For Trade in Food Grains and Similar Items -- For Gold Trade -- For Silver Trade -- 1.2.7 Volume Measurements -- 1.2.8 Numeration -- References -- Further Readings -- 2 System of Quantities and Units -- 2.1 Quantities -- 2.2 System of Quantities -- 2.2.1 Quantity -- 2.2.2 Base Quantity -- 2.2.3 System of Base Quantities -- 2.2.4 Derived Quantity -- 2.2.5 Quantity Equation -- 2.3 Measurement Unit -- 2.3.1 System of Measurement Units -- 2.3.2 System of Base Units -- Properties of Base Units -- Minimum Number of Base Units -- 2.3.3 Derived Unit -- 2.3.4 Unit Equation -- 2.3.5 Properties of Units of Measurement -- 2.3.6 Coherent Derived Unit -- 2.4 Quantity of Dimension 1 or Dimensionless Quantity -- 2.4.1 Dimension of a Quantity -- 2.4.2 Quantities of Dimension 1 or Dimensionless Quantities -- 2.4.3 Ordinal Quantity -- 2.4.4 Quantity Scale, Measurement Scale -- 2.4.5 Ordinal Quantity Scale, Ordinal Scale -- 2.4.6 Nominal Property -- 2.5 Conversion Factor Between Units -- 2.6 Quantity Relations -- 2.6.1 Quantity Value -- 2.6.2 Numerical Quantity Value -- 2.6.3 Quantity Calculus -- 2.7 Units Used in Biology Biochemistry, Molecular Biology, Forensic Science for Biological Effects -- 2.7.1 Photochemical or Photo-biological Quantitiesand Their Units -- 2.8 Units Used in Photometry -- 2.8.1 Photometry -- 2.8.2 Actinic Action Spectrum -- 2.8.3 Types of Visions. , 2.9 Unit in the Field of Sound -- 2.10 Units in the Field of Ionizing Radiations -- 2.11 SI Units in the Framework of General Relativity -- References -- 3 Various Systems of Units -- 3.1 Introduction -- 3.2 Relations Between the Quantities -- 3.2.1 Derived Quantities by Definition -- 3.2.2 Derived Quantities by a Phenomenon -- 3.3 Three-Dimensional Systems of Units -- 3.3.1 Gauss System -- 3.3.2 CGS System -- 3.3.3 FPS System -- 3.4 Four-Dimensional Systems of Units -- 3.4.1 Giorgi System -- 3.4.2 Maxwell System -- 3.4.3 Hartree System -- 3.4.4 Units for Atomic and Molecular Measurements -- 3.4.5 McWeeny System -- 3.4.6 Ohm, Ampere, Second and Metre System -- 3.4.7 Force, Length and Time System -- 3.4.8 System in Terms of Universal Constants (G, H, E and Q) -- 3.4.9 System in Terms of Electric Charge, Flux,Length and Time -- 3.4.10 System in Terms of L, M, T and R -- 3.5 Derived Quantities in Terms of L, M, T and R: An Example -- References -- 4 Metre Convention and Evolution of Base Units -- 4.1 BIPM and Metre Convention -- 4.1.1 General Conference on Weights and Measures (CGPM) -- 4.1.2 International Committee for Weightsand Measures (CIPM) -- 4.1.3 Consultative Committees -- Consultative Committee for Electricity and Magnetism (CCEM) -- Consultative Committee for Photometry and Radiometry (CCPR) -- Consultative Committee for Thermometry (CCT) -- Consultative Committee for Length (CCL) -- Consultative Committee for Time and Frequency (CCTF) -- Consultative Committee for Ionizing Radiation (CCRI) -- Consultative Committee for Units (CCU) -- Consultative Committee for Mass and Related Quantities (CCM) -- Consultative Committee for Amount of Substance: Metrology in Chemistry (CCQM) -- Consultative Committee for Acoustics, Ultrasound and Vibration(CCAUV) -- 4.1.4 International Bureau of Weights and Measures (BIPM) -- Scientific Activities. , Objects of BIPM -- Staff at BIPM -- Publications -- Metrologia -- 4.1.5 Linkages of Various Organs of Metre Convention -- 4.2 International System of Units (SI) -- 4.2.1 Base Units -- 4.3 Evolution of Base Units -- 4.3.1 Unit of Length -- 4.3.2 Unit of Mass -- International Prototype of Kilogram -- 4.3.3 Unit of Time -- 4.3.4 Unit of Electric Current -- 4.3.5 Unit of Luminous Intensity -- 4.3.6 Unit of Temperature -- Unit of Thermodynamic Temperature (Kelvin) -- 4.3.7 Unit of Amount of Substance (Mole) -- 4.3.8 Dependence of Base Units -- References -- 5 Realization of Base Units -- 5.1 The Metre -- 5.1.1 Standard Radiations -- 5.2 The Kilogram -- 5.2.1 Method of Cleaning -- Cleaning with Chamois Leather -- Cleaning with Steam -- Efficacy of the Cleaning Procedure -- 5.2.2 Uncertainty in National Standards -- 5.3 The Second -- 5.4 The Ampere -- 5.4.1 Josephson and Klitzing Constants -- 5.4.2 Values of Josephson and Klitzing Constants -- 5.5 The Candela -- 5.6 The Kelvin -- 5.6.1 Triple Point of Water -- 5.6.2 Temperature Scales -- 5.6.3 ITS-90 -- Defining Fixed Points on ITS-90 -- ITS-90 and PLTS-2000 -- Defining Fixed Points on PLTS-2000 -- 5.7 The Mole -- References -- 6 Derived Quantities and Their Units -- 6.1 Derived Quantities -- 6.2 Units of Derived Quantities -- 6.3 SI Derived Units -- 6.3.1 Units Expressed in Terms of Base Units -- 6.3.2 Derived Units with Special Names -- 6.3.3 Derived Units Formed from the Derived Units with Special Names -- 6.3.4 Derived Quantities of Dimension 1 -- 6.4 Units Outside the SI -- 6.4.1 Units Accepted for Use with the SI -- 6.4.2 Non-SI Units with Experimentally Obtained Values -- 6.4.3 Non-SI Units Used by Special Groups -- 6.4.4 Other Non-SI Units with Special Names -- 6.4.5 Other Non-SI Units Found in the Old Literature -- References -- 7 Expressing SI Units -- 7.1 Introduction -- 7.2 SI Prefixes. , 7.2.1 Rules for Using SI Prefixes -- 7.2.2 Prefix About the Kilogram -- 7.3 Writing of SI Unit Symbols -- 7.3.1 Unit Symbols and Their Combinations -- 7.3.2 Names of Units -- 7.3.3 Quantity Calculus -- Value of Quantity -- Numerical Value of a Given Quantity -- Formatting the Value of a Quantity -- Symbols of Quantities -- Quantity Symbols and Unit Symbols -- 7.3.4 Stating Values of Quantities of Dimension 1 -- Use of Symbol % -- 7.4 Expression of Numbers -- 7.4.1 Formatting Numbers, and the Decimal Marker -- 7.4.2 Expressing the Measurement Uncertainty -- 7.5 Advantages of SI Units -- 7.5.1 Harmonization of Units -- General Principle -- 7.5.2 