A comment on the index of the lattice Dirac operator and the Ginsparg-Wilson relation
a r X i v :h e p -l a t /9911017v 2 25 N o v 1999
A comment on the index of the lattice Dirac operator
and the Ginsparg-Wilson relation.
Atsushi Yamada
Department of Physics,University of Tokyo,Tokyo,113Japan
ABSTRACT
We pursue Ginsparg and Wilsons’block spin approach in the derivation of the Ginsparg-Wilson relation and study the correspondence of the eigenmodes of the Dirac operators in the continuum and lattice theories.After introducing a suitable cut-o?in the continuum theory,we identify unphysical modes of the lattice Dirac operator which do not correspond to any physical modes of the regulated continuum Dirac operator.We also consider zero modes in the continuum and lattice theories.Our studies give a physical interpretation of the expression of the index de?ned on a lattice and a formal argument on the relation of the indices between the continuum and lattice theories.
One of the recent developments in the treatment of the chiral symmetry on a lattice based on the Ginsparg-Wilson relation[1]
D latγ5+γ5D lat=aD latγ5D lat(1) is the interesting index relation[2,3]
tr latγ5(1?
a
2D lat)in Eq.(2),which is
absent in the continuum index relation[14,15]
tr cγ5=n c+?n c?,(3) is further studied in Refs.[10,11]based on the representation of the algebra(1),leading to the observation that the mismatch of the chiralities between the zero modes of D lat should be compensated by the mismatch of the chiralities of its eigenmodes with the eigenvalue2
a and the zero modes of D c and
D lat are investigated after introducing a suitable cut-o?in D c to make our analysis free from divergences.This cut-o?procedure,which was not considered in Ref.[1],is an important step to derive a clear correspondence of the eigenmodes in our study.We will see that the eigenmodes of D lat with the eigenvalue2
2D lat)in
the tr latγ5(1?a
a λ
are omitted in the evaluation of the trace.Also we will show that the zero modes of D c are transformed to the zero modes of D lat preserving the chirality so that n c±=n lat±. These two observations provide us a physical interpretation of the index expression(2) and the identity
tr cγ5=tr latγ5(1?
a
new action S lat(ˉψn,ψn)on a lattice by block spin transformation.First we de?ne the block variablesρn andˉρn corresponding to the continuum?eldsφx andˉφx as
ρn= x f nxφx,ˉρn= xˉφx f?xn,(5) where the functions f nx and f?xn have a sharp peak at x=n and are proportional to the unit matrix in Dirac https://www.sodocs.net/doc/4d17540991.html,ing these variables,the new action S lat(ˉψn,ψn)is de?ned by means of the block spin transformation[17]as
Ce?S lat(ˉψ,ψ)= x dˉφx dφx e?S c(ˉφ,φ)?α n(ˉψn?ˉρn)(ψn?ρn),(6) whereαis a constant and will be equated to2/a later.Assuming that S c(ˉφ,φ)is quadratic in the fermion?elds then so is S lat(ˉψ,ψ),and we may write
S c(ˉφ,φ)= xyˉφx D c xyφy,S lat(ˉψ,ψ)= mnˉψm D lat mnψn.(7) The Ginsparg-Wilson relation is a relation satis?ed by D lat mn by virtue of its having been constructed from an initially chirally invariant action S c(ˉφ,φ).The exponent of the right-hand side of Eq.(6)is
? xyˉφx D c xyφy?α n(ˉψn?ˉρn)(ψn?ρn)
= xyˉφx{D c xy+α n f?xn f ny}φy+ xˉφxξx+ yˉξyφy?α nˉψnψn,(8)
ξx=α n f?xnψn,ˉξy=α nˉψn f ny.
Here we assume that our continuum theory is made well-de?ned by a certain regulariza-tion procedure and the spectrum of the Dirac operator D c xy(namely the absolute value
of its eigenvalues)is bounded from above.Therefore all the eigenmodesλphys
x of the
Dirac operator D c xy,which we want to simulate on a lattice,satisfy
y D c xyλi,phys
y
=εiλi,phys
x
,|εi|≤Λ,(9)
for some cut-o?Λ.Then for su?ciently largeα(as will be seen later,αplays the role of the cut-o?in the lattice theory),the operator M xy=D c xy+α n f?xn f ny has no zero mode so that its inverse M?1xy exists.For this choice ofα,the result of the path integral in Eq.(6)is given by
Ce?S lat(ˉψ,ψ)=detMe xyˉξx M?1xyξy?α nˉψnψn
=detMe? mnˉψm{?α2 xy f mx M?1xy f?yn+αδmn}ψn(10)
so we see [18]
D lat mn
={?α
2
xy
f mx M ?1xy f ?
yn +αδmn },
(11)M xy =D c
xy +α
n
f ?
xn f ny .
