Energy-momentum conservation laws in higher-dimensional Chern-Simons models

a r X i v :h e p -t h /0303148v 1 17 M a r 2003Energy-momentum conservation laws in higher-dimensional Chern–Simons models

G.Sardanashvily

Department of Theoretical Physics,Moscow State University,117234Moscow,Russia E-mail:sard@grav.phys.msu.su

URL:http://webcenter.ru/～sardan/

Abstract.Though a Chern–Simons (2k ?1)-form is not gauge-invariant and it depends on a background connection,this form seen as a Lagrangian of gauge theory on a (2k ?1)-dimensional manifold leads to the energy-momentum conservation law.

The local Chern–Simons (henceforth CS)form seen as a Lagrangian of the gauge theory on a 3-dimensional manifold is well known to lead to the local conservation law of the canonical energy-momentum tensor.Generalizing this result,we show that a global higher-dimensional CS gauge theory admits an energy-momentum conservation law in spite of the fact that its Lagrangian depends on a background gauge potential and that one can not ignore its gauge non-invariance.The CS gravitation theory here is not considered (e.g.,[1,3]).We derive Lagrangian energy-momentum conservation laws from the ?rst variational formula (e.g.,[5,7,8,9,10]).Let us consider a ?rst order ?eld theory on a ?bre bundle Y →X over an n -dimensional base X .Its Lagrangian is de?ned as a density L =L d n x on the ?rst order jet manifold J 1Y of sections of Y →X .Given bundle coordinates (x λ,y i )on a ?bre bundle Y →X ,its ?rst and second order jet manifolds J 1Y and J 2Y are equipped with the adapted coordinates (x λ,y i ,y i μ)and (x λ,y i ,y i μ,y i λμ),respectively.We will use the notation ω=d n x and ωλ=?λ?ω.

Given a Lagrangian L on J 1Y ,the corresponding Euler–Lagrange operator reads

δL =δi L θi ∧ω=(?i L ?d λ?λi )L θi ∧ω,(1)

where θi =dy i ?y i λdx λare contact forms and d λ=?λ+y i λ

?i +y i λμ?μi are the total derivatives,which yield the total di?erential

d H ?=dx λ∧d λ?(2)

acting on the pull-back of exterior forms on J 1Y onto J 2Y .The kernel Ker δL ?J 2Y of the Euler–Lagrange operator (1)de?nes the Euler–Lagrange equations δi L =0.A

1

Lagrangian L is said to be variationally trivial ifδL=0.This property holds i?L=h0(?), where?is a closed n-form on Y and h0is the horizontal projection

h0(dxλ)=dxλ,h0(dy i)=y iλdxλ,h0(dy iμ)=y iλμdxλ.(3) The relation d H?h0=h0?d holds.

Any projectable vector?eld

u=uλ(xμ)?λ+u i(xμ,y j)?i(4) on Y→X is the in?nitesimal generator of a local one-parameter group of bundle auto-morphisms of Y→X,and vice versa.Its prolongation onto J1Y is

J1u=uλ?λ+u i?i+(dλu i?y iμ?λuμ)?λi.(5) Then,the Lie derivative of a Lagrangian L along J1u reads

L J1u L=J1u?dL+d(J1u?L)=[?λ(uλL)+u i?i L+(dλu i?y iμ?λuμ)?λi L]ω.(6) The?rst variational formula provides its canonical decomposition

L J1u L=u V?δL+d H h0(u?H L)=(7)

(u i?y iμuμ)δi Lω?dλ[(uμy iμ?u i)?λi L?uλL]ω,

where u V=(u?θi)?i,H L is the Poincar′e–Cartan form,and

J u=?h0(u?H L)=Jλuωλ=[(uμy iμ?u i)?λi L?uλL]ωλ(8) is the symmetry current along u.On KerδL,the?rst variational formula(7)leads to the weak equality

L J1u L≈?d H J u,(9)

?λ(uλL)+u i?i L+(dλu i?y iμ?λuμ)?λi L≈?dλ[(?uμy iμ?u i)?λi L?uλL].

