Physico-chemical elementary processes in flotation

1 Complex Numbers Sums and Products Basic Algebraic Properties Further Properties Vectors and Moduli Complex Conjugates Exponential Form Products and Powers in Exponential Form Arguments of Products and Quotients Roots of Complex Numbers Examples Regions in the Complex Plane 2 Analytic Functions Functions of a Complex Variable Mappings Mappings by the Exponential Function Limits Theorems on Limits Limits Involving the Point at Infinity Continuity Derivatives Differentiation Formulas Cauchy-Riemann Equations Sufficient Conditions for Differentiability Polar Coordinates Analytic Functions Examples Harmonic Functions Uniquely Determined Analytic Functions Reflection Principle 3 Elementary Functions The Exponential Function The Logarithmic Function Branches and Derivatives of Logarithms Some Identities Involving Logarithms Complex Exponents Trigonometric Functions Hyperbolic Functions Inverse Trigonometric and Hyperbolic Functions 4 Integrals Derivatives of Functions w(t) Definite Integrals of Functions w(t) Contours Contour Integrals Some Examples Examples with Branch Cuts Upper Bounds for Moduli of Contour Integrals Antiderivatives Proof of the Theorem Cauchy-Goursat Theorem Proof of the Theorem Simply Connected Domains Multiply Connected Domains Cauchy Integral Formula An Extension of the Cauchy Integral Formula Some Consequences of the Extension Liouville's Theorem and the Fundamental Theorem of Algebra Maximum Modulus Principle 5 Series Convergence of Sequences Convergence of Series Taylor Series Proof of Taylor's Theorem Examples Laurent Series Proof of Laurent's Theorem Examples Absolute and Uniform Convergence of Power Series Continuity of Sums of Power Series Integration and Differentiation of Power Series Uniqueness of Series Representations Multiplication and Division of Power Series 6 Residues and Poles Isolated Singular Points Residues Cauchy's Residue Theorem Residue at Infinity The Three Types of Isolated Singular Points Residues at Poles Examples Zeros of Analytic Functions Zeros and Poles Behavior of Functions Near Isolated Singular Points 7 Applications of Residues Evaluation of Improper Integrals Example Improper Integrals from Fourier Analysis Jordan's Lemma Indented Paths An Indentation Around a Branch Point Integration Along a Branch Cut Definite Integrals Involving Sines and Cosines Argument Principle Rouche's Theorem Inverse Laplace Transforms Examples 8 Mapping by Elementary Functions Linear Transformations The Transformation w = 1/z Mappings by 1/z Linear Fractional Transformations An Implicit Form Mappings of the Upper Half Plane The Transformation w = sin z Mappings by z2 and Branches of z1/2 Square Roots of Polynomials Riemann Surfaces Surfaces for Related Functions 9 Conformal Mapping Preservation of Angles Scale Factors Local Inverses Harmonic Conjugates Transformations of Harmonic Functions Transformations of Boundary Conditions 10 Applications of Conformal Mapping Steady Temperatures Steady Temperatures in a Half Plane A Related Problem Temperatures in a Quadrant Electrostatic Potential Potential in a Cylindrical Space Two-Dimensional Fluid Flow The Stream Function Flows Around a Corner and Around a Cylinder 11 The Schwarz-Christoffel Transformation Mapping the Real Axis onto a Polygon Schwarz-Christoffel Transformation Triangles and Rectangles Degenerate Polygons Fluid Flow in a Channel Through a Slit Flow in a Channel with an Offset Electrostatic Potential about an Edge of a Conducting Plate 12 Integral Formulas of the Poisson Type Poisson Integral Formula Dirichlet Problem for a Disk Related Boundary Value Problems Schwarz Integral Formula Dirichlet Problem for a Half Plane Neumann Problems Appendixes Bibliography Table of Transformations of Regions Index

Complex variables and applications

A review of CFD modelling studies on the flotation process

Prediction of froth flotation responses based on various conditioning parameters by Random Forest method

Grinding kinetics of quartz and chlorite in wet ball milling

Application of basic process modeling in investigating the breakage behavior of UG2 ore in wet milling

A laboratory scale application of the attainable region technique on a platinum ore

Measurement of a proxy for froth phase bubble sizes as a function of froth depth in flotation machines Part 1. Theoretical development and testing of a new technique

In this work, methods to measure froth phase bubble sizes in mineral froth flotation are reviewed. For each method, the state of development, the equipment set-up, bubble size estimation procedure,...

Flotation Froth Phase Bubble Size Measurement

A fundamental investigation on the breakage of a bed of silica sand particles: An attainable region approach

C. Bhondayi

Papers

Application of basic process modeling in investigating the breakage behavior of UG2 ore in wet milling

A laboratory scale application of the attainable region technique on a platinum ore

Measurement of a proxy for froth phase bubble sizes as a function of froth depth in flotation machines Part 1. Theoretical development and testing of a new technique

Flotation Froth Phase Bubble Size Measurement

A fundamental investigation on the breakage of a bed of silica sand particles: An attainable region approach