(12)
Now we consider the eigenmodes of D lat
mn and identify unphysical modes.Since the eigenvalues of M xy de?ned in Eq.(12)for the eigenmodes λphys x are non-zero and ?nite,neither y M xy λphys
y nor y M ?1xy λphys y is equal to zero;
y
M xy λphys y
=0,
y
M ?1xy λphys
y =0.
(13)
Therefore,a mode λn of D lat
mn which satis?es
n
M ?1xy f ?
yn λn =0
(14)
is considered to be unphysical,because the eigenmode λn on a lattice does not simulate
a mode similar to any physical mode {λphys x }.For λn satisfying n M ?1xy f ?
yn λn =0,we have
n
D lat mn λn =αλn
(15)
so the eigenmodes of D lat
mn with the eigenvalue αare considered to be unphysical on a
lattice,because they have no counterparts among the physical spectrum {λphys y
}of D c
xy .Next we consider a zero mode λ0,phys x
of D c
xy .The eigenvalue equation y D c xy λ0,phys y =0and Eq.(12)yield
y
M xy λ0,phys
y
=
y
α
n
f ?xn f ny λ0,phys
y
.(16)
Since M ?1
xy exists,multiplying
z
f mz M ?1
zx for both sides of the above equation,we obtain
λ0,phys m =α
z,x,n
f mz M ?1zx f ?xn λ0,phys
n ,
(17)λ0,phys m
=
x
f mx λ0,phys x
.(18)
Because of the identity (17),we have
n
D lat mn λ0,phys
n
=
n
{?α
2
xy
f mx M ?1xy f ?yn +αδmn }λ0,phys
n
=?αλ0,phys m +αλ0,phys
m
=0,(19)
thereforeλ0,phys
n is a zero mode of D lat mn.The functions{f nx}are proportional to the unit
matrix in Dirac space so that the chirality ofλ0,phys
m is same as that ofλ0,phys
x
.So all the
zero modes of D c xy have the corresponding zero modes of D lat mn preserving their chiralities. This is in some sense desirable and naively expected result,and we have seen that it is in fact shown regardless of the details of the block spin transformation,e.g.,the choice of the functions f and f?.Here we assume that our lattice is?ne enough so that the
shape of the zero modesλ0,phys
x is well preserved on a lattice when transformed to the
zero modesλ0,phys
n
of D lat mn and they are distinguishable with each other on a lattice.
Our criterion of the unphysical modes on a lattice leads us to de?ne the index on a lattice among the physical modes to be
tr latγ5(1?
1
αD lat),
the index(20)is equal to n lat+?n lat?where n lat+and n lat?are the number of the right-handed and left-handed zero modes of D lat[2,3].Our analysis on the zero modes in the continuum and lattice theories naively yields n c±=n lat±,where n c+and n c?are the number of the right-handed and left-handed zero modes of D c.These two observations give rise to the index relation among the physical modes as
tr cγ5=tr latγ5(1?
1
α)?
=(1+2i?tr cγ5)[1?2i?{tr latγ5+1
?ψn
γ5
?
αD lat)}+2i?
1
α
D latγ5D lat(25)
withα=2/a and the index relation
2tr cγ5=2tr latγ5(1?
1
α
D lat)mnψn,P m= nˉψmγ5(1?1
αD lat)is to eliminate the contributions of the
unphysical modes.
The precise relation between the high energy modes of D c and the high energy modes of D lat with the eigenvalue not equal toαdepends on the choice of the cut-o?scalesΛin Eq.(9)andα.However these high energy modes are always vector-like both in the continuum and lattice theories[10,11]and will decouple from the low energy physics. Thus detailed prescriptions of the ultraviolet cut-o?do not change our observations.
I would like to thank K.Fujikawa for encouraging me to write this short note.I am also grateful to M.Ishibashi for careful reading of the manuscript and useful comments, and to K.Nagai for useful comments.