Let the Lie derivative(6)reduces to the total di?erential

L J r u L=d Hσ,(10) e.g.,if L is a variationally trivial Lagrangian or L is invariant under a one-parameter group of bundle automorphisms of Y→X generated by u.Then,the weak equality(9) takes the form

0≈?d H(J u+σ),(11)

2

regarded as a conservation law of the modi?ed symmetry current

of the tangent bundle T P of P with respect to the canonical action of G on P.Given a basis{?r}for the right Lie algebra g r of the group G,let{?λ,e r}be the corresponding ?bre bases for the vector bundle T G P.Then,a sectionξof T G P→X reads

ξ=ξλ?λ+ξr e r.(16) The in?nitesimal generator of a one-parameter group of vertical automorphisms is a G-invariant vertical vector?eld on P identi?ed to a sectionξ=ξr e r of the quotient

V G P=V P/G?T G P

of the vertical tangent bundle V P of P→X by the canonical action of G on P.The Lie bracket of two sectionsξandηof the vector bundle T G P→X reads

[ξ,η]=(ξμ?μηλ?ημ?μξλ)?λ+(ξλ?ληr?ηλ?λξr+c r pqξpηq)e r,

where c r pq are the structure constants of the Lie algebra g r.Puttingξλ=0andημ=0, we obtain the Lie bracket

[ξ,η]=c r pqξpηq e r(17) of sections of the vector bundle V G P→X.A glance at the expression(17)shows that the typical?bre of V G P→X is the Lie algebra g r.The structure group G acts on g r by the adjoint representation.

Note that the connection bundle C(14)is an a?ne bundle modelled over the vector bundle T?X?V G P,and elements of C are represented by local V G P-valued1-forms a rμdxμ?e r.Bundle automorphisms of a principal bundle P→X generated by the vector ?eld(16)induce bundle automorphisms of the connection bundle C whose generator is

ξC=ξλ?λ+(?μξr+c r pq a pμξq?a rν?μξν)?μr.(18) The connection bundle C→X admits the canonical V G P-valued2-form

1

F=(da rμ∧dxμ+

F rλμdxλ∧dxμ?e r,F rλμ=?λA rμ??μA rλ+c r pq A pλA qμ,(20)

2

of F onto X is the strength form of a gauge potential A.

4

Let I k(?)=b r

1...r k ?r1···?r k be a G-invariant polynomial of degree k>1on the Lie

algebra g r written with respect to its basis{?r},i.e.,

I k(?)= j b r1...r k?r1···c r j pq e p···?r k=kb r1...r k c r1pq?p?r2···?r k=0.

Let us associate to I(?)the2k-form

P2k(F)=b r

1...r k

F r1∧···∧F r k(21) on C.It is a closed form which is invariant under vertical automorphisms of C.Let A be a section of C→X.Then,the pull-back

P2k(F A)=A?P2k(F)(22) of P2k(F)is a closed characteristic form on X.Recall that the de Rham cohomology of C equals that of X since C→X is an a?ne bundle.It follows that P2k(F)and P2k(F A) possess the same cohomology class

[P2k(F)]=[P2k(F A)](23) for any principal connection A.Thus,I k(?)→[P2k(F A)]∈H?(X)is the familiar Weil homomorphism.

Let B be a?xed section of the connection bundle C→X.Given the characteristic form P2k(F B)(22)on X,let the same symbol stand for its pull-back onto C.By virtue of the equality(23),the di?erence P2k(F)?P2k(F B)is an exact form on C.Moreover, similarly to the well-known transgression formula on a principal bundle P,one can obtain the following transgression formula on C:

P2k(F)?P2k(F B)=d S2k?1(B),(24)

S2k?1(B)=k

1

P2k(t,B)dt,(25)

P2k(t,B)=b r

1...r k (a r1μ

1

?B r1μ

1

)dxμ1∧F r2(t,B)∧···∧F r k(t,B),

F r j(t,B)=[d(ta r jμ

j +(1?t)B r jμ

j

)∧dxμj+

1

on X.For instance,if P2k(F A)is the characteristic Chern2k-form,then S2k?1(A,B)is the familiar CS(2k?1)-form.Therefore,we agree to call S2k?1(B)(25)the CS form on the connection bundle C.In particular,one can choose the local section B=0.Then, S2k?1=S2k?1(0)is the local CS form.Let S2k?1(A)denote its pull-back onto X by means of a section A of C→X.Then,the CS form S2k?1(B)admits the decomposition

S2k?1(B)=S2k?1?S2k?1(B)+dK2k?1(B).(26)

