Towards Gravity solutions of AdSCMT

a r X i v :0808.3232v 2 [h e p -t h ] 30 A u g 2008

arXiv:0808.3232

Towards Gravity solutions of AdS/CMT

Shesansu Sekhar Pal

Barchana,Jajpur,754081,Orissa,India

https://www.wendangku.net/doc/d95778113.html,

Abstract

In this short note,we have generalised and constructed gravity solutions with two “exponents”a la Kachru,Liu and Mulligan.The two point correlation function of the scalar ?eld in the mass less limit is computed in a special case that is a/b=2.

Recently,it has been becoming very interesting to understand the gravity duals to2+1dimensional CFT’s so as to understand the strongly coupled be-havior of these CFT’s,which may resemble some of the systems that we know in condensed matter theories(CMT).In this context several gravity solutions have been generated[1],[5]-[12]and more solutions need to be constructed so as to understand better the dual?eld theories at strong coupling.

The way to understand these systems is by constructing new gravity solutions with speci?c symmetry group.The scaling symmetry that we shall consider is

r

t→λa t,(x,y)→λb(x,y),r→

(2)

r2

for a=b=1,the system has the SO(2,3)symmetry group and is described as AdS4spacetime.This particular choice of the metric makes the time reversal manifest without the need to depend on the parity of the other direction and the consequence is that there will be particle production.

For a=2and b=1,the?eld theory action,which preserves the scaling symmetry,may be written as[2]and[3]

1

S C=

d2xdt (?tχ)2?K[(?2χ)2+4σ(?2xχ)(?2yχ)] ,

2

S int= d2xdt u2(?xχ)2(?yχ)2 (5) and the isotropic point corresponds toσ=0and u=v.

2

Now if we want to have a symmetry like eq(1)for generic a and b then the simplest dual?eld theory action,may be described as

S=

1

a =1+

2b

2b

=1+

a

b

=2.

Till now,the?eld theory action consistent with the scaling symmetry eq(1)that we have been discussing contains?rst derivative in time and sec-ond derivative in space coordinates.Now,the question arises:can we have an action that contains both second order derivatives in time and space co-ordinates?The answer to this is:yes1.

S=

1

2a =

1

a

,β=

2b+a

2b

(9)

and again for a/b=2,the action is not any more quadratic in?elds or for any other value of a/b.Hence,the most general action2consistent with the scaling symmetry and quadratic in?elds is eq(6).

The metric eq(2)is non-singular and is well de?ned everywhere.The coordinate invariant quantities are displayed in eq(20).The action that gen-erates such a solution can be obtained from the action written in[1],which is a system containing gravity and?uxes of2-from and3-form type,as the relevant degrees of freedom

S=1

?g(R?2Λ)?12κ2

B2∧F2,

(10) 2 d2xdt[(t?2tχ)α??K(?2χ)β],we dot know whether this kind of action is useful

or not.

2As far as time reversal is concerned,the Lagrangian density is invariant but not the action,which changes sign by an overall factor.Under parity the action remains invariant.

3

where F3=dB2and c is the topological coupling.The equations of motion that follows from it are

d?F2=?cF3,d?F3=cF2,

G MN+Λg MN=1

p!

pF MM2M3

···M p F NM2M3···M p?

1

r1?a

dr∧dt,F3=

BL3

L

d

L

d

r2

(15)

Finally,the equation of motion of the metric components give

L2(A2+B2)=?4(3b2+L2Λ)

L2(A2+B2)=4(a2+b2+ab+L2Λ)

L2(B2?A2)=4(2ab+b2+L2Λ),(16) where these equations arise from tt,xx and rr components,respectively. From these equations,we see that the right hand side of it are constants,

4

which means the functions A(r)and B(r)better be constants.In this case, eq(13)give

A

cL =

cL

L2

,

B2=

4b(a?b)

2L2

(18) It just follows that the coupling c is not any more arbitrary but is related to the exponents a and b

c2L2=2ab(19) Some of the interesting properties about the solution eq(2)

R(scalar curvature)=?

