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Preface to the Third Edition | |

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Preface to the Second Edition | |

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Introduction | |

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The Original Mixture Problem | |

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General Remarks About Response Surface Methods | |

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A Factorial Experiment or a Mixture Experiment? | |

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An Historical Perspective | |

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References and Recommended Reading | |

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Questions | |

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The Original Mixture Problem: Designs and Models for Exploring the Entire Simplex Factor Space | |

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The Simplex-Lattice Designs | |

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The Canonical Polynomials | |

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The Polynomial Coefficients as Functions of the Responses at the Points of the Lattices | |

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Estimating the Parameters in the {q, m} Polynomials | |

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Properties of the Estimate of the Response, y(x) | |

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A Three-Component Yarn Example Using a {3, 2} Simplex-Lattice Design | |

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The Analysis of Variance Table | |

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Analysis of Variance Calculations of the Yarn Elongation Data | |

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The Plotting of Individual Residuals | |

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Testing the Degree of the Fitted Model: A Quadratic Model or Planar Model? | |

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Some Comments on the Use of Check Points for Testing Model Lack of Fit | |

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A Numerical Example Illustrating the Use of Check Points for Testing Lack of Fit | |

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The Simplex-Centroid Design and the Associated Polynomial Model | |

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An Application of a Four-Component Simplex-Centroid Design. Blending Chemical Pesticides for Control of Mites | |

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Axial Designs | |

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Comments on a Comparison Made Between an Augmented Simplex-Centroid Design and a Full Cubic Lattice for Three Components Where Each Design Contains Ten Points | |

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Reparameterizing Scheffe's Mixture Models to Contain a Constant ([beta subscript 0]) Term: A Numerical Example | |

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Questions to Consider at the Planning Stages of a Mixture Experiment | |

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Summary | |

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References and Recommended Reading | |

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Questions | |

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Least-Squares Estimation Formulas for the Polynomial Coefficients and Their Variances: Matrix Notation | |

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Cubic and Quartic Polynomials and Formulas for the Estimates of the Coefficients | |

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The Partitioning of the Sources in the Analysis of Variance Table When Fitting the Scheffe Mixture Models | |

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The Use of Independent Variables | |

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Transforming from the q Mixture Components to q-1 Mathematically Independent Variables | |

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A Numerical Example: Sensory Flavor Rating of Fish Patties | |

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Defining a Region of Interest Inside the Simplex: An Ellipsoidal Region | |

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A Numerical Illustration of the Inverse Transformation from the Design Variables to the Mixture Components | |

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Enlarging the Unit Spherical Region of Interest | |

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Some Discussion on Design Strategy When Fitting Response Surfaces | |

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Rotatable Designs | |

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A Second-Order Rotatable Design for a Four-Component System | |

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Defining a Cuboidal Region of Interest in the Mixture System | |

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Summary | |

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References and Recommended Reading | |

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Questions | |

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An Alternative Transformation from the Mixture Component System to the Independent Variable System | |

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A Form of the Orthogonal Matrix T | |

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Multiple Constraints on the Component Proportions | |

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Lower-Bound Restrictions on Some or All of the Component Proportions | |

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Introducing L-Pseudocomponents | |

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A Numerical Example of Fitting an L-Pseudocomponent Model | |

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Upper-Bound Restrictions on Some or All of the Component Proportions | |

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An Example of the Placing of an Upper Bound on a Single Component: The Formulation of a Tropical Beverage | |

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Introducing U-Pseudocomponents | |

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The Placing of Both Upper and Lower Bounds on the Component Proportions | |

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Formulas for Enumerating the Number of Extreme Vertices, Edges, and Two-Dimensional Faces of the Constrained Region | |

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Some Procedures for Calculating the Coordinates of the Extreme Vertices of a Constrained Region | |

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Multicomponent Constraints | |

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Some Examples of Designs for Constrained Mixture Regions: CONVRT and CONAEV Programs | |

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The Use of Symmetric-Simplex Designs for Fitting Second-Order Models in Constrained Regions | |

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Multiple Lattices for Major and Minor Component Classifications | |

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Categorizing the Mixture Components: An Ellipsoidal Region of Interest | |

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A Numerical Example of a Categorized Component Experiment | |

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Summary | |

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References and Recommended Reading | |

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Questions | |

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An Orthogonal Matrix for the Categorized-Components Problem | |

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The Relationship Between the Coefficients of the Terms in the Double-Scheffe Model (4.82) and the Interaction Model (4.83) | |

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The Analysis of Mixture Data | |

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Techniques Used in the Analysis of Mixture Data | |

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Test Statistics for Testing the Usefulness of the Terms in the Scheffe Polynomials | |

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Model Reduction | |

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An Example of Reducing the System from Three to Two Components | |

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A Criterion for Selecting Subsets of the Terms in the Scheffe Models | |

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A Numerical Example Illustrating the Integrated Mean-Square Error Criterion | |

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Screening Components | |

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A Seven-Component Octane-Blending Experiment: An Exercise in Model Reduction | |

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Other Techniques Used to Measure Component Effects | |

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The Slope of the Response Surface Along the Component Axes | |

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A Numerical Example Illustrating the Slope Calculations for a Three-Component System: Studying the Flavor Surface Where Peanut Meal Is Considered a Substitute for Beef in Sandwich Patties | |

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Leverage and the Hat Matrix | |

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A Three-Component Propellant Example | |

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Summary | |

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References and Recommended Reading | |

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Questions | |

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The Derivation of the Moments of the Simplex Region | |

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Other Mixture Model Forms | |

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The Inclusion of Inverse Terms in the Scheffe Polynomials | |