Let J1C be the?rst order jet manifold of the connection bundle C→X equipped with the adapted coordinates(xλ,a rμ,a rλμ).Let us consider the pull-back of the CS form (25)onto J1C denoted by the same symbol S2k?1(B),and let

S2k?1(B)=h0S2k?1(B)(27)

be its horizontal projection.This is given by the formula

S2k?1(B)=k

1

P2k(t,B)dt,

P2k(t,B)=b r

1...r k (a r1μ

1

?B r1μ

1

)dxμ1∧F r2(t,B)∧···∧F r k(t,B),

F r j(t,B)=

1

2c r j pq(ta pλ

j

+(1?t)B pλ

j

)(ta qμ

j

+(1?t)B qμ

j

]dxλj∧dxμj?e r.

The decomposition(26)induces the decomposition

S2k?1(B)=S2k?1?S2k?1(B)+d H K2k?1(B),K2k?1(B)=h0K2k?1(B).(28) Now,let us consider the CS gauge model on a(2k?1)-dimensional base manifold X whose Lagrangian

L CS=S2k?1(B)(29) is the CS form(27)on J1C.Let

ξC=(?μξr+c r pq a pμξq)?μr(30) be a vertical vector?eld on C.We have shown that

L J1ξ

C

S2k?1(B)=d Hσ(31)

6

[11].As a consequence,the CS gauge model with the Lagrangian(29)admits the Noether conservation law

0≈?d H(Jξ+σ),

where

Jξ=?λμr S2k?1(B)(?μξr+c r pq a pμξq)

is the symmetry current along the vertical vector?eldξC(30).

Using this fact,let us study energy-momentum conservation laws in the CS gauge model with the Lagrangian(29).Let B′be some section of the connection bundle C→X. Given a vector?eldτon X,there exists its lift

τB′=τλ?λ+[?μ(τνB′rν)+c r pq a pμ(τνB′qν)?a rν?μτν]?μr.(32) onto the connection bundle C→X[5,7,8].Comparing the expressions(18)and(32), one easily observes that the lift τB′is the in?nitesimal generator of bundle automorphisms of C with parametersξλ=τλ,ξr=τνB rν.Let us bring locally the vector?eld(32)into the sum

τB′= τ1+ τ2=[τλ?λ?a rν?μτν?μr]+[?μ(τνB′rν)+c r pq a pμ(τνB′qν)]?μr.(33) One can think of τ1as being the local in?nitesimal generator of general covariant trans-formations of C,while τ2is a local vertical vector?eld on C→X(cf.(30)).Then,the weak equality(9)for the Lie derivative L J1 τS2k?1(B)reads

L

J1 τ1S2k?1(B)+L J1 τ2S2k?1(B)≈?d H J τ,(34) where J τis the energy-momentum current along τB′.The second term in the left-hand side of this equality takes the form(31),and the?rst one does so as https://www.sodocs.net/doc/668466573.html,ing the decomposition(28),one can write

L

J1 τ1S2k?1(B)=L J1 τ1S2k?1+L J1 τ1(S2k?1(B)+d H K2k?1(B)).

The?rst term in the right-hand side of this relation vanishes because the local CS form S2k?1is invariant under general covariant transformations.The second one takes the form (10)because S2k?1(B)+d H K2k?1(B)is a variationally trivial Lagrangian.Consequently, the weak equality(34)comes to the conservation law

0≈?d H(J τ+σ′)

7

of the modi?ed energy-momentum current.

For instance,let G be a semi-simple group and a G the Killing form on g r.Let

P(F)=

h

2ha G mnεαβγa mα(F nβγ?

1

2ha G mnεαβγB mα(F(B)nβγ?

1

2

F rλμdxλ∧dxμ?e r,F rλμ=a rλμ?a rμλ+c r pq a pλa qμ.

Since(?S3(B)+d H K3(B))is a variationally trivial local Lagrangian,the?rst variational formula for the CS Lagrangian(37)reduces to that for the local CS Lagrangian

S3=1

3

c n pq a pβa qγ)d3x.(38)

On-shell,it reads

L

J1 τ2S3≈?d H J τ,(39) where J τis the symmetry current(8)of S3(38)along the vector?eld τB′(33).A simple calculation gives

L

J1 τ2S3=?dα[ha G mnεαβγ?β(τνB′mν)a nγ]d3x,

Jα τ=?ha G mnεαβγ[a mβdγ(τνa nν)+?β(τn uB′mν+c m pq a pβτνB′qν)a nγ]?ταS3.