2

L4

(a4+2a3b+5a2b2+4ab3+6b4),

R MNKL R MNKL=

4

u2a +

dx2+dy2

u2

(21)

The equation of motion for a minimally coupled scalar?eldφof mass m is

?2uφ?a+2b?1

u2

]φ=0(22)

5

Using AdS/CFT correspondence,the?eldφis dual to an operator of dimen-sion?for which

?(??a?2b)=m2L2(23) From[13],if the mass of the scalar?eld stays

(mL)2>1? a+2b

2<(mL)2<1? a+2b

2

2(26)

2

and if the mass stays below this bound then there is an instability in the system.

It is well known that in a CFT the two point correlation of an operator with dimension?go as

1

～

For the minimally coupled scalar?eld with generic values of a and b,it is not easy to compute the correlation function,analytically.However for a speci?c choice of a/b=2,one can solve eq(22).If we recall from eq(6),the value of a/b for which the action is quadratic in?eld is a/b=2.

For this particular choice of a/b,the normalised solution is

G(u,k)=c1×214b2+m2L22b u2b×u2b+√

b×

U k2+2bw+2w √

4bw ,1+

√

b

,

w

2

d3xdu√

2

d3x[√2F(k)=[G(u,?k)

√

In order to proceed further let us restrict ourselves to the mass less sector and in this case the functions are G (u,k )=1?

w

2b 2

+

w 2

Γ(α)

w 2

b

)+4blog u ]

+O (u )6b

?u G (u,k )=u

4b ?1

?wu

?2b

+

2αw 2

2b

?

Γ(α+2)

b

[?4+2γ+2H 1+α+2log (

w

gg uu =L 2u 1?4b

(35)

where

α=?1

4bw

(36)

and γis the Euler-Mascheroni constant,ψ(x )is the digamma function and

H n is the harmonic number H n = n k =1

1

2k 2

w +

L 2

2

+

k 2

[3]G.Grinstein,Anisotropic sine-Gordon model and in?nite-order phase

transitions in three dimensions,Phys.Rev,B23,(1981)4615.

[4]A.Vishwanath,L.Balents and T.Senthil,Quantum criticality and de-

con?nement in phase transitions between the valence bond solids,Phys.

Rev.B69,(2004)224416.

[5]D.T.Son,Towards an Ads/cold atoms correspondence:a geometric

realization of the Schr¨o dinger symmetry,arXiv:0804.3972[hep-th] [6]K.Balasubramanian and J.McGreevy,Gravity duals for non-relativistic

CFTs,arXiv:0804.4053[hep-th]

[7]W.D.Goldberger,AdS/CFT duality for non-relativistic?eld theory,

arXiv:0806.22867[hep-th]

[8]J.L.Barbon and C.A.Fuertes On the spectrum of non-relativistic

AdS/CFT,arXiv:0806.3244[hep-th]

[9]C.P.Herzog,M.Rangamani and S.F.Ross,Heating up Galilean holog-

raphy,arXiv:0807.1099[hep-th]

[10]A.Adams,K.Balasubramanian and J.McGreevy,Hot spacetimes for

cold atoms,arXiv:0807.1111[hep-th]

[11]J.Maldacena,D.Martelli and Y.Tachikawa,Comments on string theory

backgrounds with non-relativistic conformal symmetry,arXiv:0807.1100 [hep-th]

[12]S.S.Pal,Null Melvin Twist to Sakai-Sugimoto model,

arXiv:0808.3042[hep-th].

[13]I.R.Klebanov and E.Witten,AdS/CFT correspondence and symmetry

breaking,Nucl.Phys.B556,(1999)89,hep-th/9905104.

[14]P.Breitenlohner and D.Z.Freedman,Phys.Lett.B115(1982)197.

[15]E.Witten,Anti-de Sitter space and holography,Adv.Theor.Math.Phys.

2,(1998)253,hep-th/9802150.

9

[16]S.S.Gubser,I.R.Klebanov and A.M.Polyakov,Gauge theory cor-

relators from noncritical string theory,Phys.Lett.B428,(1998)105, hep-th/9802109.