Expressing the Values of o and o in Terms of SI Units -- 7.5.3 Expressing Electrostatic and ElectromagneticQuantities in SI Units -- Charge and Current -- Potential -- Electrical Resistance -- Electrical Capacitance -- emu of Magnetic Flux -- Magnetic field Strength (Flux Density) -- Electric field -- Inductance -- 7.5.4 SI Units of Quantities in Magnetic Field -- SI Unit of Magnetic Pole Strength -- Magnetic Flux Density/Magnetizing Force -- Intensity of Magnetization -- 7.5.5 Homogenizing of Units of Energy in Heat -- 7.5.6 Coherent System -- Coherent Derived Unit -- 7.5.7 Well-Defined Units -- References -- 8 Future Definitions of SI Units -- 8.1 In Terms of Physical Constants -- 8.1.1 Basis of SI Units -- 8.2 From Single Source -- 8.2.1 In Terms of Hydrogen Atom -- 8.2.2 In Terms of Only One Standard (Frequency) -- 8.2.3 In Terms of Fundamental Constants UsingMaxwell Equations -- 8.2.4 A Consistent Set of Fundamental Constants by BIPM -- 8.3 CIPM Recommendation 1 (CI-2005) -- 8.4 A Proposal to Redefine Kilogram, Ampere, Kelvin and Mole -- 8.4.1 Kilogram -- 8.4.2 Ampere -- 8.4.3 Kelvin -- 8.4.4 Mole -- 8.5 The Values of h, e, k and NA -- 8.5.1 Observations -- 8.6 Practical Standards to Realize Kilogram. , 8.6.1 Other Methods of Redefining Kilogram -- 8.6.2 Conclusion in Regard to the Kilogram -- 8.6.3 Measurement Standards -- Embodiment of Units of Measurements -- References -- 9 Scientists Associated with Units of Measurements -- 9.1 Scientists Associated with Base Units -- 9.1.1 Lord Kelvin -- 9.1.2 Anders Celsius -- 9.1.3 Andre Marie Ampere -- 9.2 Scientists Associated with Derived Units -- 9.2.1 Sir Isaac Newton -- 9.2.2 Heinrich Rudolf Hertz -- 9.2.3 Blaise Pascal -- 9.2.4 James Prescott Joule -- 9.2.5 James Watt -- 9.2.6 Charles Augustin Coulomb -- 9.2.7 Alessandro Volta -- 9.2.8 Michael Faraday -- 9.2.9 Wilhelm Eduard Weber -- 9.2.10 Nickola Tesla -- 9.2.11 Joseph Henry -- 9.2.12 Antoine Henri Becquerel -- 9.2.13 Louis Harold Gray -- 9.2.14 Rolf M. Sievert -- Sievert Chamber -- 9.2.15 Georg Simon Ohm -- 9.2.16 Werner von Siemens -- 9.3 Some Units Not Named After Any Scientist -- Appendix A: National Physical laboratory -- A.1 Metre -- A.2 Kilogram -- A.3 Second -- A.4 Ampere -- A.5 Kelvin -- A.6 Candela -- A.7 Mole -- A.8 Radiation -- References -- Index.

Note: Cover -- Contents -- Chapter 1. The Stefan Problem and its Classical Formulation -- 1.1 Some Stefan and Stefan-like Problems -- 1.2 Free Boundary Problems with Free Boundaries of Codimension-two -- 1.3 The Classical Stefan Problem in One-dimension and the Neumann Solution -- 1.4 Classical Formulation of Multi-dimensional Stefan Problems -- Chapter 2. Thermodynamical and Metallurgical Aspects of Stefan Problems -- 2.1 Thermodynamical Aspects -- 2.2 Some Metallurgical Aspects of Stefan Problems -- 2.3 Morphological Instability of the Solid--Liquid Interface -- 2.4 Non-material Singular Surface: Generalized Stefan Condition -- Chapter 3. Extended Classical Formulations of n-phase Stefan Problems with n > -- 1 -- 3.1 One-phase Problems -- 3.2 Extended Classical Formulations of Two-phase Stefan Problems -- 3.3 Stefan problems with Implicit Free Boundary Conditions -- Chapter 4. Stefan Problem with Supercooling: Classical Formulation and Analysis -- 4.1 Introduction -- 4.2 A Phase-field Model for Solidification using Landau Ginzburg Free Energy Functional -- 4.3 Some Thermodynamically Consistent Phase-field and Phase Relaxation Models of Solidification -- 4.4 Solidification of Supercooled Liquid Without Curvature Effect and Kinetic Undercooling: Analysis of the Solution -- 4.5 Analysis of Supercooled Stefan Problems with the Modified Gibbs Thomson Relation -- Chapter 5. Superheating due to Volumetric Heat Sources: The Formulation and Analysis -- 5.1 The Classical Enthalpy Formulation of a One-dimensional Problem -- 5.2 The Weak Solution -- 5.3 Blow-up and Regularization -- Chapter 6. Steady-State and Degenerate Classical Stefan Problems -- 6.1 Some Steady-state Stefan Problems -- 6.2 Degenerate Stefan Problems -- Chapter 7. Elliptic and Parabolic Variational Inequalities -- 7.1 Introduction -- 7.2 The Elliptic Variational Inequality. , 7.3 The Parabolic Variational Inequality -- 7.4 Some Variational Inequality Formulations of Classical Stefan Problems -- Chapter 8. The Hyperbolic Stefan Problem -- 8.1 Introduction -- 8.2 Model I: Hyperbolic Stefan Problem with Temperature Continuity at the Interface -- 8.3 Model II: Formulation with Temperature Discontinuity at the Interface -- 8.4 Model III: Delay in the Response of Energy to Latent and Sensible Heats -- Chapter 9. Inverse Stefan Problems -- 9.1 Introduction -- 9.2 Well-posedness of the solution -- 9.3 Regularization -- 9.4 Determination of Unknown Parameters in Inverse Stefan Problems -- 9.5 Regularization of Inverse Heat Conduction Problems by Imposing Suitable Restrictions on the solution -- 9.6 Regularization of Inverse Stefan Problems Formulated as Equations in the form of Convolution Integrals -- 9.7 Inverse Stefan Problems Formulated as Defect Minimization Problems -- Chapter 10. Analysis of the Classical Solutions of Stefan Problems -- 10.1 One-dimensional One-phase Stefan Problems -- 10.2 One-dimensional Two-phase Stefan Problems -- 10.3 Analysis of the Classical Solutions of Multi-dimensional Stefan Problems -- Chapter 11. Regularity of the Weak Solutions of Some Stefan Problems -- 11.1 Regularity of the Weak solutions of One-dimensional Stefan Problems -- 11.2 Regularity of the Weak solutions of Multi-dimensional Stefan Problems -- Appendix A. Preliminaries -- Appendix B. Some Function Spaces and Norms -- Appendix C. Fixed Point Theorems and Maximum Principles -- Appendix D. Sobolev Spaces -- Bibliography -- Captions for Figures -- Subject Index.