References
[1]P.H.Ginsparg and K.G.Wilson,Phys.Rev.D25,2649,(1982).For Dirac operators
satisfying the Ginsparg-Wilson relation,see H.Neuberger,Phys.Lett.B417,141, (1998);R.Narayanan and H.Neuberger,Nucl.Phys.B412,574,(1994);P.Hasen-frats and F.Niedermayer,Nucl.Phys.B414,785,(1994).
[2]P.Hasenfrats,https://www.sodocs.net/doc/4d17540991.html,liena and F.Niedermayer,Phys.Lett.B427,125,(1998).
[3]M.L¨u scher,Phys.Lett.B428,342,(1998);Nucl.Phys.B538,515,(1999).
[4]P.Hasenfrats,Nucl.Phys.B525,401,(1998).
[5]H.Neuberger,Phys.Rev.D57,5417,(1998).
[6]S.Chandrasekharan,hep-lat/9805015.
[7]S.Randjbar-Daemi and J.Strathdee,Nucl.Phys.B443,386,(1995);Phys.Lett.
B402,134,(1997).
[8]R.Narayanan and P.Vranas,Nucl.Phys.B506,373,(1997).
[9]Y.Kikukawa and A.Yamada,Phys.Lett.B448,265,(1999);Nucl.Phys.B547,
413,(1999).
[10]T.W.Chiu,hep-lat/9810052;Phys.Lett.B445,371,(1999);Phys.Rev.D58,
075411,(1998).T.W.Chiu and T.H.Hsieh,hep-lat/9901011.
[11]K.Fujikawa,Nucl.Phys.B546,480,(1999);Phys.Rev.D60,074505,(1999).
[12]H.Suzuki,hep-th/9812019.
[13]D.H.Adams,hep-lat/9812003.
[14]R.Jackiw and C.Rebbi,Phys.Rev.D16,1052,(1977).
[15]K.Fujikawa,Phys.Rev.Lett.42,1195,(1979);Phys.Rev.D21,2848,(1980);
Phys.Rev.D22,1499(E),(1980);Phys.Rev.D29,285,(1984).
[16]Fujikawa called the eigenmodes of D lat with the eigenvalue2
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螺纹通止规
螺纹通止规 定是:螺纹止规进入螺纹不能超过2.5圈,一般的要实际不得超过2圈,并且用得力度不能大,我们的经验是用拇指和食指轻轻夹持螺纹规以刚好能转动螺纹规的力度为准.力大了就相当于在使用丝锥或牙板了,那样规就用不了几次了. 螺纹通止规 螺纹通止规是适用于标准规定型号的灯头作为灯用附件电光源产品时候的设计和生产、检验的工具设备。 用途 一般用于检验螺纹灯头或灯座的尺寸是否符合标准要求，分别检验螺纹灯头的通规和止规尺寸或灯座的通规或止规尺寸。 工作原理 具体检验要求及介绍详见中国人民国国家标准：GB/T1483.1-2008或 IEC60061-3:2004标准规定容。 操作方法 具体检验要求及介绍详见中国人民国国家标准：GB/T1483.1-2008或 IEC60061-3:2004标准规定容。 通止规
通止规，是量规的一种。作为度量标准，用于大批量的检验产品。 通止规是量具的一种，在实际生产批量的产品若采取用计量量具（如游标卡尺，千分表等有刻度的量具）逐个测量很费事．我们知道合格的产品是有一个度量围的.在这个围的都合格，所以人们便采取通规和止规来测量． 通止规种类 （一）对统一英制螺纹，外螺纹有三种螺纹等级：1A、2A和3A级，螺纹有三种等级：1B、2B和3B级，全部都是间隙配合。等级数字越高，配合越紧。在英制螺纹中，偏差仅规定1A和2A级，3A级的偏差为零，而且1A和2A级的等级偏差是相等的等级数目越大公差越小，如图所示：1B 2B 3B 螺纹基本中径3A 外螺纹2A 1A 1、1A和1B级，非常松的公差等级，其适用于外螺纹的允差配合。 2、2A和2B级，是英制系列机械紧固件规定最通用的螺纹公差等级。 3、3A和3B级，旋合形成最紧的配合，适用于公差紧的紧固件，用于安全性的关键设计。 4、对外螺纹来说，1A和2A级有一个配合公差，3A级没有。1A级公差比2A级公差大50，比3A级大75，对螺纹来说，2B级公差比2A公差大30。1B级比2B级大50，比3B级大75。 （二）公制螺纹，外螺纹有三种螺纹等级：4h、6h和6g，螺纹有三种螺纹等级：5H、6 H、7H。（日标螺纹精度等级分为I、II、III三级，通常状况下为II级）在公制螺纹中，H 和h的基本偏差为零。G的基本偏差为正值，e、f和g的基本偏差为负值。如图所示：公差G H 螺纹偏差基本中径外螺纹f g h e 1、H是螺纹常用的公差带位置，一般不用作表面镀层，或用极薄的磷化层。G位置基本偏差用于特殊场合，如较厚的镀层，一般很少用。 2、g常用来镀6-9um的薄镀层，如产品图纸要6h的螺栓，其镀前螺纹采用6g的公差带。 3、螺纹配合最好组合成H/g、H/h或G/h，对于螺栓、螺母等精制紧固件螺纹，标准推荐采用6H/6g的配合。 （三）螺纹标记M10×1–5g 6g M10×1–6H 顶径公差代号中径和顶径公差代号（相同）中径公差代号。 通止规是两个量具分为通规和止规．举个例子：M6－7h的螺纹通止规一头为通规（T）如果能顺利旋进被测螺纹孔则为合格，反之不合格需返工（也就是孔小了）．然后用止规（Z）如果能顺利旋进被测螺纹孔2.5圈或以上则为不合格反之合格．且此时不合格的螺纹孔应报废，不能进行返工了．其中2.5圈为国家标准，若是出口件最多只能进1.5圈（国际标准）．总之通规过止规不过为合格，通规止规都不过或通规止规都过则为不合格。
