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 Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate.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

Based on the mathematical model, this study investigated the process of electro-slag remelting. Maxwell equations are firstly solved to calculate the magnetic field and the distribution of joule heating. Then these two terms are implemented in momentum and energy equations via “User Defined Functions” in FLUENT. The Volume of Fluid method and the enthalpy-porosity approach are applied to capture the multiphase flow and the melting process. The magnetic field, the resulting Lorentz forces and the joule heating are modeled assuming they are independent of the flow. The results show that the molten steel film can generate at the tip of consumable electrode and converge into droplets which fall down through the slag bath and into the liquid metal pool. In addition, an intense non-axisymmetric flow occurs that cannot be realized by conventional two-dimensional model.

3D Mathematics Model of Formation and Motion of Metal Droplets during Electro‐Slag Remelting Process

The invention relates to the field of iron and steel production, and provides a control method for promoting homogenization treatment of continuous casting billet. Pure iron wire is welded with a coreof continuous casting billet, an instantaneous pulse current is generated by a high-power electric pulse device, and the solute migration rate is increased by high-energy electronic wind, so that homogenization treatment in the heat treatment process of the continuous casting billet is promoted. Dynamic control of electric pulse processing is conducted by the following steps: calculating real-time temperature distribution of the continuous casting billet by online simulation, accessing an optimal electric pulse parameter database, calculating the difference between a current electric pulse parameter and an optimal value, and dynamically adjusting the electric pulse parameter by adjusting the preset value of the pulse device, so as to promote homogenization treatment of the continuous casting billet and reduce strip defects of rolled products. The electric pulse parameter is adjusted in real time according to steel composition and the size and temperature of the continuous casting billet, the solute atom diffusion migration rate is increased, intercrystalline solute segregation is effectively reduced, the banded structure defect of the rolled material is improved, and mechanical properties and stability of steel are improved.

Control method for promoting homogenization treatment of continuous casting billet

The internal cracks often occurred on the continuous casting slab of AH36 steels, which caused serious quality problems. In this work, a great number of production data were collected to analyze the primary factors that caused the internal crack. Various techniques such as acid etching, metallographic microscope and SEM-EDS detection were used to analyze the macro-and micro- characteristics of the cracks. High temperature mechanical properties of the steel were studied using Gleeblel 500. The results showed that the impurity element segregation, such as S, P and Cu, overheat and inclusion accumulation are the main reasons for the generation of internal cracks in the AH36 steel slabs.

Study on Internal Cracks in Continuous Casting Slab of AH36 Steels

The effects of titanium addition (0 wt.%, 0.2 wt.%, and 0.5 wt.%) on the boron removal from metallurgical-grade silicon during slag refining have been studied. According to the findings, the addition of Ti improved the removal of 92.5 wt.% B with 0.5 wt.% Ti addition compared to 79.4 wt.% B removal without Ti addition. Furthermore, acid leaching reduced excess Ti to 27 ppmw.

Enhancement of boron removal from metallurgical-grade silicon by titanium addition during slag refining

In the current study, a three-dimensional mold model was established by Fluent software to investigate the fluid flow of three phases (steel–slag–air) in the mold. A quarter of the mold was simulated through the k-e model, volume of fluid (VOF) model, solidification model and continuum surface force (CFS) method. The interfacial tension between liquid steel and liquid slag and the oscillation of the mold were added into the model to show the 3D steel–slag interface. The liquid steel exiting from the submerged entry nozzle (SEN) existed as the upper backflow and lower backflow, and flowed towards the wide face and the SEN. The largest speed on the steel–slag interface was located at approximately 0.25 m from the narrow face, which was approximately 0.15 m/s. Under the influence of the upper backflow and the movement of the shell, the slag on the steel–slag interface moved from the narrow face to the SEN, and infiltrated into the gap, which affected the lubrication in the gap.

Lifeng Zhang

Papers

3D Mathematics Model of Formation and Motion of Metal Droplets during Electro‐Slag Remelting Process

Control method for promoting homogenization treatment of continuous casting billet

Study on Internal Cracks in Continuous Casting Slab of AH36 Steels

Enhancement of boron removal from metallurgical-grade silicon by titanium addition during slag refining

Modeling of Steel–Slag–Air Three-Phase Flow in Continuous Casting Strand