Nther-type theorem of piecewise algebraic curves on quasi-cross-cut partition  

作　　者：ZHU ChunGang & WANG RenHong School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China 

出　　处：《Science China Mathematics》2009年第4期701-708,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 60373093, 60533060,10726068, 10801024);the Innovation Foundation of Key Laboratory of High Temperature Gasdynamics of Chinese Academy of Sciences, China

摘　　要：The effect of Pr substitution for Dy on the magnetic and magnetostrictive properties, anisotropy, spin reorientation and Mssbauer effect of a series of Tb0.3Dy0.7-xPrx(Fe0.9Al0.1)1.95 (x=0,0.1,0.20,0.25,0.30,0.35) alloys at room temperature have been investigated. It was found that a small amount of Pr substitution is beneficial to a decrease in the magnetocrystalline anisotropy for the Tb0.3Dy0.7-xPrx(Fe0.9Al0.1)1.95 alloys. The magnetostriction decreases drastically with increasing x and the magnetostrictive effect disappears for x>0.2. However, the magnetostriction exhibits a slightly bigger value at x=0.1 than the free alloys and is saturated more easily with the magnetic field H. The saturation magnetization and Curie temperature decrease monotonously, but the spontaneous magnetostriction increases linearly with increasing x, whereas the spin reorientation temperature increases first, then decreases rapidly and reaches the maximum at x=0.1. The analysis of Mssbauer spectra indicated that the easy magnetization direction in the {110} plane deviates slightly from the main axis of symmetry with the Pr concentration x, namely spin reorientation. Compared with Al substitution for Fe, the effect of Pr substitution for Dy on spin reorientation is relatively small. The hyperfine field increases with Pr concentration increasing, and the isomer shifts and the quadrupole splitting (QS) show weak concentration dependence.Nther's theorem of algebraic curves plays an important role in classical algebraic geometry. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nther-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.

关 键 词：MAGNETOSTRICTION ANISOTROPY spin reorientation MSSBAUER 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]