There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

비만아 부모의 돌봄 경험: q 방법론

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 Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate.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

Fluid Flow, Solidification and Inclusion Entrapment during Steel Centrifugal Casting Process

Hydrogenation of nitrile butadiene rubber in a multistage agitated contactor: Experiments and numerical simulation

The effect of the diameter and contact angle on the aggregation of solid inclusions in molten steel was investigated based on the cavitation theory. Larger inclusions aggregated more easily, owing to the lower stable energy and larger critical aggregation spacing. The critical aggregation spacing had an explicit relationship with inclusion diameters: $$ d_{{{\text{C}},{\text{Al}}_{{\text{2}}} {\text{O}}_{{\text{3}}} }} $$
 = 0.195(RP1RP2)0.5−0.021(RP1+RP2), dC,MgO = 0.099(RP1RP2)0.5−0.013(RP1+RP2) and $$ d_{{{\text{C}},{\text{SiO}}_{{\text{2}}} }} $$
 = 0.031(RP1RP2)0.5−0.0061(RP1+RP2). Furthermore, calculated results showed that the aggregation tendency of the three considered types of inclusions was Al2O3 > MgO > SiO2.

Effect of Diameter and Contact Angle on Initial Aggregation of Solid Inclusions in Molten Steels

Effect of Slag Modification on Inclusions in Si–Mn‐Killed 304 Stainless Steels

In the current study, the wettability between 304 stainless steels and refractory materials was investigated using the sessile drop method in a reducing atmosphere at 1550 °C. The contact angle between the stainless steel and the original refractory was 133°, and was 126° between the stainless steel and the used refractory. The lower dissolved oxygen content in the stainless steel after the reaction with the original refractory was responsible for the higher contact angle. Adhesion work of original and used refractories per mole was 41 kJ/m and 53 kJ/mol, respectively, indicating that the physical bond energy was dominant at the interface between the stainless steel and the refractory. The penetration of the steel into the used refractory was more serious than that into the original refractory, which was mainly influenced by the angle between the liquid drop meniscus and refractory pores based on the force analysis. The liquid slag phase formed in the refractory at the high temperature entered refractory pores, decreased the meniscus angle and promoted the steel penetration.

Lifeng Zhang

Papers

Fluid Flow, Solidification and Inclusion Entrapment during Steel Centrifugal Casting Process

Hydrogenation of nitrile butadiene rubber in a multistage agitated contactor: Experiments and numerical simulation

Effect of Diameter and Contact Angle on Initial Aggregation of Solid Inclusions in Molten Steels

Effect of Slag Modification on Inclusions in Si–Mn‐Killed 304 Stainless Steels

Wettability between 304 stainless steel and refractory materials