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Fitting Gasoline Octane Numbers Using Inverse Terms in the Model | |

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An Alternative Model Form for Modeling the Additive Blending Effect of One Component in a Multicomponent System | |

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A Biological Example on the Linear Effect of a Powder Pesticide in Combination with Two Liquid Pesticides Used for Suppressing Mite Population Numbers | |

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Other Models That Are Homogeneous of Degree One | |

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The Use of Ratios of Components | |

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Cox's Mixture Polynomials: Measuring Component Effects | |

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An Example Illustrating the Fits of Cox's Model and Scheffe's Polynomial | |

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Log Contrast Models | |

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A Numerical Example Illustrating the Testing of Inactivity and Additivity Effects of the Components in a Three-Component System Using Log Contrast Models | |

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Octane Blending Models | |

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A Numerical Example Illustrating the Calculations Required for Obtaining the Research and Motor Octane Prediction Equations for a Group of Blends | |

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Fitting a Slack-Variable Model | |

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A Numerical Example Illustrating the Fits of Different Reduced Slack-Variable Models: Tint Strength of a House Paint | |

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Summary | |

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References and Recommended Reading | |

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Questions | |

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The Form of the Multiplier Matrix B[subscript 2] for Expressing the Parameters in Cox's Quadratic Model as Functions of the Parameters in Scheffe's Model | |

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Estimation Equations for Coefficients That Are Subject to Linear Restrictions | |

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The Inclusion of Process Variables in Mixture Experiments | |

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Designs Consisting of Simplex-Lattices and Factorial Arrangements | |

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A Numerical Example of a Fish Patty Experiment: Studying Blends of Three Fish Species Prepared with Three Processing Factors | |

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Testing the Component Blending Properties and the Effects of the Process Variables When the Set of Mixture Blends Is Embedded in the Processing Conditions | |

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A Numerical Example of a Three-Component by Two-Process Variable Split-Plot Experiment: Fitting a Quadratic Mixture Model in the Presence of Interacting Process Variables | |

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A Reparameterization of the Combined Model Form for Measuring the Effects of the Process Variables: An Example of Model Reduction | |

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The Use of Fractional Designs in the Process Variables | |

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A Numerical Example of the Fit of a Combined Model to Data Collected on Fractions of the Fish Patty Experimental Design | |

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Computer-Aided Fractionation of Lattice Designs | |

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Mixture-Amount Experiments | |

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Process Variables and q-1 Mixture-Related Variables | |

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A Numerical Example Involving Three Mixture Components and One Process Variable | |

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Questions Raised and Recommendations Made When Fitting a Combined Model Containing Mixture Components and Other Variables | |

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Summary | |

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References and Recommended Reading | |

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Questions | |

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A Generalized Least-Squares Solution for Fitting the Mixed Model in the Mixture Components and Process Variables to Data from a Split-Plot Experiment | |

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Additional Topics | |

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Block Designs for Mixture Experiments | |

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Symmetric-Simplex Block Designs for Fitting the Scheffe Second-Order Model | |

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An Example of Orthogonal Blocking Using a Symmetric-Simplex Design | |

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Constructing Orthogonal Blocks Using Latin Squares | |

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Weighted Versus Unweighted Least-Squares Estimates of the Parameters in the Scheffe Models | |

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Some Comments on Design Criteria and Some Results Using the ACED Program | |

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Constant Prediction Variance on Concentric Triangles for Three-Component Systems | |

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Altering the Terms in the Scheffe-Type Models to Improve the Accuracy and/or Stability of the Coefficient Estimates | |

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Collinearity Problems Resulting from Performing Experiments in Highly Constrained Regions | |

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A Numerical Example Illustrating the Fitting of Segmented Scheffe Models to Freezing-Point Data from a Two-Component System | |

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Biplot Displays for Multiple Responses | |

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A Five-Response Plastics-Compounding Example | |

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Optimizing Several Responses Simultaneously | |

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Recalling the Three-Component Propellant Example of Section 5.13 | |

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Summary | |

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References and Recommended Reading | |

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Questions | |

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The Modified L-Pseudocomponent Model and the Centered and Scaled Intercept Model | |

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Expressing the Coefficients in the Scheffe Quadratic Model As Functions of the Coefficients in the L-Pseudocomponent, Modified L-Pseudocomponent, and Centered and Scaled Intercept Models | |

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Matrix Algebra, Least Squares, and the Analysis of Variance | |

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Matrix Algebra | |

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Some Fundamental Definitions | |

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A Review of Least Squares | |

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The Analysis of Variance | |

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A Numerical Example: Modeling the Texture of Fish Patties | |

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The Adjusted Multiple Correlation Coefficient | |

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The Press Statistic and Studentized Residuals | |

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Testing Hypotheses About the Form of the Model: Tests of Significance | |

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References and Recommended Reading | |

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Data Sets from Mixture Experiments with Partial Solutions | |

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Experiment One: Fruit Punch Experiment | |

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Experiment Two: Chick Feeding Experiment | |

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Experiment Three: Concrete Batches | |

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Experiment Four: Surface Resistivity of Paper Coatings | |

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Experiments Five, Six, and Seven: Estimating Solubilities of Multisolvent Systems | |

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References and Recommended Reading | |

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CONVRT Program Listing for Calculating the Coordinates of the Extreme Vertices of a Constrained Region | |

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CONAEV Program Listing for Calculating the Coordinates of the Centroids (Approximate) of the Boundaries of a Constrained Region | |

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Listings of Subroutines Called by CONVRT and CONAEV | |

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Bibliography and Index of Authors | |

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Answers to Selected Questions | |

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Appendix | |

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Index | |