Thus,we come to the conservation law of the modi?ed energy-momentum current

References

[1]G.Allemandi,M.Francaviglia and M.Raiteri,Covariant charges in Chern–Simons

AdS3gravity,Class.Quant.Grav.20(2003)483;E-print arXiv:gr-qc/0211098.

[2]A.Borowiec,M.Ferraris and M.Francaviglia,Lagrangian symmetries of Chern–

Simons theories,J.Phys.A31(1998)8823:E-print arXiv:hep-th/9801126. [3]A.Borowiec,M.Ferraris and M.Francaviglia,A covariant formalism for Chern–

Simons gravity,J.Phys.A36(2003)2589;E-print arXiv:math-ph/0301146. [4]M.Ferraris and M.Francaviglia,Energy-momentum tensors and stress tensors in

geometric?eld theories,J.Math.Phys.26(1985)1243.

[5]G.Giachetta,L.Mangiarotti and G.Sardanashvily,New Lagrangian and Hamiltonian

Methods in Field Theory(World Scienti?c,Singapore,1997).

[6]M.Gotay and J.Marsden,Stress-energy-momentum tensors and the Belinfante–

Rosenfeld formula,Contemp.Mathem.132(1992)367.

[7]L.Mangiarotti and G.Sardanashvily,Connections in Classical and Quantum Field

Theory(World Scienti?c,Singapore,2000).

[8]G.Sardanashvily,Stress-energy-momentum tensor in constraint?eld theories,J.

Math.Phys.38(1997)847.

[9]G.Sardanashvily,Ten lectures on jet manifold in classical and quantum?eld theory,

E-print arXiv:math-ph/0203040.

[10]G.Sardanashvily,Energy-momentum conservation laws in gauge theory with broken

gauge invariance,E-print arXiv:hep-th/0203275.

[11]G.Sardanashvily,Gauge conservation laws in higher-dimensional Chern–Simons

models,E-print arXiv:hep-th/0303059.

9

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糖生物学_植物糖基转移酶研究进展

期末考核 课程：Glycobiology 植物糖基转移酶研究进展 ：*** 学号：*** 班级：*** 时间：****

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Laws of Logic

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THE_48_LAWS_OF_POWER 《权力的48条规则》

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the injured party/victim 被害人 witness/eyewitness 见证人，目击者 the prosecution 原告及其代理律师；代表原告的律师the accused/defendant 被告人 the defense lawyer/counselor 被告辩护律师【（三）、违法】 【案件种类】 case 案件 crime - criminal adj. a criminal case 刑事案件 a civil case 民事案件 【行为/罪名--criminal behavior】 guilt n. [Antonym] innocence guilty adj. [Antonym]innocent guilty of a crime/charge

innocent of a crime/charge commit a crime violate a criminal law murder 谋杀罪 first-degree murder (deliberately)一级谋杀罪；故意杀人罪manslaughter (not intentionally) 一般杀人罪；过失杀人罪forgery 伪造罪 sexual harassment 性骚扰 malfeasance 渎职罪 criminal: n. 罪犯 a convicted criminal ：one who has been judged guilty in a court of law a hardened criminal ：someone who has committed many crimes stab v. 用刀具行凶，捅，刺 to kill or hurt someone by pushing a knife or other sharp object into their body