10

to与for的用法和区别

to与for的用法和区别 一般情况下, to后面常接对象; for后面表示原因与目的为多。 Thank you for helping me. Thanks to all of you. to sb.表示对某人有直接影响比如，食物对某人好或者不好就用to; for表示从意义、价值等间接角度来说，例如对某人而言是重要的，就用for. for和to这两个介词，意义丰富，用法复杂。这里仅就它们主要用法进行比较。 1. 表示各种“目的” 1. What do you study English for? 你为什么要学英语？ 2. She went to france for holiday. 她到法国度假去了。 3. These books are written for pupils. 这些书是为学生些的。 4. hope for the best, prepare for the worst. 作最好的打算，作最坏的准备。 2．对于 1．She has a liking for painting. 她爱好绘画。 2．She had a natural gift for teaching. 她对教学有天赋/ 3．表示赞成同情，用for不用to. 1. Are you for the idea or against it? 你是支持还是反对这个想法？ 2. He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 3. I felt deeply sorry for my friend who was very ill. 4 for表示因为，由于（常有较活译法） 1 Thank you for coming. 谢谢你来。 2. France is famous for its wines. 法国因酒而出名。 5．当事人对某事的主观看法，对于（某人），对…来说（多和形容词连用）用介词to，不用for.. He said that money was not important to him. 他说钱对他并不重要。 To her it was rather unusual. 对她来说这是相当不寻常的。 They are cruel to animals. 他们对动物很残忍。 6．for和fit, good, bad, useful, suitable 等形容词连用，表示适宜，适合。 Some training will make them fit for the job. 经过一段训练，他们会胜任这项工作的。 Exercises are good for health. 锻炼有益于健康。 Smoking and drinking are bad for health. 抽烟喝酒对健康有害。 You are not suited for the kind of work you are doing. 7. for表示不定式逻辑上的主语，可以用在主语、表语、状语、定语中。 1．It would be best for you to write to him. 2．The simple thing is for him to resign at once. 3．There was nowhere else for me to go. 4．He opened a door and stood aside for her to pass.

地球物理勘查名词术语

中华人民共和国国家标准 GB XXXX--XX 地球物理勘查名词术语 Terms Of geophysical exploration 1 主题内容及适用范围 本标准规定了地球物理勘查(包括重力勘查、磁勘查、电勘查、地震勘查、测井及核物探)中常用的、主要的、本学科专有的名词术语。 本标准适用于地球物理勘查工作的语言和文字交流。 2 基本术语 2.1 地球物理勘查geophysical exploration 运用物理学的原理、方法和仪器以研究地质情况或寻查埋藏物的一类勘查。 同义词物探；地球物理勘探：(勘探地球物理；地球物理探矿) 注：1.取决于使用场合，该术语可附加后缀“法”或“学”。 2.根据具体情况，可以使用“航空物探”，“海洋物探”，“地面物探”，“地下物探”，“深部物探”，“区域物探”， “工程物探”，“环境物探”，……等术语。 2.2 正常场normal field 物理场的相对平稳部分。 2.3 异常anomaly 物理场对正常场的偏离。 2.3.1 理论异常theoretical anomaly 正演所获得的异常。 同义词计算异常 2.4 物性physical properties 岩(矿)石或其它探测对象的物理性质。 2.5 异向性系数coefficient of anisotropy 描述介质垂直层理(片理、节理等)方向与平行层理方向的物性差异的一种参数。 同义词(各向异性系数;非各向同性系数) 2.6 地球物理正演geophysical direct problem 根据地质体或其它探测对象的几何参数和物理参数计算地球物理场值。 同义词物探正演 2.7 地球物理反演geophysical inversion 根据地球物理场值，计算地质体或其它探测对象的几何参数和物性参数。 同义词物探反演 国家技术监督局XXXX—XX—XX批准 XXXX—XX—XX实施