Note: Front Cover -- The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods -- Copyright -- Dedication -- Contents -- List of Symbols -- Preface to the New Edition -- Preface -- Acknowledgements -- Chapter 1: The Stefan Problem and Its Classical Formulation -- 1.1 Some Stefan and Stefan-Like Problems -- Linearization of the Above Problem -- 1.2 Free Boundary Problems With Free Boundariesof Codimension-Two -- 1.3 The Classical Stefan Problem in One-Dimension and the Neumann Solution -- 1.3.1 Melting Problem -- 1.3.2 Neumann Solution -- 1.4 Classical Formulation of Multidimensional Stefan Problems -- 1.4.1 Two-Phase Stefan Problem in Multiple Dimensions -- 1.4.2 Alternative Forms of the Stefan Condition -- 1.4.3 The Kirchhoff's Transformation -- 1.4.4 Boundary Conditions at the Fixed Boundary -- (A) Standard Boundary Conditions -- (AI) Type I Boundary Condition -- (AII) Boundary Condition of Radiative-Convective Type -- (B) Nonstandard Boundary Conditions -- (BI) Nonlocal Boundary Condition -- (BII) Boundary Condition of the Fifth Type -- (C) Boundary Conditions With Multivalued Functions -- 1.4.5 Conditions at the Free Boundary -- Implicit Free Boundary Condition -- 1.4.6 The Classical Solution -- 1.4.7 Conservation Laws and the Motion of the Melt -- Control Volume and Applications of Conservation Laws -- Conservation of Mass: Equation of Continuity -- Equation of Conservation of Linear Momentum -- The Equation of Conservation of Energy -- Chapter 2: Thermodynamical and Metallurgical Aspects of Stefan Problems -- 2.1 Thermodynamical Aspects -- 2.1.1 Microscopic and Macroscopic Models -- 2.1.2 Laws of Classical Thermodynamics -- First Law of Thermodynamics -- Second Law of Thermodynamics: Entropy -- 2.1.3 Some Thermodynamic Variables and Thermal Parameters. , 2.1.4 Equilibrium Temperature: Clapeyron's Equation -- 2.2 Some Metallurgical Aspects of Stefan Problems -- 2.2.1 Nucleation and Supercooling -- Degree of Supercooling -- 2.2.2 The Effect of Interface Curvature -- 2.2.3 Nucleation of Melting, Effect of Interface Kinetics and Glassy Solids -- 2.3 Morphological Instability of the Solid-Liquid Interface -- 2.4 Nonmaterial Singular Surface: Generalized Stefan Condition -- Conservation of Forces in R -- Conservation of Energy in the Singular Surface Γ -- Chapter 3: Extended Classical Formulations of n-Phase Stefan Problems With n ≥1 -- 3.1 One-Phase Problems -- 3.1.1 An Extended Formulation of One-Dimensional One-Phase Problem -- 3.1.2 Solidification of Supercooled Liquid -- 3.1.3 Multidimensional One-Phase Problems -- A Three-Dimensional Ablation Problem -- A Signorini-Type Boundary Condition -- 3.2 Extended Classical Formulations of Two-Phase Stefan Problems -- 3.2.1 An Extended Formulation of the One-Dimensional Two-Phase Problem -- 3.2.2 Multidimensional Stefan Problems of Classes II and III -- 3.2.3 Classical Stefan Problems With n-Phases, n> -- 2 -- Some One-Dimensional Problems With More Than Two Phases -- 3.2.4 Solidification With Transition Temperature Range -- 3.3 Stefan Problems With Implicit Free Boundary Conditions -- 3.3.1 Schatz Transformations and Implicit Free Boundary Conditions -- Conversion of a Stefan-Type Problem to a Stefan Problem -- 3.3.2 Unconstrained and Constrained Oxygen-Diffusion Problem -- Constrained and Unconstrained ODP -- ODP in a Radially Symmetric Domain -- Quasi-Static Two-Dimensional ODP and the Hele-Shaw Problem -- Chapter 4: Stefan Problem With Supercooling: Classical Formulation and Analysis -- 4.1 Introduction -- 4.2 A Phase-Field Model for Solidification Using Landau-Ginzburg Free Energy Functional. , 4.3 Some Thermodynamically Consistent Phase-Field and Phase Relaxation Models of Solidification -- Entropy Functional -- Some Thermodynamically Consistent Phase Relaxation Modelsfor Supercooling -- Superheating and Supercooling Effects -- 4.4 Solidification of Supercooled Liquid Without Curvature Effect and Kinetic Undercooling: Analysis of the Solution -- 4.4.1 One-Dimensional One-Phase Solidification of Supercooled Liquid (SSP) -- 4.4.2 Regularization of a Blow-Up in SSP by Looking at CODP -- 4.4.3 Analysis of Problems With Some Changes in the Initialand Boundary Conditions in SSP -- 4.5 Analysis of SSPs With the Modified Gibbs-Thomson Relation -- 4.5.1 Introduction -- 4.5.2 One-Dimensional One-Phase SSPs With the Modified Gibbs-Thomson Relation -- 4.5.3 One-Dimensional Two-Phase Stefan Problems Withthe Modified Gibbs-Thomson Relation -- 4.5.4 Multidimensional SSPs and Problems With the Modified Gibbs-Thomson Relation -- Concluding Remarks -- 4.5.5 Weak Formulation With Supercooling and Superheating Effects -- Chapter 5: Superheating due to Volumetric Heat Sources -- 5.1 The Classical Enthalpy Formulation (CEF) -- 5.2 The Weak Solution (WS) -- 5.2.1 The WS and Its Relation to Classical Solution -- 5.2.2 Structure of the Mushy Region in the Presence of Heat Sources -- 5.3 Blow-Up and Regularization -- Chapter 6: Steady-State and Degenerate Classical Stefan Problems -- 6.1 Some Steady-State Stefan Problems -- 6.2 Degenerate Stefan Problems -- Quasi Steady-State Stefan Problems -- Degenerate Parabolic-Elliptic Problems -- 6.2.1 A Quasi Steady-State Problem (QSSP) and Its Relationto the HSP -- Chapter 7: Elliptic and Parabolic Variational Inequalities -- 7.1 Introduction -- 7.2 The Elliptic Variational Inequality -- 7.2.1 Definition and the Basic Function Spaces -- 7.2.2 Minimization of a Functional -- 7.2.3 The Complementarity Problem. , 7.2.4 Some Existence and Uniqueness Results Concerning Elliptic Inequalities -- Lions-Stampacchia Theorem -- Variational Equation -- 7.2.5 Equivalence of Different Inequality Formulations of an Obstacle Problem of the String -- Equivalence of Formulations (I), (II) and (III) -- 7.3 The Parabolic Variational Inequality -- 7.3.1 Formulation in Appropriate Spaces -- 7.4 Some Variational Inequality Formulations of Classical Stefan Problems -- 7.4.1 One-Phase Stefan Problems -- Duvait's Transformation -- One-Phase Continuous Casting Model and Its Variational Inequality Formulation -- Oxygen-Diffusion Problem -- 7.4.2 A Stefan Problem With a Quasi-Variational Inequality Formulation -- 7.4.3 The Variational Inequality Formulation of a Two-Phase Stefan Problem -- Chapter 8: The Hyperbolic Stefan Problem -- 8.1 Introduction -- 8.1.1 Relaxation Time and Relaxation Models -- 8.2 Model I: Hyperbolic Stefan Problem With Temperature Continuity at the Interface -- 8.2.1 The Mathematical Formulation -- A One-Dimensional Two-Phase Hyperbolic Stefan Problem -- Differential