Four Laws of Ecology中英对照

Four Laws of Ecology 1 In broad outline,there are environmental cycles which govern the behavior of the three great global systems:the air,the water,and the soil.Within each of them live many thousands of different species of living things.Each species is suited to its particular environmental niche,and each,through its life processes,affects the physical and chemical properties of its immediate environment. 1概括来讲,地球的三大系统—空气、水和土壤的行为由环境循环所决定。每个系统中都生活着成千上万个不同物种的生物,每个物种都有与之相适宜的独特的环境生位,并且每一物种,在其整个生命历程中,都影响着它的周边环境的物理和化学特性。 2 Each living species is also linked to many others.These links are bewildering in their variety and marvelous in their intricate detail.An animal,such as a deer,may depend on plants for food;the plants depend on the action of soil bacteria for their nutrients;the bacteria in turn live on the organic wastes dropped by the animal on the soil.At the same time.the deer is food for the mountain lion. Insects may live on the juices of plants or gather pollen from their flowers.Other insects suck blood from animals.Bacteria may live on the internal tissues of animals and plants.Fungi degrade the bodies of dead plants and animals.All this,many times multiplied and organized species by species in intricate,precise relationships,makes up the vast network of life on the earth. 2每个生物物种也与许多其他的物种相联系。1.这些联系的多样性令人迷惑不解,其错综复杂的细节令人惊叹不已。某一动物,如一只鹿,可能依靠植物来获取食物;植物依靠土壤细菌的活动来获取其营养;相应地,细菌以陆地上的动物排泄出来的有机废物为生。同时,鹿是美洲狮的食物。昆虫可能以植物的汁液为生,或者从其花朵里采集花粉。其他的昆虫则吸吮动物的血液。细菌可能以动物和植物的内部组织为生。真菌分解死亡的植物和动物的躯体。所有这一切,由各个物种通过复杂而严密的关系多次繁殖和组织,构成了地球上巨大的生命之网。 3 The science that studies these relationships and the processes linking each living thing to the physical and chemical environment is ecology.It is the science of planetary housekeeping For the environment is,so to speak,the house created on the earth by living things for living things.It is a

基于Laws能量和变化频次的伪装色移动目标检测_李金屏

中国体视学与图像分析2011年第16卷第1期18CHINESE JOURNAL OF STEREOLOGY AND IMAGE ANALYSIS Vol．16No．1March2011文章编号:1007－1482(2011)01－0018－0023·图像技术·基于Laws能量和变化频次的伪装色移动目标检测 李金屏1，2，李倩1，2 (1．济南大学信息科学与工程学院，济南250022; 2．山东省网络环境智能计算技术重点实验室，济南250022) 摘要:动态背景下的移动目标检测是视频监控的研究热点之一，具有伪装色的移动目标检测是其中的一个难点。传统的高斯混合模型不适合检测这类移动目标。通过分析动态背景下具有伪装色移动目标的颜色变化规律，提出了利用Laws能量和一种称为变化频次的特殊统计量的检测方法。实验表明，该方法能够有效地检测某些动态背景下一些具有伪装色的移动目标，即在摄像头固定情况下，对于平缓变化的动态背景中颜色变化幅度较大或者表面纹理复杂的具有伪装色的移动目标，该方法具有良好的检测效果。 关键词:动态背景;伪装色;移动目标检测;Laws能量;变化频次 中图分类号:TP391文献标识码:A Detection of camouflaged moving objects based on Laws energy and varying frequency LI Jinping1，2，LI Qian1，2 (1．School of Information Science and Engineering，University of Jinan，Jinan250022，China; 2．Shandong Provincial Key Laboratory of Network based Intelligent Computing，Jinan250022，China) Abstract:The detection of moving objects in dynamic background is a research focus in video surveil-lance．Detecting camouflaged moving objects is a challenge．The traditional Gaussian mixture model (GMM)is not advantageous for detecting these moving objects．By analyzing the color change of camou-flaged moving objects in dynamic background，we put forward an effective method for camouflaged moving objects using energy of Laws and a special statistic quantity called varying frequency．The experiment shows that，when the camera is fixed，the method is effective for detecting camouflaged moving objects in dynamic background when the color of moving objects change greatly or moving objects have complicated texture． Key words:dynamic background;camouflage;moving object detection;energy of Laws;varying frequency 收稿日期:2010-12-23 基金项目:国家自然科学基金(60873089);山东省研究生教育创新计划(SDYY08032);山东省教育科学规划课题重点项目(2008ZK007) 作者简介:李金屏(1968－)，男，河南焦作人，教授，博士，硕士生导师。研究方向:图像处理，运动目标跟踪。