英语造句
一般过去式 时间状语：yesterday just now (刚刚) the day before three days ag0 a week ago in 1880 last month last year 1. I was in the classroom yesterday. I was not in the classroom yesterday. Were you in the classroom yesterday. 2. They went to see the film the day before. Did they go to see the film the day before. They did go to see the film the day before. 3. The man beat his wife yesterday. The man didn’t beat his wife yesterday. 4. I was a high student three years ago. 5. She became a teacher in 2009. 6. They began to study english a week ago 7. My mother brought a book from Canada last year. 8.My parents build a house to me four years ago . 9.He was husband ago. She was a cooker last mouth. My father was in the Xinjiang half a year ago. 10.My grandfather was a famer six years ago. 11.He burned in 1991
螺纹通止规要求螺纹通规通
螺纹通止规要求螺纹通规通，止规止。 但是如果螺纹通规止，说明什么？ 螺纹止规通，又说明什么？ 我也来说两句查看全部回复 最新回复 ?wpc (2008-11-07 20:11:20) 在牙型正确的前提下螺纹通止规检测螺纹中径 ?lobont (2008-11-08 11:16:32) 对外螺纹而言，螺纹通规是做到中径上偏差，所以能通过就表示产品合格，通不过就表示螺纹做大了，要再修一刀； 螺纹止规做到中径下偏差，所以只能通过2～3牙，如果也通过，就表示外螺纹做小了，产品成为废品 ?qubin8512 (2008-11-18 15:36:05) 螺纹赛规与螺纹环规主要测量螺纹的中径。 ?datafield (2008-11-29 19:12:51) 检具不是万能的，只是方便而已。具体没什么的我有在哪本书上看过，是一本螺纹手册上的。 ?ZYC007 (2009-2-09 20:31:13) 在牙型正确的前提下螺纹通止规检测螺纹中径。 对外螺纹而言，但是如果螺纹通规止，说明螺纹中径大；螺纹止规通，又说明螺纹中径小。 ?WWCCJJ (2009-3-19 09:27:19) 检测的是螺纹的中径,螺纹检测规在检定时,也是检测其中径. ?tanjiren (2009-3-20 22:23:06) 螺纹通止规只能检测螺纹的作用中径,大径和底径等均无法准确测量出来. ?月夜(2009-4-01 21:47:13) 用来测量中径 ?丽萍(2009-4-02 10:11:41)
只能检测工件螺纹的中径 yg196733456 (2009-4-03 09:15:56)原来是测中径的知道了
NPT螺纹以及检测方法详解
N P T螺纹以及检测方法详 解 Prepared on 22 November 2020
一、目的：规范公司技术员，检验员，操作员对NPT螺纹的了解。 二、适用范围：适用于公司任何NPT螺纹类产品，参考资料为通用管螺 纹和国家标准GB/T12716-2011。 三、目录 1、NPT和NPTF介绍 2、螺纹技术参数参数讲解 3、NPT与NPTF加工工艺 4、NPT和NPTF的检测方法 四、内容： NPT和NPTF螺纹介绍 NPT 是 National (American) Pipe Thread 的缩写，属於美国标准的 60 度锥管 密封螺纹，用於北美地区，美国标准为13)通用管螺纹．国家标准可查阅 GB/T12716-2011。NPTF：美制干密封圆锥管螺。NPTF = National Pipe Thread Fine 称之为一般用途的锥管螺纹，这也是我们以前称之为的布氏锥螺纹。NPTF 螺纹称之为干密封式锥管螺纹，它连接密封的原理是在没有润滑剂或密封填 料情况下完全依靠螺纹自身形成密封，设计意图是使内、外螺纹牙的侧面、 牙顶和牙底同时接触，来达到密封的目的。它们两者的牙型角、斜度等指标 都是相同的，关键是牙顶和牙底的削平高度不一样，所以，量规的设计也是 不一样的。NPTF干密封管螺纹的牙形精度比NPT螺纹高，旋合时不用任何 填料，完全依靠螺纹自身形成密封，螺纹间无任何密封介质。干密封管螺纹 规定有较为严格的公差，属精密型螺纹，仅用在特殊场合。这种螺纹有较高 的强度和良好的密封性，在具有薄截面的脆硬材料上采用此螺纹可以减少断 裂现象。NPTF内、外螺纹牙顶与牙底间没有间隙，是过盈配合，而NPT螺 纹是过渡配合。NPTF螺纹主要用于高温高压对密封要求严格的场所。NPT