Equations -- Initial Conditions -- Boundary Conditions at the Fixed Boundaries -- Boundary Conditions at the Free Boundary -- 8.2.2 Some Existence, Uniqueness and Well-Posedness Results -- A One-Dimensional One-Phase Hyperbolic Stefan Problem -- Global Solution for the One-Phase Problem -- A Two-Phase Problem -- 8.3 Model II: Formulation With Temperature Discontinuity at the Interface -- 8.3.1 The Mathematical Formulation -- Admissibility Conditions -- 8.3.2 The Existence and Uniqueness of the Solution and Its Convergence as τ → 0 -- Dirichlet Problem -- Neumann Problem -- 8.4 Model III: Delay in the Response of Energy to Latent and Sensible Heats -- 8.4.1 The Classical and the Weak Formulations -- Derivation of Energy Conservation Equation for the Two-Phase Problem. , Chapter 9: Inverse Stefan Problems -- 9.1 Introduction -- 9.2 Well-Posedness of the Solution -- Nonexistence of the Solution -- Nonuniqueness of the Solution -- Continuous Dependence of the Solution on the Input Data -- 9.2.1 Approximate Solutions -- 9.3 Regularization -- 9.3.1 The Regularizing Operator and Generalized Discrepancy Principle -- 9.3.2 The Generalized Inverse -- 9.3.3 Regularization Methods -- 9.3.4 Rate of Convergence of a Regularization Method -- 9.4 Determination of Unknown Parameters in Inverse Stefan Problems -- 9.4.1 Unknown Parameters in the One-Phase Stefan Problems -- 9.4.2 Determination of Unknown Parameters in the Two-Phase Stefan Problems -- 9.5 Regularization of Inverse Heat conduction Problems by Imposing Suitable Restrictionson the Solution -- 9.6 Regularization of Inverse Stefan Problems Formulated as Equations in the Form of Convolution Integrals -- 9.7 Inverse Stefan Problems Formulated as Defect Minimization Problems -- Chapter 10: Analysis of the Classical Solutions of Stefan Problems -- 10.1 One-Dimensional One-Phase Stefan Problems -- 10.1.1 Analysis Using Integral Equation Formulations -- 10.1.2 Infinite Differentiability and Analyticity of the Free Boundary -- 10.1.3 Unilateral Boundary Conditions on the Fixed Boundary: Analysis Using Finite-Difference Schemes -- 10.1.4 Cauchy-Type Free Boundary Problems -- 10.1.5 Existence of Self-Similar Solutions of Some Stefan Problems -- 10.1.6 The Effect of Density Change -- 10.2 One-Dimensional Two-Phase Stefan Problems -- 10.2.1 Existence, Uniqueness and Stability Results -- 10.2.2 Differentiability and Analyticity of the Free Boundaryin the One-Dimensional Two-Phase Stefan Problems -- 10.2.3 One-Dimensional n-Phase Stefan Problems With n > -- 2 -- 10.3 Analysis of the Classical Solutionsof Multidimensional Stefan Problems. , 10.3.1 Existence and Uniqueness Results Valid for a Short Time.

Note: Intro -- MODERN HYDROLOGY AND SUSTAINABLE WATER DEVELOPMENT -- Contents -- Foreword -- Preface -- Acknowledgements -- A note for students and teachers -- 1 Fundamentals of hydrology -- 1.1 Properties of water -- 1.2 Common water quality parameters -- 1.3 Hydrologic cycle and global water distribution -- 1.4 Units and dimensions -- 1.5 Significant figures and digits -- 2 Surface water hydrology -- 2.1 Lakes -- 2.2 Glaciers -- 2.3 Streams -- 2.4 Watershed concept -- 2.5 Instrumentation and monitoring -- 2.6 Runoff processes and flow measurement -- 2.7 Rainfall-runoff analysis and modelling -- 2.8 Stream processes -- 2.9 Stream characteristics -- 2.10 River and reservoir routing -- 2.11 Scales and scaling -- 2.12 The invisible resource: groundwater -- 2.13 Tutorial -- 3 Groundwater hydrology -- 3.1 Occurrence of groundwater -- 3.2 Movement of groundwater -- 3.3 Hydraulic head -- 3.4 Dispersion -- 3.5 Specialized flow conditions -- 3.6 Groundwater measurements -- 3.7 Groundwater pollution -- 3.8 Composite nature of surface water and groundwater -- 3.9 Conjunctive use of surface water and groundwater -- 3.10 Tutorial -- 4 Well hydraulics and test pumping -- 4.1 Steady flow -- 4.2 Superposition in space and time -- 4.3 Boundaries and images in flow modelling -- 4.4 Well flow under special conditions -- 4.5 Well losses -- 4.6 Tutorial -- 5 Surface and groundwater flow modelling -- 5.1 Surface water flow modelling -- 5.2 Groundwater flow modelling -- 5.3 Surface and groundwater interactions and coupled/integrated modelling -- 6 Aqueous chemistry and human impacts on water quality -- 6.1 Principles and processes controlling composition of natural waters -- 6.2 Natural hydrochemical conditions in the subsurface -- 6.3 Presenting inorganic chemical data -- 6.4 Impact of human activities -- 6.5 Geochemical modelling -- 6.6 Chemical tracers. , 6.7 Groundwater - numerical modelling of solute transport -- 6.8 Relation between use and quality of water -- 6.9 Industrial use -- 6.10 Tutorial -- 7 Hydrologic tracing -- 7.1 Isotopes and radioactivity -- 7.2 Hydrologic tracers -- 7.3 Tracers and groundwater movement -- 7.4 Stable isotopes of oxygen and hydrogen -- 7.5 Dissolved noble gases -- 7.6 Models for interpretation of groundwater age -- 7.7 Tracers for estimation of groundwater recharge -- 7.8 Tutorial -- 8 Statistical analyses in hydrology -- 8.1 Descriptive statistics -- 8.2 Probability theory -- 8.3 Hydrologic frequency analysis -- 8.4 Nonparametric density estimation methods -- 8.5 Error analysis -- 8.6 Time series analysis -- 8.7 Tutorial -- 9 Remote sensing and GIS in hydrology -- 9.1 Principle of remote sensing -- 9.2 Approaches to data/image interpretation -- 9.3 Radar and microwave remote sensing -- 9.4 Geographic Information Systems (GIS) -- 9.5 Applications in hydrology -- 10 Urban hydrology -- 10.1 Water balance in urban areas -- 10.2 Disposal of waterborne wastes -- 10.3 New approaches and technologies for sustainable urbanization -- 11 Rainwater harvesting and artificial groundwater recharge -- 11.1 Historical perspective -- 11.2 Rainwater harvesting - some general remarks -- 11.3 Watershed management and water harvesting -- 11.4 Tutorial -- 12 Water resource development: the human dimensions -- 12.1 The global water crisis -- 12.2 Global initiatives -- 12.3 Water and ethics -- 12.4 Global water tele-connections and virtual water -- 13 Some case studies -- 13.1 The Yellow River Basin, China -- 13.2 The Colorado River Basin, United States -- 13.3 The Murray-Darling River Basin, Australia -- 13.4 The North Gujarat-Cambay region, Western India -- 14 Epilogue -- 14.1 Water and its properties, quality considerations, movement, and modelling of surface- and groundwater. , 14.2 Distribution of water in space and time -- 14.3 Water resource sustainability -- Bibliography -- Index -- Plate section faces page 172.