三维机场模型中纹理处理方法研究

三维机场模型中纹理处理方法研究 汪 洋1杨国庆2 (1.中国民用航空学院计算机科学与技术学院　２．中国民航总局３．天津市智能信号与图像处理重点实验室纹理是影响三维模型逼真程度的最主要因素需要将纹理映射在三维模型上在机场三维建模工作中 因此纹理处理方法在三维建模中起着不可忽视的作用以及某些纹理的特殊处理方法三维机场纹理 Investigation on T exture Disposal Modeling of Three-dimensional Airport WANG Yang 1, HE Huaiqing 1,3, YANG Guoqing 2 (1.College of Computer Science and Technology, Civil Aviation University of China, Tianjin 300300; 2. Civil Aviation Administration of China, Beijing 100710; 3. Tianjin Key Lab for Advanced Signal Processing, Tianjin 300300) The texture is a main factor which influences the fidelity of the three-dimensional model. When the three-dimensional model is created,textures are mapped on its surfaces to truly simulat e three-dimensional scene. In the three-dimensional modeling work of an airport, the workload of texture disposal is very heavy. Therefore Key words 1000214图像处理与模式识别常常是在三维图形上加上光影效果和分层设色可以采用纹理映射技术来增强地形的显示效果 遥感影像等)和地形的融合提高地形的表现力既可以表现机场目标之间的几何关系 把这种三维模型通过计算机技术实现机场的可视化如建筑结构和机场设计的透视效果 相邻建筑的合理性评估等[1]?°??Dèòa?ù?Yí???à′?¨á￠èy???￡Dí?°???ù?Yé????ú?￡Dí????àíí? ó°μ???ì?±í??2?????±?D? ?°?? μ???àíí¨3￡?aD±êóí??°????àíê???????ì?±í????2?í? 2 纹理获取 像片纹理的来源主要有两部分前者可用作数字模型中地面和建筑物顶部的纹理两者相互补充对机场三维景观模型的表面镶嵌以相片纹理不仅可以给出现实世界真实直观的表达而 且利用像片纹理还可以弥补三维几何模型里所表现不出的详细信息标注所需采集纹理的建筑物以航片编号为管理单位 纹理采集应整体全面以保证采集的完整性建筑物各个面的纹理方向都应标明并记录在手薄上编辑地物取样应尽量完整因摄影条件限制或建筑物过大无法一次采集时建筑物在整个地物取样中所占比例的大小会直接影响建筑物获取的信息量 所以以获取足够的信息可采用分段摄影方法由于将来要把这些照片拼接成一张纹理贴图光照强度等指标的一致性虽然精细的纹理渲染可以使场景看起来更加逼真因为过于精细的纹理对于三维景观的复原没有必要会影响到浏览速度为了减少数据存储量民航总局科技基金资助项目 作者简介）硕士图形图像与虚拟现实博士杨国庆教授2005-05-20 E -mail A 中图分类号

By-Laws(新版)

(合同范本) 姓名：____________________ 单位：____________________ 日期：____________________ 编号：YW-HT-020288 By-Laws(新版) By-Laws

By-Laws(新版) A _________(PLACENAME) CORPORATION Article I CORPORATE OFFICES The principal office of the corporation in the State of _________(PLACENAME) shall be located at _________(ADDRESS). The corporation may have such other offices, either within or without the State of incorporation as the board of directors may designate or as the business of the corporation may from time to time require. Article II SHAREHOLDERS' MEETINGS Section 1. Place of Meetings The directors may designate any place, either within or without the State unless otherwise prescribed by statute, as the place of meeting for any annual meeting or for any special meeting called by the directors. A waiver of notice signed by all stockholders entitled to vote at a meeting may designate any place, either within or without the State unless otherwise prescribed by statute, as the place for holding such meeting. If no designation is made, or if a special meeting be otherwise called, the

中考英语阅读理解专项：laws for children

中考英语阅读理解专项：laws for children In general，laws for children are a good thing. One hundred years ago in industrial countries, children worked 18 hours a day in a factory at age seven. The factory owner could beat a child who fell asleep or was not fast enough. Both parents and teachers could do the same. Today, there are many laws about children all over the world. Some people think children must obey rules or they should be punished，others do not agree. The Inuits or Eskimos in Alaskaalmost never punish their children. The parents don’t hit them. If the children go too far，the parents punish them by making fun of them. Children in other parts of the world are not as lucky as Eskimo children. American parents can spank(打……臀部) their children at home，but a teacher cannot hit a child in a public school. This is also true inGermany. In contrast(对比), it is against the law for anyone to hit a child in Sweden. Swedish parents cannot spank their children. The children also have a special government official who works for their rights. There is even a plan for children to divorce from their parents though this is not a law yet!