学生造句--Unit 1
●I wonder if it’s because I have been at school for so long that I’ve grown so crazy about going home. ●It is because she wasn’t well that she fell far behind her classmates this semester. ●I can well remember that there was a time when I took it for granted that friends should do everything for me. ●In order to make a difference to society, they spent almost all of their spare time in raising money for the charity. ●It’s no pleasure eating at school any longer because the food is not so tasty as that at home. ●He happened to be hit by a new idea when he was walking along the riverbank. ●I wonder if I can cope with stressful situations in life independently. ●It is because I take things for granted that I make so many mistakes. ●The treasure is so rare that a growing number of people are looking for it. ●He picks on the weak mn in order that we may pay attention to him. ●It’s no pleasure being disturbed whena I settle down to my work. ●I can well remember that when I was a child, I always made mistakes on purpose for fun. ●It’s no pleasure accompany her hanging out on the street on such a rainy day. ●I can well remember that there was a time when I threw my whole self into study in order to live up to my parents’ expectation and enter my dream university. ●I can well remember that she stuck with me all the time and helped me regain my confidence during my tough time five years ago. ●It is because he makes it a priority to study that he always gets good grades. ●I wonder if we should abandon this idea because there is no point in doing so. ●I wonder if it was because I ate ice-cream that I had an upset student this morning. ●It is because she refused to die that she became incredibly successful. ●She is so considerate that many of us turn to her for comfort. ●I can well remember that once I underestimated the power of words and hurt my friend. ●He works extremely hard in order to live up to his expectations. ●I happened to see a butterfly settle on the beautiful flower. ●It’s no pleasure making fun of others. ●It was the first time in the new semester that I had burned the midnight oil to study. ●It’s no pleasure taking everything into account when you long to have the relaxing life. ●I wonder if it was because he abandoned himself to despair that he was killed in a car accident when he was driving. ●Jack is always picking on younger children in order