Note: Intro -- Preface -- Contents -- 1 Flow Through Capillary -- Abstract -- 1.1…Types of Flow -- 1.1.1 Turbulent Flow -- 1.1.2 Laminar Flow -- 1.2…Motion in Laminar Flow -- 1.3…Unit of Dynamic Viscosity -- 1.4…Rate of Flow in a Capillary -- 1.4.1 Kinetic Energy Correction -- 1.4.2 End Correction -- 1.5…Units of Kinematic Viscosity -- 1.6…Corrections to C Due to Various Parameters -- 1.6.1 Correction Due to Gravity -- 1.6.2 Buoyancy Correction -- 1.6.3 Correction Due to Thermal Expansion of Viscometer Bulb -- 1.6.4 Correction to C Due to Different Temperatures of Loading and Use -- 1.6.5 Correction to C Due to Change in Surface Tension -- 1.6.6 Temperature Correction to Kinematic Viscosity -- References -- 2 Kinematic Viscosity Scale and Uncertainty -- Abstract -- 2.1…Primary Standard -- 2.2…Establishing a Viscosity Scale -- 2.3…Viscosity Measurement System -- 2.3.1 At Level I -- 2.3.2 At Level II -- 2.3.3 At Level III -- 2.4…Equipment Required -- 2.4.1 Master Viscometers -- 2.4.1.1 Cannon U Tube Master Viscometer -- 2.4.1.2 Dimensions of Master Viscometer -- 2.4.1.3 Ubbelohde Master Viscometer -- 2.4.2 Thermometers -- 2.4.3 Bath -- 2.4.4 Timer -- 2.4.5 Cleaning Agents -- 2.4.6 Standard Liquids -- 2.4.6.1 Primary Standard -- 2.4.6.2 Standard Oils -- 2.5…Detailed Procedure -- 2.5.1 Calibration of Master Viscometers -- 2.5.1.1 Preparing the Bath -- 2.5.1.2 Cleaning of Viscometer -- 2.5.1.3 Charging the Cannon Master Viscometer -- 2.5.1.4 Charging the Ubbelohde Master Viscometer -- 2.5.1.5 Waiting for Thermal Equilibrium -- 2.5.1.6 Measurement of Efflux Time -- 2.5.2 Calibration of Second Viscometer with Water -- 2.5.3 Determination of Viscosity of Oil (Measurement at 40 degC) -- 2.5.3.1 Preparation of Oil Standard -- 2.5.3.2 Preparation of Bath -- 2.5.3.3 Charging the Viscometer -- 2.5.3.4 Waiting for Thermal Equilibrium. , 2.5.3.5 Measurement of Efflux Time -- 2.5.4 Measurement with Second Viscometer -- 2.5.5 Corrections and Calculation of Kinematic Viscosity at 40 degC -- 2.5.5.1 Different Temperatures of Measurement and Statement -- 2.5.5.2 Buoyancy Correction -- 2.5.5.3 Temperature Correction -- 2.5.5.4 Surface Tension Correction -- 2.5.6 Calculation of Kinematic Viscosity -- 2.5.6.1 Cannon Master Viscometer -- 2.5.6.2 Ubbelohde Master Viscometer -- 2.6…Standards Maintained at NPLI -- 2.6.1 Viscometers -- 2.6.2 Standard Oils -- 2.7…Propagation of Uncertainty in Establishing the Viscosity Scale -- 2.7.1 Expression for Uncertainty in the nth Step -- 2.7.2 Planning for Uncertainty -- 2.7.3 Correction Due to Different Measuring and Stated Temperatures -- 2.7.4 Uncertainty in the Value of Viscosity of Water -- References -- 3 Capillary Viscometers -- Abstract -- 3.1…Broad Classification -- 3.2…Three Groups of Viscometers -- 3.2.1 Modified Ostwald Viscometers -- 3.2.2 Suspended Level Viscometers -- 3.2.3 Reverse Flow Viscometers -- 3.3…Modified Ostwald Viscometers -- 3.3.1 Cannon Fenske Routine Viscometers -- 3.3.1.1 Dimensions -- 3.3.1.2 Charging -- 3.3.2 Zeitfuchs Viscometers -- 3.3.2.1 Dimensions -- 3.3.2.2 Charging -- 3.3.3 SIL Viscometers -- 3.3.3.1 Dimensions -- 3.3.3.2 Charging -- 3.3.4 Cannon-Manning Viscometers -- 3.3.4.1 Dimensions -- 3.3.4.2 Charging -- 3.3.5 BS/U-Tube Viscometer -- 3.3.5.1 Dimensions -- 3.3.5.2 Charging of BS/U -- 3.3.6 Miniature Viscometers BS/U-Tube or BS/U/M -- 3.3.6.1 Dimensions -- 3.3.6.2 Charging -- 3.3.7 Pinkevitch Viscometers -- 3.3.7.1 Dimensions -- 3.3.7.2 Charging -- 3.3.8 Equilibrium Time -- 3.3.9 Bringing the Sample up to the Timing Mark -- 3.4…Suspended Level Viscometers -- 3.4.1 Ubbelohde Viscometers -- 3.4.1.1 Dimensions -- 3.4.1.2 Charging -- 3.4.2 Cannon Ubbelohde viscometer -- 3.4.2.1 Dimensions -- 3.4.2.2 Charging. , 3.4.3 Cannon-Ubbelohde Semi-Micro Viscometer -- 3.4.3.1 Dimensions -- 3.4.3.2 Charging -- 3.4.4 BS/IP/SL (S) Viscometer -- 3.4.4.1 Dimensions -- 3.4.4.2 Charging -- 3.4.5 BS/IP/MSL Viscometer -- 3.4.5.1 Dimensions -- 3.4.5.2 Charging -- 3.4.6 Fitz-Simons Viscometer -- 3.4.6.1 Dimensions -- 3.4.6.2 Charging -- 3.4.7 Atlantic Viscometer -- 3.4.7.1 Dimensions -- 3.4.7.2 Charging -- 3.4.8 Equilibrium Time -- 3.5…Reverse Flow Viscometers -- 3.5.1 Zeitfuchs Cross-arm viscometer -- 3.5.1.1 Dimensions -- 3.5.1.2 Charging -- 3.5.2 Cannon-Fenske Viscometer -- 3.5.2.1 Dimensions -- 3.5.2.2 Charging -- 3.5.3 Lantz-Zeitfuchs Viscometer -- 3.5.3.1 Dimensions -- 3.5.3.2 Charging -- 3.5.4 BS/IP/RF U-Tube Reverse Flow -- 3.5.4.1 Dimensions -- 3.5.4.2 Charging -- 3.5.5 Equilibrium Time -- 3.5.6 Flow of Sample Through Capillary -- 3.6…For all Samples -- 3.6.1 Sample for Charging Viscometers -- References -- 4 Rotational and Other Types of Viscometers -- Abstract -- 4.1…Introduction -- 4.2…Rotational Viscometers -- 4.2.1 Coaxial Cylinders Viscometers -- 4.2.2 Concentric Spheres Viscometer -- 4.2.3 Rotating Disc Viscometer -- 4.2.4 Cone and Plate Viscometer -- 4.2.5 Coni-Cylindrical Viscometer -- 4.3…Falling Ball/Piston Viscometers -- 4.3.1 Falling Ball Viscometer -- 4.3.2 Falling Piston Viscometer -- 4.4…Rolling Ball Viscometer -- 4.4.1 Measurement with Rolling Ball Viscometer -- 4.5…Torsion Viscometer -- 4.6…Oscillating Piston Viscometer -- 4.7…Michell Cup and Ball Viscometer -- 4.7.1 Construction -- 4.7.2 Working -- 4.8…VROC -- 4.8.1 Physical Structure -- 4.8.2 Results Analysis -- 4.8.3 Advantage of Small Gap -- 4.9…Viscometers for Specific Field -- 4.9.1 Redwood Viscometer -- 4.9.1.1 Cup -- 4.9.1.2 Thermo-Control Bath -- 4.9.1.3 Working -- 4.9.2 Redwood No 2 Viscometer -- 4.9.2.1 Jet Dimensions -- 4.9.2.2 Construction Redwood No 2 Viscometer. , 4.9.2.3 Conversion of Redwood Seconds in Absolute Units of Viscosity -- 4.9.3 Saybolt Universal Viscometer -- 4.9.3.1 Construction of Saybolt Universal Viscometer -- 4.9.3.2 Conversion of Saybolt Seconds in Absolute Units of Viscosity -- 4.9.4 Saybolt Furol Viscometer -- 4.9.4.1 Conversion of Kinematic Viscosity in SI to TSU -- 4.9.5 Engler Viscometer -- 4.10…Bubble Viscometer -- References -- 5 Oscillating Viscometers -- Abstract -- 5.1…Oscillating Viscometers -- 5.2…Damped Oscillations -- 5.3…Measurement of \updelta and T -- 5.3.1 Logarithmic Decrement by Linear Measurement -- 5.3.2 Logarithmic Decrement by Time Measurement -- 5.3.3 Logarithmic Decrement by Time Measurement Between Two Fixed Points -- 5.4…Viscosity Equations -- 5.4.1 Right Circular Cylinder as Oscillating Body -- 5.4.2 Sphere as an Oscillating Body -- 5.5…Viscometer Used by Roscoe and Bainbridge -- 5.5.1 Viscometer -- 5.6…Viscometer Used by Torklep and Oye -- 5.6.1 Support System -- 5.6.2 Torsion Pendulum -- 5.6.3 Torsion Wire -- 5.6.4 Cross-Sectional View of the Viscometer -- 5.6.5 Oscillation Initiator -- 5.6.6 Measurement of delta and T -- 5.6.7 Calculation of Viscosity -- 5.7…Viscometer Used by Kestin and Shankland -- 5.7.1 Original Viscometer due to Kestin et al. -- 5.8…Viscometer Used by Berstad et al. -- 5.8.1 Sample Container and Temperature Control -- 5.9…NBS Torsion Pendulum -- 5.9.1 Torsion Pendulum -- 5.9.2 Torsion Viscometer -- 5.9.2.1 Suspension Wire and Its k Value -- 5.9.2.2 Sphere (Bob) -- 5.9.2.3 Moment of Inertia of the Empty Sphere -- 5.9.2.4 Measurement of Time period -- 5.9.2.5 Calculation of Kinematic Viscosity -- 5.9.3 Theory for Calculations of Viscosity -- 5.9.3.1 Viscous Torque -- 5.9.3.2 Dynamic Equation of the Shell -- 5.9.3.3 Computations of Tables for {{\varvec{f}}}({\varvec{\tau ,\alpha}} ) -- References -- 6 New Trends in Viscometers -- Abstract. , 6.1…Tuning-Fork Viscometers -- 6.2…Ultrasonic Viscometer -- 6.2.1 Longitudinal Waves and Acoustic Impedance of Fluid -- 6.2.2 Shear Waves and Shear Impedance of Fluid -- 6.3…Ultrasonic Plate Waves Viscometer -- 6.3.1 Device and Operation -- 6.3.2 Basic Theory -- 6.3.2.1 Viscous Mass Loading -- 6.3.2.2 Viscous Attenuation -- 6.3.3 ResultsResults -- 6.4…Viscosity by Love Waves -- 6.4.1 Outline of the Device -- 6.4.2 Advantages of Micro-Acoustic Device -- 6.4.2.1 Special Advantage of Love Wave Device -- 6.4.3 Sensitivity of Love Wave Device -- 6.5…Piezoelectric Resonator -- 6.5.1 Change in Frequency Versus Change in Mass -- 6.5.2 Change in Frequency Versus Viscosity -- 6.5.3 Impedance Versus Viscosity -- 6.5.4 Piezoelectric Resonator in Biochemical Reactions -- 6.5.5 Quartz Microbalance -- 6.5.6 Piezoelectric Resonator as Density and Viscosity Sensor -- 6.6…Micro-Cantilevers for Viscosity Measurement -- 6.6.1 Introduction -- 6.6.2 Theory -- 6.6.3 Simultaneous Determination of Density and Viscosity -- 6.7…Optical Fibre Viscometer -- 6.7.1 Introduction -- 6.7.2 Frequency Change of a Partially Immersed Fibre -- 6.7.3 Experimental Arrangement -- 6.7.3.1 Detection of Small Amplitude Vibration -- 6.8…Vibrating Wire Viscometer -- References -- Bibliography -- 7 Commercial Viscometers -- Abstract -- 7.1…Introduction -- 7.2…Cambridge Viscometers -- 7.2.1 Range of Products -- 7.2.2 Viscolab 3000 and Viscopro 8000 -- 7.2.3 Various Other Viscometers -- 7.3…HAAKE Viscometer -- 7.3.1 Range of Products -- 7.3.2 Rotational Viscometers -- 7.3.2.1 Metrological Specifications -- 7.3.2.2 Main Features -- 7.3.3 Haake Viscotesters 6 Plus and 7 Plus (Features) -- 7.3.3.1 Additional Features of the HAAKE Viscotester 7 Plus -- 7.3.3.2 Complying Standards -- 7.3.4 Falling Ball Viscometer -- 7.3.4.1 Users -- 7.3.4.2 Technical Data -- 7.3.4.3 Ball Selection. , 7.3.5 Haake MicroVisco 2.

