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 Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate.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

The dynamic behavior of a multistage agitated contactor has been numerically studied for its potential use for catalytic hydrogenation of nitrile butadiene rubber. A model consisting of stirred tanks in series with back flow is applied to describe the flow behavior in the presence of hydrogenation within a multistage agitated contactor of six stages. The coupled behavior between kinetics and mass transfer is analyzed by manipulating parameters involved in the model. The model predicted that the performance of the reactor is completely governed by the ability of the catalyst in activating hydrogen, the loading level of C=C double bonds, the relative capacity of the reaction to mass transfer, and the backmixing. Mass transfer and backmixing are important factors for the hydrogenation process and enhancing mass transfer and minimizing backmixing helps in increasing hydrogenation conversion. The effects of backmixing and the number of stages for the hydrogenation are discussed, and optimal operation conditions are suggested.

Modeling and Simulation of a Multistage Agitated Contactor for Hydrogenation of Nitrile Butadiene Rubber

The clogging of the Submerged Entry Nozzle (SEN) during
 billet continuous casting of mid-carbon steel is studied.
 Clogging materials and inclusions in steel samples taken at
 ladles, tundish and billets are investigated. The total oxygen on
 the whole section of the billet is measured. Steel cleanliness at
 unsteady casting states, including cast start, ladle change, SEN
 change, cast end, and the special unsteady pouring period
 induced by SEN clogging, are studied. Fluid flow and inclusion
 motion and entrapment to SEN surface are also simulated.

Inclusions, lining materials and nozzle clogging during middle carbon steel billet continuous casting process

With the high temperature confocal laser scanning microscope applied, the effect of cooling rate, temperature interval, and cooling mechanism on the solidification microstructure and primary carbide participation in GCr15 steel are investigated. The solute distribution in interdendritic segregation and participation carbide are analyzed by EPMA. The results show that solute concentrate is low in the dendrite zone but it increases clearly in the segregation zone. The carbon concentration in the precipitation can reach 6.49%, which means the primary carbide is M3C. In the heating process, the solute segregation zone and carbide participation melt firstly before it reaches the solidus temperature. During the solidification stage, the microstructure is refined and the size of primary carbide is reduced with a higher cooling rate, but the number density of primary carbide is increased. Moreover, it is found that the solidification microstructure has formed in the earlier solidification process, before the temperature declines to 1673 K. While the primary carbide participates in the later cooling stage and the transition temperature for the primary carbide is 1503 K. Besides, it is obtained that the primary carbide size can be reduced with the cooling rate larger than 300 K/min in the subsequent cooling stage.

Influence of Cooling Parameters on the Microstructure and Primary Carbide Precipitation in GCr15 Steel

EPD Congress 2014 : proceedings of symposia sponsored by the Extraction & Processing Division (EPD) of the Minerals, Metals & Materials Society (TMS) : held during the TMS2014 143rd Annual Meeting & Exhibition, February 16-20, 2014 San Diego Convention Center, San Diego, California, USA

The scale-up of a solid–liquid stirred tank with an Intermig impeller was characterized via experiments. Solid concentration, impeller just-off-bottom speed and power consumption were measured in stirred tanks of different scales. The scale-up criteria for achieving the same effect of solid suspension in small-scale and large-scale vessels were evaluated. The solids distribution improves if the operating conditions are held constant as the tank is scaled-up. The results of impeller just-off-bottom speed gave X = 0.868 in the scale-up relationship ND
 X
  = constant. Based on this criterion, the stirring power per unit volume obviously decreased at N = N
 js, and the power number (N
 P) was approximately equal to 0.3 when the solids are uniformly distributed in the vessels.

Lifeng Zhang

Papers

Modeling and Simulation of a Multistage Agitated Contactor for Hydrogenation of Nitrile Butadiene Rubber

Inclusions, lining materials and nozzle clogging during middle carbon steel billet continuous casting process

Influence of Cooling Parameters on the Microstructure and Primary Carbide Precipitation in GCr15 Steel

EPD Congress 2014 : proceedings of symposia sponsored by the Extraction & Processing Division (EPD) of the Minerals, Metals & Materials Society (TMS) : held during the TMS2014 143rd Annual Meeting & Exhibition, February 16-20, 2014 San Diego Convention Center, San Diego, California, USA

Experimental Study on Scale-Up of Solid–Liquid Stirred Tank with an Intermig Impeller