Bessel functions have the peculiarity of being functions of two independent variables: argument and order. They have been studied extensively because of their countless applications, but the vast majority of available literature is devoted to the case of fixed order, variable argument. This two-volume work explores the opposite case. This volume focuses on properties of the functions and mathematical operations with respect to the order.
This monograph is devoted to different aspects associated with citric acid, inorganic citrates and their aqueous and organic solutions. It includes information about properties, occurrence and technological applications of citric acid and inorganic citrates. Phase equilibria - melting, freezing, boiling, vapour pressures, solubilities of citric acid in water, organic solvents and ternary systems are presented, correlated, and analyzed. Dynamic properties - viscosities, diffusion coefficients, electrical conductivities and surface tensions are examined. Mathematical representations of citric acid dissociation, in electrolyte solutions and in buffers are discussed. Citric acid chemistry - syntheses of citric acid, neutralization, degradation, oxidation, esterification, formation of anhydrides, amides and citrate-based siderophores is reviewed.
Bessel functions have the peculiarity of being functions of two independent variables: argument and order. They have been studied extensively because of their countless applications, but the vast majority of available literature is devoted to the case of fixed order, variable argument. This two-volume work explores the opposite case. This volume collects tabulations of the first, second, and third derivatives with respect to the order.
Bessel functions have the peculiarity of being functions of two independent variables: argument and order. They have been studied extensively because of their countless applications, but the vast majority of available literature is devoted to the case of fixed order, variable argument. This two-volume work explores the opposite case. This volume focuses on properties of the functions and mathematical operations with respect to the order.
Bessel functions have the peculiarity of being functions of two independent variables: argument and order. They have been studied extensively because of their countless applications, but the vast majority of available literature is devoted to the case of fixed order, variable argument. This two-volume work explores the opposite case. This volume collects tabulations of the first, second, and third derivatives with respect to the order.
This monograph is devoted to different aspects associated with citric acid, inorganic citrates and their aqueous and organic solutions. It includes information about properties, occurrence and technological applications of citric acid and inorganic citrates. Phase equilibria - melting, freezing, boiling, vapour pressures, solubilities of citric acid in water, organic solvents and ternary systems are presented, correlated, and analyzed. Dynamic properties - viscosities, diffusion coefficients, electrical conductivities and surface tensions are examined. Mathematical representations of citric acid dissociation, in electrolyte solutions and in buffers are discussed. Citric acid chemistry - syntheses of citric acid, neutralization, degradation, oxidation, esterification, formation of anhydrides, amides and citrate-based siderophores is reviewed.
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