(完整版)介词for用法归纳

介词for用法归纳 用法1：(表目的)为了。如： They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做？ That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了？ He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下，英语不用for doing sth 来表示目的。如： 他去那儿看他叔叔。 误：He went there for seeing his uncle. 正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的。如： He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。(见下面的有关用法) 用法2：(表利益)为，为了。如： What can I do for you? 你想要我什么？ We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗？ Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通常用for 来引出间接宾语，表示间接宾语为受益者。如： She made her daughter a dress. / She made a dress for her daughter. 她为她女儿做了件连衣裙。 He cooked us some potatoes. / He cooked some potatoes for us. 他为我们煮了些土豆。 注意，类似下面这样的句子必须用for： He bought a new chair for the office. 他为办公室买了张新办公椅。 (2) 注意不要按汉语字面意思，在一些及物动词后误加介词for： 他们决定在电视上为他们的新产品打广告。 误：They decided to advertise for their new product on TV. 正：They decided to advertise their new product on TV. 注：advertise 可用作及物或不及物动词，但含义不同：advertise sth＝为卖出某物而打广告；advertise for sth＝为寻找某物而打广告。如：advertise for a job=登广告求职。由于受汉语“为”的影响，而此处误加了介词for。类似地，汉语中的“为人民服务”，说成英语是serve the people，而不是serve for the people，“为某人的死报仇”，说成英语是avenge sb’s death，而不是avenge for sb’s death，等等。用法3：(表用途)用于，用来。如： Knives are used for cutting things. 小刀是用来切东西的。 This knife is for cutting bread. 这把小刀是用于切面包的。 It’s a machine for slicing bread. 这是切面包的机器。 The doctor gave her some medicine for her cold. 医生给了她一些感冒药。 用法4：为得到，为拿到，为取得。如： He went home for his book. 他回家拿书。 He went to his friend for advice. 他去向朋友请教。 She often asked her parents for money. 她经常向父母要钱。

android layout_gravity 和 android gravity 的区别

1.gravity 这个英文单词是重心的意思，在这里就表示停靠位 置的意思。 android:layout_gravity 和android:gravity 的区别 从名字上可以看到，android:gravity是对元素本身说的，元素本身的文本显示在什么地方靠着换个属性设置，不过不设置默认是在左侧的。 android:layout_gravity是相对与它的父元素说的，说明元素显示在父元素的什么位置。 比如说button：android:layout_gravity 表示按钮在界面上的位置。android:gravity表示button上的字在button上的位置。 可选值 这两个属性可选的值有：top、bottom、left、right、center_vertical、fill_vertical、center_horizontal、fill_horizontal、center、fill、clip_vertical。

而且这些属性是可以多选的，用“|”分开。 默认这个的值是：Gravity.LEFT 对这些属性的描述： 出自： https://www.wendangku.net/doc/d95778113.html,/guide/topics/resources/drawable-res ource.html https://www.wendangku.net/doc/d95778113.html,/reference/android/graphics/drawable /ClipDrawable.html Value Description top Put the object at the top of its container, not changing its size. 将对象放在其容器的顶部，不改变其大小. bottom Put the object at the bottom of its container, not changing its size. 将对象放在其容器的底部，不改变其大小.

常用介词用法(for to with of)

For的用法 1. 表示“当作、作为”。如: I like some bread and milk for breakfast. 我喜欢把面包和牛奶作为早餐。 What will we have for supper? 我们晚餐吃什么? 2. 表示理由或原因,意为“因为、由于”。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 3. 表示动作的对象或接受者,意为“给……”、“对…… (而言)”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 4. 表示时间、距离,意为“计、达”。如: I usually do the running for an hour in the morning. 我早晨通常跑步一小时。 We will stay there for two days. 我们将在那里逗留两天。 5. 表示去向、目的,意为“向、往、取、买”等。如: Let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 I paid twenty yuan for the dictionary. 我花了20元买这本词典。 6. 表示所属关系或用途,意为“为、适于……的”。如: It’s time for school. 到上学的时间了。 Here is a letter for you. 这儿有你的一封信。 7. 表示“支持、赞成”。如: Are you for this plan or against it? 你是支持还是反对这个计划? 8. 用于一些固定搭配中。如: Who are you waiting for? 你在等谁? For example, Mr Green is a kind teacher. 比如,格林先生是一位心地善良的老师。 尽管for 的用法较多，但记住常用的几个就可以了。 to的用法: 一：表示相对，针对 be strange (common, new, familiar, peculiar) to This injection will make you immune to infection. 二：表示对比，比较 1：以-ior结尾的形容词，后接介词to表示比较，如：superior ,inferior,prior,senior,junior 2: 一些本身就含有比较或比拟意思的形容词，如equal，similar，equivalent，analogous A is similar to B in many ways.