Note: Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- About the Lead Editor -- About the Senior Editor-in-Chief -- About the Editor -- List of Contributors -- List of Abbreviations -- Foreword 1 -- Foreword 2 -- Preface 1 -- Preface 2 -- Preface 3 -- PART I: Management of Saline/Sodic Stress: Field Practices -- 1: Nomenclature and Reclamation of Sodic (Alkali) Soils Using Gypsum: A Review of Historical Perspective -- 2: Soil Salinity Management in Fruit Crops: A Review of Options and Challenges -- 3: Role of Conservation Agriculture in Mitigating Soil Salinity in Indo-Gangetic Plains of India -- PART II: Physiological and Molecular Innovations to Enhance Salt Tolerance -- 4: Physiological and Biochemical Changes in Plants Under Soil Salinity Stress: A Review -- 5: Biochemical, Physiological, and Molecular Approaches for Improving Salt Tolerance in Crop Plants: A Review -- 6: Genomics Technologies for Improving Salt Tolerance in Wheat -- PART III: Adaptations and Screening of Plants Under Water Logging and Salinity Stresses -- 7: Morpho-Biochemical and Molecular Markers for Screening and Assessing Plant Response to Salinity -- 8: Plants Under Waterlogged Conditions: An Overview -- PART IV: Non-Conventional and High-Value Crops for Salt-Affected Lands -- 9: Potential and Role of Halophyte Crops in Saline Environments -- 10: Approaches for Enhancing Salt Tolerance in Seed Spices -- Index.

Note: Front Cover -- Foreword -- Preface -- Contents -- List of Contributors -- Chapter 1. Sites of Generation and Physicochemical Basis of Formation of Reactive Oxygen Species in Plant Cell -- Chapter 2. Multiple Roles of Radicals in Plants -- Chapter 3. Reactive Oxygen Species and Ascorbate-Glutathione Interplay in Signaling and Stress Responses -- Chapter 4. Reactive Oxygen Species and Programmed Cell Death -- Chapter 5. Oxidative Burst-mediated ROS Signaling Pathways Regulating Tuberization in Potato -- Chapter 6. ROS Regulation of Antioxidant Genes -- Chapter 7. The Role of Antioxidant Enzymes during Leaf Development -- Chapter 8. Antioxidants Involvement in the Ageing of Non-green Organs: The Potato Tuber as a Model -- Chapter 9. Metal Toxicity, Oxidative Stress and Antioxidative Defense System in Plants -- Chapter 10. ROS, Oxidative Stress and Engineering Resistance in Higher Plants -- Chapter 11. Role of Free Radicals and Antioxidants in in vitro Morphogenesis -- Chapter 12. ROS as Biomarkers in Hyperhydricity -- Chapter 13. Antioxidant Effects of Plant Polyphenols: A Case Study ofa Polyphenol-rich Extract from Geranium sanguineum L. -- Chapter 14. LC-(Q) TOF-MS Characterization of Phenolic Antioxidants -- Chapter 15. Antioxidant Properties of Chinese Medicinal Plants -- Back Cover.

Note: Intro -- Measurement Uncertainties -- Preface -- Contents -- Chapter 1: Some Important Definitions -- 1.1 Introduction -- 1.2 Terms Pertaining to Quantity -- 1.2.1 Quantity -- 1.2.2 System of Base Quantities -- 1.2.3 Derived Quantity -- 1.2.4 Quantity Equation -- 1.2.5 Dimension of a Quantity -- 1.2.6 Measurand -- 1.2.7 True Value of a Quantity -- 1.2.8 Conventional True Value of a Quantity -- 1.2.9 Measured Value -- 1.2.10 Relation in Between Measured Valueand True or Conventional True Value -- 1.3 Terms Pertaining to Measurement -- 1.3.1 Measurement -- 1.3.2 Method of Measurement -- 1.3.3 Substitution Method -- 1.3.4 Differential Method -- 1.3.5 Null Method -- 1.3.6 Measurement Procedure -- 1.3.7 Result of Measurement -- 1.3.8 Error -- 1.3.9 Spurious Error -- 1.3.10 Relative Error -- 1.3.11 Random Error -- 1.3.12 Systematic Error -- 1.3.13 Accuracy of Measurement -- 1.3.14 Precision of Measurement Result -- 1.3.15 Repeatability -- 1.3.16 Reproducibility (of Measurement Results) -- 1.3.17 Correction -- 1.4 Terms Pertaining to Statistics -- 1.4.1 Observation -- 1.4.2 Independent Observations -- 1.4.3 Population -- 1.4.4 Sample -- 1.4.5 Measurement -- 1.4.6 Population of Measurement -- 1.4.7 Sample of Measurements -- 1.4.8 Frequency/Relative Frequency -- 1.4.9 Mean -- 1.4.10 Sample Mean -- 1.4.11 Population Mean -- 1.4.12 Merits and Demerits of Arithmetic Mean [3] -- 1.4.12.1 Merits -- 1.4.12.2 Demerits -- 1.4.13 Median -- 1.4.14 Quartiles -- 1.4.15 Dispersion -- 1.4.16 Standard Deviation -- 1.4.17 Variance -- 1.4.18 Sample Standard Deviation -- 1.4.19 Population Standard Deviation -- 1.4.20 Estimate of Population Standard Deviation -- 1.4.21 Estimate of Population and Sample Standard Deviations-Relation -- 1.4.22 Independent Variable -- 1.4.23 Dependent Variable or Response Variable -- 1.4.24 Correlation -- 1.4.25 Correlation Coefficient. , 1.4.26 Covariance -- 1.4.27 Random Variable -- 1.4.28 Discrete Random Variable -- 1.4.29 Continuous Random Variable -- 1.4.30 Probability -- 1.4.31 Probability Distribution -- 1.4.32 Normal Distribution -- 1.4.32.1 Alternative Definition -- 1.4.33 Properties of Normal Distribution -- 1.4.34 Probable Error -- 1.4.35 Range -- 1.4.36 Confidence Level -- 1.4.37 Confidence Interval -- 1.4.38 Outlier -- 1.4.39 Parameter -- 1.4.40 Random Selection -- 1.4.41 Sample Statistic -- 1.4.42 Error -- 1.4.43 Standard Error, or Standard Deviationof the Mean -- 1.4.44 Uncertainty -- 1.4.45 Evaluations of Uncertainty -- 1.4.46 Random Uncertainty(er) -- 1.4.47 Systematic Uncertainty(Us) -- 1.4.48 Standard Uncertainty -- 1.4.49 Expanded Uncertainty -- 1.4.50 Expressing Uncertainty of Measurement -- 1.4.51 Coverage Interval -- 1.4.52 Coverage Probability -- 1.4.53 Central Limit Theorem -- 1.5 Influence Quantity -- 1.6 Instruments and Standards -- 1.6.1 Repeatability of an Instrument -- 1.6.2 Precision of the Instrument -- 1.6.3 Accuracy of an Instrument -- 1.6.4 Accuracy of a Standard -- 1.6.5 Difference Between Uncertaintyand Accuracy -- 1.6.6 Difference Between the Correction, Errorand Uncertainty -- 1.6.7 Correction Factor -- 1.6.8 Discrimination Threshold -- 1.7 Some Special Integrals and Functions -- 1.7.1 Gamma Function -- 1.7.1.1 Gamma Probability Density Function -- 1.7.2 Beta Function of First Kind B(m,n) -- 1.7.2.1 Beta Probability Functions of