上一章多重积分中,面积和体积微元是有方向性的,即与坐标顺序有关,但表达式 dxdy等并不反映它的方向性.在作变量替换时dxdh=(x,y 要出现一个 Jacobi行 a(,v) 列式,这显然也不能从通常的实数乘法推导出来这一章我们将用 Grassmann代数工具将这 乘法讲清楚.事实上面积微元dxdy应该用 grassmann代数中乘法(外积)来定义d?dy, 这样既解决了方向性问题:

Michelle Banks, Erin Bealmear, Laura Standley Berger, Joann Cerrito, Jim Craddock, Steve Cusack, Nicolet V. Elert, Miranda H. Ferrara, Kristin Hart Melissa Hill, Laura S Kryhoski, Margaret Mazurkiewicz, Carol Schwartz, and Christine Tomassini, St James Press Staff laria Franklin, Permissions Manager Debra J. Freitas. Permissions assistant Mary Grimes, Leitha Etheridge-Sims, Image Catalogers

Social welfare function W: Rn-R gives social utility W(u1, u2,. un ). W is strictly increasing is socially optimal if it solves max Wu(a1), u2(a2),., un(n) st>Tis>w Proposition 1.29. If is SO, it is PO. I Proposition 1. 30. Suppose that preferences are continuous, strictly monotonic, and strictly convex. Then, for any PO allocation x* with >>0,v i, there exist ai

Unit Eight Text A Unit Eight Text A I. Pre-reading Task II. Related Information III. Outline& Summary IV. Detailed Study V. Home Assignment

Unit Seven Text A Unit Seven Text A I. Pre-reading Task II. Related Information III. Outline& Summary IV. Detailed Study V. Home Assignment By Zhu Ruina

体循环的静脉包括上腔静脉系、下腔静脉系和心静脉系。静脉的特点是: 1、可分为浅静脉和深静脉 2、静脉之间有丰富吻合; 3、有特殊v如哽脑膜窦等和板障静脉 4、腔大壁薄; 5、管壁內有静脉瓣;

物质三种聚集状态:固态、液态、气态 水的三态:冰、水、蒸汽 Ice Water Steam 热力学面:以p,v,表示的物质各种状态的曲面

一、理论工作循环[Working cycle] 理论循环p-v图特点,绝热、等温、多变压缩过程 二、实际工作循环 影响实际工作循环的因素

经典力学在伽利略变换下形式不变(具有伽利略 协变性),一般仅适用于v<