(精校版)沪教牛津版初中英语单词表

(完整word版)沪教牛津版初中英语单词表 编辑整理： 尊敬的读者朋友们： 这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（(完整word版)沪教牛津版初中英语单词表）的内容能够给您的工作和学习带来便利。同时也真诚的希望收到您的建议和反馈，这将是我们进步的源泉，前进的动力。 本文可编辑可修改，如果觉得对您有帮助请收藏以便随时查阅，最后祝您生活愉快业绩进步，以下为(完整word版)沪教牛津版初中英语单词表的全部内容。

沪教版七年级上单词表 Unit 1 German adj. 德国的 blog n. 博客 grammar n。语法 sound n. 声音complete v。完成 hobby n. 爱好 country n. 国家 age n。年龄 dream n.梦想 everyone pron. 人人；所有人 Germany n. 德国mountain n。山；山脉elder adj. 年长的friendly adj。友爱的；友好的 engineer n.工程师 world n. 世界 Japan n。日本 flat n. 公寓 yourself pron.你自己 US n. 美国close to （在空间、时间上） 接近 go to school 去上学 （be) good at 擅长 make friends with 与..。... 交朋友 all over 遍及 ’d like to = would like to 愿意 Unit2 daily adj。每日的；日常 的 article n。文章 never adv. 从不 table tennis n.兵乓球 ride v. 骑；驾驶 usually adv。通常地 so conj. 因此;所以 seldom adv.不常；很少 Geography n. 地理 break n. 休息 bell n。钟；铃 ring v。（使）发出钟声， 响起铃声 end v。结束；终止 band n。乐队 practice n. 练习 together adv。在一起 market n。集市；市场 guitar n。吉他 grade n. 年级 junior high school 初级 中学 on foot步行 take part in 参加 have a good time 过得愉快 go to bed 去睡觉 get up 起床 Unit3 Earth n. 地球 quiz n。知识竞赛；小测 试 pattern n。模式;形式 protect v.保护 report n。报告 part n. 部分

for和to区别

1.表示各种“目的”，用for （1）What do you study English for 你为什么要学英语？ （2）went to france for holiday. 她到法国度假去了。 （3）These books are written for pupils. 这些书是为学生些的。 （4）hope for the best, prepare for the worst. 作最好的打算，作最坏的准备。 2．“对于”用for （1）She has a liking for painting. 她爱好绘画。 （2）She had a natural gift for teaching. 她对教学有天赋/ 3．表示“赞成、同情”，用for （1）Are you for the idea or against it 你是支持还是反对这个想法？ （2）He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 （3）I felt deeply sorry for my friend who was very ill. 4. 表示“因为，由于”（常有较活译法），用for （1）Thank you for coming. 谢谢你来。

（2）France is famous for its wines. 法国因酒而出名。 5．当事人对某事的主观看法，“对于（某人），对…来说”，（多和形容词连用），用介词to，不用for. （1）He said that money was not important to him. 他说钱对他并不重要。 （2）To her it was rather unusual. 对她来说这是相当不寻常的。 （3）They are cruel to animals. 他们对动物很残忍。 6．和fit, good, bad, useful, suitable 等形容词连用，表示“适宜，适合”，用for。（1）Some training will make them fit for the job. 经过一段训练，他们会胜任这项工作的。 （2）Exercises are good for health. 锻炼有益于健康。 （3）Smoking and drinking are bad for health. 抽烟喝酒对健康有害。 （4）You are not suited for the kind of work you are doing. 7. 表示不定式逻辑上的主语，可以用在主语、表语、状语、定语中。 （1）It would be best for you to write to him. （2） The simple thing is for him to resign at once.

双宾语 to for的用法

1.两者都可以引出间接宾语，但要根据不同的动词分别选用介词to 或for：(1) 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。 如： 请把那本字典递给我。 正：Please hand me that dictionary. 正：Please hand that dictionary to me. 她去年教我们的音乐。 正：She taught us music last year. 正：She taught music to us last year. (2) 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose,prepare, spare 等之后用介词for 。如： 他为我们唱了首英语歌。 正：He sang us an English song. 正：He sang an English song for us. 请帮我把钥匙找到。 正：Please find me the keys. 正：Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正：Can you spare me a few minutes? 正：Can you spare a few minutes for me? 注：有的动词由于搭配和含义的不同，用介词to 或for 都是可能的。如：do sb a favour＝do a favour for sb 帮某人的忙 do sb harm＝do harm to sb 对某人有害