Laws W6 Contract Law2 合同法

Terms of a contract: The terms of the contract are the specific details of the agreement, including each party’s rights and obligations. （Term和representation的区别：a term contains a promise and therefore has promissory effect, whereas a representation does not involve a promise.） Express terms明示条款 Express term can be either in writing or oral. If a particular term has not been consciously acknowledged and agreed to by a party, it will still be an express term binding upon that party if: 1. the term is in a written contract signed by the party, or - See: L’Estrange v Graucob (1934) 2. the term was brought to the attention of the party by reasonable notice before the contract was formed. - See: Thornton v Shoe Lane Parking (1971) Once it is established that a particular statement is an express term, Courts then determine the importance parties may have attached to them. Conditions and Warranties一旦确认是明示术语，法院就会确定当事人对其可 能的重视程度 1. Conditions – major terms of the contract. A breach will entitle the innocent party to rescind (terminate终止) the contract and sue for damages. See: Poussard v Spiers (1876) 2. Warranties – minor terms of the contract. A breach will entitle the parties to sue for damages. See: Bettini v Gye (1876) 3. Third Type (Intermediate) – hybrid混合term that is capable of being a condition or a warranty. See: Koompathoo v Sanpine (2007) To determine whether a term is a condition or a warranty, the courts apply the test of essentiality.判断是条件还是保证 See: Associated Newspapers v Bancks (1951) 例子：Online Contracts: Clickwrap and Browsewrap

自然法则之三大定律(The three laws of the law of nature)

自然法则之三大定律（The three laws of the law of nature）Natural law The natural law is no place to omnipresent, not the small to big no, all that is hidden order governing the universe. Its scope is three times as poor vertical, horizontal ten square, covering all the time and space: lacking beginning and end, boundless. It is the universal drive, the universal movement, and the universal rules of the game. It defines the internal relationship and interaction between the universe. It defines the relation between force and reaction. The three laws of the law of nature: The law of attraction Law, of, Attraction Law of Deliberate Creation to create independent law law Law of Allowing let things drift The three natures of the laws of nature: The essence of everything is energy, Everything, is, about, energy The essence of everything is vibration, Everything, is, about,

永恒的投资七律 James-Montier-Immutable-Laws-of-Investing

GMO W HITE P APER March 2011 The Seven Immutable Laws of Investing James Montier In my previous missive I concluded that investors should stay true to the principles that have always guided (and should always guide) sensible investment, but I left readers hanging as to what I believe those principles might actually be. So, now, for the moment of truth, I present a set of principles that together form what I call The Seven Immutable Laws of Investing. They are as follows: 1. Always insist on a margin of safety 2. This time is never different 3. Be patient and wait for the fat pitch 4. Be contrarian 5. Risk is the permanent loss of capital, never a number 6. Be leery of leverage 7. Never invest in something you don’t understand So let’s brie? y examine each of them, and highlight any areas where investors’ current behavior violates one (or more) of the laws. 1. Always Insist on a Margin of Safety Valuation is the closest thing to the law of gravity that we have in ? nance. It is the primary determinant of long-term returns. However, the objective of investment (in general) is not to buy at fair value, but to purchase with a margin of safety. This re? ects that any estimate of fair value is just that: an estimate, not a precise ? gure, so the margin of safety provides a much-needed cushion against errors and misfortunes. When investors violate Law 1 by investing with no margin of safety, they risk the prospect of the permanent impairment of capital. I’ve been waiting a decade to use Exhibit 1. It shows the performance of a $100 investment split equally among a list of stocks that Fortune Magazine1put together in August 2000. For the article, they used this lead: “Admit it, you still have nightmares about the ones that got away. The Microsofts, the Ciscos, the Intels. They're the top holdings in your ultimate ‘coulda, woulda, shoulda’ portfolio. Oh, what might have been, you tell yourself, had you ignored all the naysayers back in 1990 and plopped a modest $5,000 into, say, both Dell and EMC and then closed your eyes for the next ten years. That's $8.4 million you didn't make. “Now, hold on a minute. This is no time for mea culpas. Okay, so you didn't buy the fastest growers of the past decade. Get over it. This is a new era – a new millennium, in fact – and the time for licking old wounds has passed. Indeed, the importance of stocks like Dell and EMC is no longer their potential as investments (which, though still lofty, is unlikely to compare with the previous decade's run). It's in their ability to teach us some valuable lessons about investing from here on out.” 1