First Kind -- 1.7.3 Alternative Form of Beta Function -- 1.7.4 Beta Function of Second Kind B (m,n) -- 1.7.4.1 Beta Probability Functions of Second Kind -- 1.7.5 Cauchy Distribution -- 1.7.6 Arc Sine(U-Shaped) Distribution -- References -- Chapter 2: Distribution Functions -- 2.1 Introduction -- 2.2 Random Variable -- 2.3 Discrete and Continuous Variables -- 2.4 Discrete Functions. , 2.4.1 Probability Distribution of a Random Variable -- 2.4.2 Discrete Probability Function -- 2.5 Distribution Function -- 2.5.1 Continuous Distribution Function -- 2.5.2 Discrete Distribution -- 2.6 Probability Density Function -- 2.6.1 Discrete Probability Function -- 2.7 Discrete Probability Functions -- 2.7.1 Binomial Probability Distribution -- 2.7.1.1 Probability of the Binomial Distribution -- 2.7.1.2 Moments -- 2.7.1.3 Arithmetic Mean -- 2.7.1.4 Standard Deviation -- 2.7.2 Poisson's Distribution -- 2.7.2.1 Mean of the Poisson's Distribution -- 2.7.2.2 Standard Deviation of the Poisson's Distribution -- 2.8 Continuous Probability Distributions -- 2.8.1 Normal Probability Function -- 2.8.2 Cumulative Distribution of the NormalProbability Function -- 2.8.3 Normal Distribution and Probability Tables -- 2.8.4 Mean and Variance of a Linear Combinationof Normal Variates -- 2.8.5 Standard Deviation of Mean -- 2.8.6 Deviation from the Mean -- 2.8.7 Standard Deviation of Standard Deviation -- 2.8.8 Nomenclature for Normal Distribution -- 2.8.9 Probability Function of the Ratio of TwoNormal Variates [1] -- 2.8.10 Importance of Normal Distribution -- 2.8.11 Collation of Data from VariousLaboratories [2] -- 2.8.11.1 Most Probable Mean of the Data -- 2.8.11.2 Standard Deviation of the Most Probable Mean -- References -- Chapter 3: Other Probability Functions -- 3.1 Introduction -- 3.2 Important Distributions -- 3.2.1 Rectangular Distribution -- 3.2.1.1 Mean of the Rectangular Function -- 3.2.1.2 Variance of Rectangular Function -- 3.2.2 Triangular Probability Function -- 3.2.2.1 Mean of the Triangular Probability Function Is Given as -- 3.2.2.2 Variance 2 of Triangular Distribution -- 3.2.3 Trapezoidal Probability Function -- 3.2.3.1 Mean of the Trapezoidal Distribution -- 3.2.3.2 Variance of the Trapezoidal Distribution -- 3.3 Small Sample Distributions. , 3.3.1 The Student's t Distribution -- 3.3.1.1 Mean and Variance of Student's t Function -- 3.3.1.2 Comparison of Normal and t Distributions -- 3.3.1.3 Applications of t-Statistic -- 3.3.1.4 t-Test for a Sample Mean -- 3.3.1.5 Numerical Example -- 3.3.1.6 t-Test for Difference of Two Means -- 3.3.1.7 Numerical Example -- 3.3.1.8 Assumption Made for Student's t Test -- 3.3.1.9 Paired t-Test for Difference of Means -- 3.3.1.10 Numerical Example -- 3.3.2 The 2 Distribution -- 3.3.2.1 Use of 2 Distribution to Find a Range of Standard Deviationfor Given Probability -- 3.3.3 The F-Distribution -- 3.3.3.1 Parameters of F Distribution -- 3.3.4 Upper and Lower Percentage Points -- 3.3.4.1 Notation -- 3.3.5 Application of F-Test -- 3.3.5.1 Testing for Equality of Population Variances -- 3.3.5.2 Numerical Example -- 3.3.6 For Equality of Several Means -- 3.4 Combining of Variances of Variables Following Different Probability Distribution Functions -- References -- Chapter 4: Evaluation of Measurement Data -- 4.1 Introduction -- 4.2 Evaluation of Validity of Extreme Valuesof Measurement Results -- 4.2.1 Outline (Dixon)Test -- 4.3 Evaluation of the Means Obtained from Two Setsof Measurement Results -- 4.3.1 Two Means Coming from the Same Source -- 4.3.1.1 Standard Deviation of the Two Means -- 4.3.1.2 Test for Two Means of Samples of Smaller Size -- 4.3.1.3 SD and Mean Value of Two Means -- 4.3.1.4 Numerical Example -- 4.3.2 Test for Two Means Coming from Different Sources -- 4.3.2.1 Numerical Example -- 4.4 Comparison of Variances of Two Setsof Measurement Results -- 4.4.1 Numerical Example -- 4.5 Measurements Concerning Travelling Standards -- 4.5.1 Mean and Standard Deviation for each Laboratory -- 4.5.2 Inter-Laboratories Standard Deviation -- 4.5.3 Intra-Laboratory Standard Deviation -- 4.6 F-test for Internal and External Consistency. , 4.6.1 F-test for Inter- and Intra-Laboratory Variances -- 4.6.2 Weight Factors -- 4.6.2.1 Case 1 Weight Factor Is Unity -- 4.6.2.2 Case 2 Weight Factor Other than 1 -- 4.6.3 F-test for Variances -- 4.7 Standard Error of the Overall Mean -- 4.7.1 Results Inconsistent -- 4.8 Analysis of Variance -- 4.8.1 One-Way Analysis of Variance -- 4.8.1.1 Testing the Null Hypothesis -- 4.8.1.2 Numerical Example -- 4.9 Tests for Uniformity of Variances -- 4.9.1 Bartlett's Test for Uniformity of Many Variances -- 4.9.1.1 Numerical Example -- 4.9.2 Cochran Test for Homogeneity of Variances -- 4.9.2.1 Numerical Example -- References -- Chapter 5: Propagation of Uncertainty -- 5.1 Mathematical Modelling -- 5.1.1 Mean of Measurand (Dependent Variable) -- 5.1.2 Functional Relationship and Input Quantities -- 5.1.3 Expansion of a Function -- 5.1.4 Combination of Arithmetic Means -- 5.1.5 Combination of Variances -- 5.1.6 Variance of the Mean -- 5.2 Uncertainty -- 5.2.1 Combined Standard Uncertainty -- 5.2.1.1 Measurand (Output Quantity) Is a Function of Single Input Quantity -- 5.2.1.2 Measurand (Output Quantity) Is a Function of Several Quantities -- 5.2.2 Expanded Uncertainty -- 5.3 Type A Evaluation of Uncertainty -- 5.3.1 Numerical Example for Calculation of Type A Evaluation of Standard Uncertainty -- 5.4 Pooled Variance -- 5.4.1 Validity -- 5.4.2 Applicable -- 5.4.3 Uses -- 5.4.4 Need -- 5.4.4.1 Calibration of Measuring Instruments -- 5.4.5 Calculation of Pooled Variance -- 5.4.5.1 Category I: The Variance Is Independent of the Input Quantity -- 5.4.5.2 Category II: The Variance Depends Upon Input Quantity -- 5.4.6 Uses of Pooled Variance -- 5.4.6.1 Estimation of Type A Uncertainty of an Instrument -- 5.4.6.2 Testing the Authenticity of Observations -- 5.4.6.3 Maintenance of Laboratory Instruments -- 5.4.6.4 Fixing Maximum Permissible Error of an Instrument. , 5.4.6.5 Rejection of an Instrument Received for Calibration.