双宾语tofor的用法

1. 两者都可以引出间接宾语，但要根据不同的动词分别选用介词to 或for： (1) 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。 如： 请把那本字典递给我。 正：Please hand me that dictionary. 正：Please hand that dictionary to me. 她去年教我们的音乐。 正：She taught us music last year. 正：She taught music to us last year. (2) 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose,prepare, spare 等之后用介词for 。如： 他为我们唱了首英语歌。 正：He sang us an English song. 正：He sang an English song for us. 请帮我把钥匙找到。 正：Please find me the keys. 正：Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正：Can you spare me a few minutes? 正：Can you spare a few minutes for me? 注：有的动词由于搭配和含义的不同，用介词to 或for 都是可能的。如： do sb a favou r do a favour for sb 帮某人的忙 do sb harnn= do harm to sb 对某人有害

Density and Specific Gravity

Density and Specific Gravity (1) Density (r)of a material is defined as mass per unit volume and is usually represented in the SI system by the units g*cm-3or kg*m-3. There are a number of different methods and devices for determining the density of a substance, and there are also a number of factors that can affect the density of a sample. If the exact composition of a non-homogeneous ) can be determined using the mass material is known, its solid density(r s and density of each of the n components using the following equation: The density of materials such as agricultural grains, which consist of many small particles, can be expressed in terms of solid density,particle density or bulk density. Solid density considers the mass and volume of the solid matter only and does not include any air spaces within the mixture. Particle density describes the mass per unit volume of an individual particle (e.g. corn kernel) from the sample. Bulk density, on the other hand, considers the total mass and total volume of a large quantity of the particles. Specific gravity is a dimensionless term used to compare the densities of different materials relative to water. Specific gravity of a substance is defined as the ratio of the substance’s density to the density of wa ter at the same temperature. From this information, it can be determined that if the specific gravity of a material is less than 1, it is less dense than water, and if the specific gravity is greater than 1, it is more dense than water. 1. Stroshine and Hamann. 1994. Physical Properties of Agricultural Materials and Food Products. 17-18.

to和for的用法有什么不同(一)

to和for的用法有什么不同（一） 一、引出间接宾语时的区别 两者都可以引出间接宾语，但要根据不同的动词分别选用介词to 或for，具体应注意以下三种情况： 1. 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。如： 请把那本字典递给我。 正：Please hand me that dictionary. 正：Please hand that dictionary to me. 她去年教我们的音乐。 正：She taught us music last year. 正：She taught music to us last year. 2. 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose, prepare, spare 等之后用介词for 。如： 他为我们唱了首英语歌。 正：He sang us an English song. 正：He sang an English song for us. 请帮我把钥匙找到。 正：Please find me the keys. 正：Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正：Can you spare me a few minutes?

正：Can you spare a few minutes for me? 3. 有的动词由于用法和含义不同，用介词to 或for 都是可能的。如： do sb a favor＝do a favor for sb 帮某人的忙 do sb harm＝do harm to sb 对某人有害 在有的情况下，可能既不用for 也不用to，而用其他的介词。如： play sb a trick＝play a trick on sb 作弄某人 请比较： play sb some folk songs＝play some folk songs for sb 给某人演奏民歌 有时同一个动词，由于用法不同，所搭配的介词也可能不同，如leave sbsth 这一结构，若表示一般意义的为某人留下某物，则用介词for 引出间接宾语，即说leave sth for sb；若表示某人死后遗留下某物，则用介词to 引出间接宾语，即说leave sth to sb。如： Would you like to leave him a message? / Would you like to leave a message for him? 你要不要给他留个话？ Her father left her a large fortune. / Her father left a large fortune to her. 她父亲死后给她留下了一大笔财产。 二、表示目标或方向的区别 两者均可表示目标、目的地、方向等，此时也要根据不同动词分别对待。如： 1. 在come, go, walk, move, fly, ride, drive, march, return 等动词之后通常用介词to 表示目标或目的地。如： He has gone to Shanghai. 他到上海去了。 They walked to a river. 他们走到一条河边。

东亚贸易gravity model应用-国际经济学

WORLD TRADE（EAST ASIA）: The Gravity Model PART1: 从更具体的省份?角度来看中韩贸易，??广东、江苏、?山东和上海稳固占据前4席位，其中??广东是中韩进出?口的第?一?大省，进出?口份额均约1/4。东部省市是中韩贸易的主体，但中?西部省市凸显?高速增?长态势。 按照gravity model，距离越?小，贸易量会越?大，从上表中可知排名第三的?山东、第六的辽宁第七的天津都是距离韩国较近的省份，故贸易量会排在较前。但是??广东、江苏、

