This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Traditional engineering instruction is deductive, beginning with theories and progressing to the applications of those theories Alternative teaching approaches are more inductive Topics are introduced by presenting specific observations, case studies or problems, and theories are taught or the students are helped to discover them only after the need to know them has been established This study reviews several of the most commonly used inductive teaching methods, including inquiry learning, problem-based learning, project-based learning, case-based teaching, discovery learning, and just-in-time teaching The paper defines each method, highlights commonalities and specific differences, and reviews research on the effectiveness of the methods While the strength of the evidence varies from one method to another, inductive methods are consistently found to be at least equal to, and in general more effective than, traditional deductive methods for achieving a broad range of learning outcomes

Inductive Teaching and Learning Methods: Definitions, Comparisons, and Research Bases

Improving emulsion formation, stability and performance using mixed emulsifiers: A review.

Stable emulsions are frequently encountered in oil production and cause a series of environmental and operational issues. Chemical demulsification is widely used for the separation of oil from water or removal of water from oil. The chemicals used in the demulsification process have a strong affinity to the oil-water interface. This review presents the various types of chemical demulsifiers used for the demulsification of water-in-oil and oil-in-water emulsions. The review covers the relevant properties of polymeric surfactants such as polyether, dendrimers, and natural biodegradable polymeric surfactants. In addition, emerging alternatives like nanoparticles-based demulsifiers and ionic liquids are also reviewed. The factors affecting the demulsification efficiency of these demulsifiers and structure-property relationships are discussed. Copolymers with high hydrophilic content and molecular weight are more efficient demulsifiers. Similarly, the position isomerism (same carbon skeleton and functi...

Polymeric Surfactants and Emerging Alternatives used in the Demulsification of Produced Water: A Review

Learning and thinking

Extended Surfactants Including an Alkoxylated Central Part Intermediate Producing a Gradual Polarity Transition—A Review of the Properties Used in Applications Such as Enhanced Oil Recovery and Polar Oil Solubilization in Microemulsions

We have studied emulsions made with two- and three-phase oil–water–surfactant systems in which one of the phases is a microemulsion, the other phases being water or/and oil excess phases. Such systems have been extensively studied in the 1970–1980s for applications in enhanced oil recovery. It was found at that time that the emulsions became very unstable in the three-phase systems, but so far few explanations have been proposed. In the most complete one, Kabalnov and colleagues related the emulsion stability to the probability of hole nucleation in the liquid film separating two nearby emulsion drops and associated this probability to the curvature elastic energy of the surfactant layer covering drop surfaces. We propose a different explanation, linked to another type of interfacial elastic energy, associated with compression of the surfactant layers. As found long ago, the three-phase systems are found near optimum formulation (hydrophile lipophile difference, HLD = 0), where the interfacial tension exh...

Instability of Emulsions Made with Surfactant–Oil–Water Systems at Optimum Formulation with Ultralow Interfacial Tension

When surfactants adsorb at liquid interfaces, they not only decrease the surface tension, they confer rheological properties to the interfaces. There are two types of rheological parameters associated to interfacial layers: compression and shear. The elastic response is described by a storage modulus and the dissipation by a loss modulus or equivalently a surface viscosity. Various types of instruments are available for the measurements of these coefficients, the most common being oscillating pendent drops instruments and rheometers equipped with bicones. These instruments are applicable to systems with large enough interfacial tensions, typically above a few mN/m. We use a new type of instrument based on spinning drop oscillations, allowing to extend the interfacial rheology studies to low and ultralow interfacial tension systems. We present examples of measurements with systems of high and low tension, discuss the possible artifacts and demonstrate the capability of this new technique. We emphasize that the data shown for low interfacial tensions are the first reported in the literature. The instrument is potentially interesting for instance in enhanced oil recovery or demulsification studies.

Interfacial rheology of low interfacial tension systems using a new oscillating spinning drop method.

The effects of surfactant molecules involved in macro-, mini-, nano-, and microemulsions used in cosmetics and pharmaceuticals are related to their amphiphilic interactions with oil and water phases. Basic ideas on their behavior when they are put together in a system have resulted in the energy balance concept labeled the hydrophilic-lipophilic deviation (HLD) from optimum formulation. This semiempirical equation integrates in a simple linear relationship the effects of six to eight variables including surfactant head and tail, sometimes a cosurfactant, oil-phase nature, aqueous-phase salinity, temperature, and pressure. This is undoubtedly much more efficient than the hydrophilic-lipophilic balance (HLB) which has been used since 1950. The new HLD is quite important because it allows researchers to model and somehow predict the phase behavior, the interfacial tension between oil and water phases, their solubilization in single-phase microemulsion, as well as the corresponding properties for various kinds of macroemulsions. However, the HLD correlation, which has been developed and used in petroleum applications, is sometimes difficult to apply accurately in real cases involving ionic–nonionic surfactant mixtures and natural polar oils, as it is the case in cosmetics and pharmaceuticals. This review shows the confusion resulting from the multiple definitions of HLD and of the surfactant parameter, and proposes a “normalized” Hydrophilic-Lipophilic Deviation (HLDN) equation with a surfactant contribution parameter (SCP), to handle more exactly the effects of formulation variables on the phase behavior and the micro/macroemulsion properties.

https://www.mdpi.com/2079-9284/7/3/57/pdf

How to Use the Normalized Hydrophilic-Lipophilic Deviation (HLDN) Concept for the Formulation of Equilibrated and Emulsified Surfactant-Oil-Water Systems for Cosmetics and Pharmaceutical Products

Water–crude oil interfaces often exhibit a viscoelastic layer with a high mechanical resistance, consisting of natural surfactants in crude oil, mainly asphaltenes, which stabilize water-in-oil emu...

Breaking of Water-In-Crude Oil Emulsions. Part 9. New Interfacial Rheology Characteristics Measured Using a Spinning Drop Rheometer at Optimum Formulation

Ronald Marquez

Papers

Extended Surfactants Including an Alkoxylated Central Part Intermediate Producing a Gradual Polarity Transition—A Review of the Properties Used in Applications Such as Enhanced Oil Recovery and Polar Oil Solubilization in Microemulsions

Instability of Emulsions Made with Surfactant–Oil–Water Systems at Optimum Formulation with Ultralow Interfacial Tension

Interfacial rheology of low interfacial tension systems using a new oscillating spinning drop method.

How to Use the Normalized Hydrophilic-Lipophilic Deviation (HLDN) Concept for the Formulation of Equilibrated and Emulsified Surfactant-Oil-Water Systems for Cosmetics and Pharmaceutical Products

Breaking of Water-In-Crude Oil Emulsions. Part 9. New Interfacial Rheology Characteristics Measured Using a Spinning Drop Rheometer at Optimum Formulation