上海、浙江的省经济贸易总量?非常?大，以?至于其影响超过了距离对东部各省与韩的贸易量的影响，使??广东各省稳居前列。 PART2: ?自1992年8?月建交以来，中韩两国间经贸往来取得了较快发展，两国双边贸易额由建交时的50亿美元增加到2012年2742．38亿美元，增长了五??十余倍。2013年，韩国是中国的第三?大贸易伙伴，?而中国已成为韩国的第?一?大贸易伙伴、第?一?大出??口?目的地和第?一?大进??口来源地。

上?方所显?示的四张图是中?日、中韩的近?几年贸易量显?示。总体来讲由于中国本?身国家经济贸易总量的增?长，中?日、中韩之间的贸易量基本都是增?长趋势，其增?长额度与速度也不容?小觑，加上本?身同为东亚的各国的距离上的优势以及?日本与韩国的GPD多年来的增?长，形成以上图的状况。图?二中2003-2013中韩贸易额占中国贸易总额微有所下降，中韩贸易额占韩国贸易总额却有明显的上升，?一?方?面是由于中国本?身国家经济贸易总量的快速?大量增?长超越了韩国的GDP增?长，另?一?方?面由于中国扩?大了贸易发展?面，贸易多边化，中韩所占中国贸易总量?比重减少。 图四所显?示，2006-2010中?日贸易同?比增?长和中国外贸同?比增?长基本趋势趋于?一致，除2009年点处，中国外贸同?比增?长数额明显?大于中?日贸易同?比增?长数额。原因还是中国贸易的国际化快速发展。 PART3:

202X中考英语：to和for的区别与用法.doc

202X中考英语：to和for的区别与用法中考栏目我为考生们整理了“202X中考英语：to和for的区别与用法”，希望能帮到大家，想了解更多考试资讯，本网站的及时更新哦。 202X中考英语：to和for的区别与用法 to和for的区别与用法是什么 一般情况下, to后面常接对象; for后面表示原因与目的为多。 Thank you for helping me. Thanks to all of you. to sb. 表示对某人有直接影响比如，食物对某人好或者不好就用to; for 表示从意义、价值等间接角度来说，例如对某人而言是重要的，就用for. for和to这两个介词，意义丰富，用法复杂。这里仅就它们主要用法进行比较。 1. 表示各种“目的” 1. What do you study English for? 你为什么要学英语? 2. She went to france for holiday. 她到法国度假去了。 3. These books are written for pupils. 这些书是为学生些的。 4. hope for the best, prepare for the worst. 作最好的打算，作最坏的准备。

2.对于 1.She has a liking for painting. 她爱好绘画。 2.She had a natural gift for teaching. 她对教学有天赋。 3.表示赞成同情，用for不用to. 1. Are you for the idea or against it? 你是支持还是反对这个想法? 2. He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 3. I felt deeply sorry for my friend who was very ill. 4 for表示因为，由于(常有较活译法) 1.Thank you for coming. 谢谢你来。 2. France is famous for its wines. 法国因酒而出名。 5.当事人对某事的主观看法，对于(某人)，对?来说(多和形容词连用)用介词to，不用for.. He said that money was not important to him. 他说钱对他并不重要。 To her it was rather unusual. 对她来说这是相当不寻常的。 They are cruel to animals. 他们对动物很残忍。

THE LOG OF GRAVITY

THE LOG OF GRAVITY J.M.C.Santos Silva and Silvana Tenreyro* Abstract—Although economists have long been aware of Jensen’s in-equality,many econometric applications have neglected an important implication of it:under heteroskedasticity,the parameters of log-linearized models estimated by OLS lead to biased estimates of the true elasticities.We explain why this problem arises and propose an appropri-ate estimator.Our criticism of conventional practices and the proposed solution extend to a broad range of applications where log-linearized equations are estimated.We develop the argument using one particular illustration,the gravity equation for trade.We?nd signi?cant differences between estimates obtained with the proposed estimator and those ob-tained with the traditional method. I.Introduction E CONOMISTS have long been aware that Jensen’s in- equality implies that E(ln y) ln E(y),that is,the expected value of the logarithm of a random variable is different from the logarithm of its expected value.This basic fact,however,has been neglected in many economet-ric applications.Indeed,one important implication of Jen-sen’s inequality is that the standard practice of interpreting the parameters of log-linearized models estimated by ordi-nary least squares(OLS)as elasticities can be highly mis-leading in the presence of heteroskedasticity. Although many authors have addressed the problem of obtaining consistent estimates of the conditional mean of the dependent variable when the model is estimated in the log linear form(see,for example,Goldberger,1968;Man-ning&Mullahy,2001),we were unable to?nd any refer-ence in the literature to the potential bias of the elasticities estimated using the log linear model. In this paper we use the gravity equation for trade as a particular illustration of how the bias arises and propose an appropriate estimator.We argue that the gravity equation, and,more generally,constant-elasticity models,should be estimated in their multiplicative form and propose a simple pseudo-maximum-likelihood(PML)estimation technique. Besides being consistent in the presence of heteroskedas-ticity,this method also provides a natural way to deal with zero values of the dependent variable. Using Monte Carlo simulations,we compare the perfor-mance of our estimator with that of OLS(in the log linear speci?cation).The results are striking.In the presence of heteroskedasticity,estimates obtained using log-linearized models are severely biased,distorting the interpretation of the model.These biases might be critical for the compara-tive assessment of competing economic theories,as well as for the evaluation of the effects of different policies.In contrast,our method is robust to the different patterns of heteroskedasticity considered in the simulations. We next use the proposed method to provide new esti-mates of the gravity equation in cross-sectional https://www.wendangku.net/doc/d95778113.html,ing standard tests,we show that heteroskedasticity is indeed a severe problem,both in the traditional gravity equation introduced by Tinbergen(1962),and in a gravity equation that takes into account multilateral resistance terms or?xed effects,as suggested by Anderson and van Wincoop(2003). We then compare the estimates obtained with the proposed PML estimator with those generated by OLS in the log linear speci?cation,using both the traditional and the?xed-effects gravity equations. Our estimation method paints a very different picture of the determinants of international trade.In the traditional gravity equation,the coef?cients on GDP are not,as gen-erally estimated,close to1.Instead,they are signi?cantly smaller,which might help reconcile the gravity equation with the observation that the trade-to-GDP ratio decreases with increasing total GDP(or,in other words,that smaller countries tend to be more open to international trade).In addition,OLS greatly exaggerates the roles of colonial ties and geographical proximity. Using the Anderson–van Wincoop(2003)gravity equa-tion,we?nd that OLS yields signi?cantly larger effects for geographical distance.The estimated elasticity obtained from the log-linearized equation is almost twice as large as that predicted by PML.OLS also predicts a large role for common colonial ties,implying that sharing a common colonial history practically doubles bilateral trade.In con-trast,the proposed PML estimator leads to a statistically and economically insigni?cant effect. The general message is that,even controlling for?xed effects,the presence of heteroskedasticity can generate strikingly different estimates when the gravity equation is log-linearized,rather than estimated in levels.In other words,Jensen’s inequality is quantitatively and qualitatively important in the estimation of gravity equations.This sug-gests that inferences drawn on log-linearized regressions can produce misleading conclusions. Despite the focus on the gravity equation,our criticism of the conventional practice and the solution we propose ex-tend to a broad range of economic applications where the equations under study are log-linearized,or,more generally, transformed by a nonlinear function.A short list of exam-ples includes the estimation of Mincerian equations for wages,production functions,and Euler equations,which are typically estimated in logarithms. Received for publication March29,2004.Revision accepted for publi- cation September13,2005. *ISEG/Universidade Te′cnica de Lisboa and CEMAPRE;and London School of Economics,CEP,and CEPR,respectively. We are grateful to two anonymous referees for their constructive comments and suggestions.We also thank Francesco Caselli,Kevin Denny,Juan Carlos Hallak,Daniel Mota,John Mullahy,Paulo Parente, Manuela Simarro,and Kim Underhill for helpful advice on previous versions of this paper.The usual disclaimer applies.Jiaying Huang provided excellent research assistance.Santos Silva gratefully acknowl- edges the partial?nancial support from Fundac?a?o para a Cie?ncia e Tecnologia,program POCTI,partially funded by FEDER.A previous version of this paper circulated as“Gravity-Defying Trade.” The Review of Economics and Statistics,November2006,88(4):641–658 ?2006by the President and Fellows of Harvard College and the Massachusetts Institute of Technology