to show off his power. ●It is because he always burns the midnight oil that he oversleeps sometimes. ●I happened to find some pictures to do with my grandfather when I was going through the drawer. ●It was because I didn’t dare look at the failure face to face that I failed again. ●I tell my friend that failure is not scary in order that she can rebound from failure. ●I throw my whole self to study in order to pass the final exam. ●It was the first time that I had made a speech in public and enjoyed the thunder of applause. ●Alice happened to be on the street when a UFO landed right in front of her. ●It was the first time that I had kept myself open and talked sincerely with my parents. ●It was a beautiful sunny day. The weather was so comfortable that I settled myself into the
通止规的用法及管理
通止规的用法及管理 1、止规 使用前：应经相关检验计量机构检验计量合格后，方可投入生产现场使用。 使用时：应注意被测螺纹公差等级及偏差代号与环规标识公差等级、偏差代号相同（如M24*1.5-6h与M24*1.5-5g两种环规外形相同，其螺纹公差带不相同，错用后将产生批量不合格品)。 检验测量过程：首先要清理干净被测螺纹油污及杂质，然后在环规与被测螺纹对正后，用大母指与食指转动环规，旋入螺纹长度在2个螺距之内为合格，否则判为不合格品。 2、通规 使用前：应经相关检验计量机构检验计量合格后，方可投入生产现场使用。 使用时：应注意被测螺纹公差等级及偏差代号与环规标识的公差等级、偏差代号相同（如M24*1.5-6h与M24*1.5-5g两种环规外形相同，其螺纹公差带不相同，错用后将产生批量不合格品)。 检验测量过程：首先要清理干净被测螺纹塞规油污及杂质，然后在环规与被测螺纹对正后，用大母指与食指转动环规，使其在自由状态下旋合通过螺纹全部长度判定合格，否则以不通判定。 3、注意事项 在用量具应在每个工作日用校对塞规计量一次。经校对塞规计量超差或者达到计量器具周检期限的环规，由计量管理人员收回、标识隔离并作相应的处理措施。 可调节螺纹环规经调整后，测量部位会产生失圆，此现象由计量修复人员经螺纹磨削加工后再次计量鉴定，各尺寸合格后方可投入使用。 报废环规应标识隔离并及时处理，不得流入生产现场。 4、维护与保养 量具（环规）使用完毕后，应及时清理干净测量部位附着物，存放在规定的量具盒内。生产现场在用量具应摆放在工艺定置位置，轻拿轻放，以防止磕碰而损坏测量表面。 严禁将量具作为切削工具强制旋入螺纹，避免造成早期磨损。可调节螺纹环规严禁非计量工作人员随意调整，确保量具的准确性。环规长时间不用，应交计量管理部门妥善保管。
英语句子结构和造句
高中英语~词性~句子成分~语法构成 第一章节：英语句子中的词性 1.名词：n. 名词是指事物的名称，在句子中主要作主语.宾语.表语.同位语。 2.形容词;adj. 形容词是指对名词进行修饰~限定~描述~的成份，主要作定语.表语.。形容词在汉语中是（的）.其标志是: ous. Al .ful .ive。. 3.动词：vt. 动词是指主语发出的一个动作，一般用来作谓语。 4.副词：adv. 副词是指表示动作发生的地点. 时间. 条件. 方式. 原因. 目的. 结果.伴随让步. 一般用来修饰动词. 形容词。副词在汉语中是（地）.其标志是：ly。 5.代词：pron. 代词是指用来代替名词的词，名词所能担任的作用，代词也同样.代词主要用来作主语. 宾语. 表语. 同位语。 6.介词：prep.介词是指表示动词和名次关系的词，例如：in on at of about with for to。其特征：
介词后的动词要用—ing形式。介词加代词时，代词要用宾格。例如：give up her（him）这种形式是正确的，而give up she（he）这种形式是错误的。 7.冠词：冠词是指修饰名词，表名词泛指或特指。冠词有a an the 。 8.叹词：叹词表示一种语气。例如：OH. Ya 等 9.连词：连词是指连接两个并列的成分，这两个并列的成分可以是两个词也可以是两个句子。例如：and but or so 。 10.数词：数词是指表示数量关系词，一般分为基数词和序数词 第二章节：英语句子成分 主语：动作的发出者，一般放在动词前或句首。由名词. 代词. 数词. 不定时. 动名词. 或从句充当。 谓语：指主语发出来的动作，只能由动词充当，一般紧跟在主语后面。 宾语：指动作的承受着，一般由代词. 名词. 数词. 不定时. 动名词. 或从句充当. 介词后面的成分也叫介词宾语。 定语：只对名词起限定修饰的成分，一般由形容
六级单词解析造句记忆MNO
M A: Has the case been closed yet? B: No, the magistrate still needs to decide the outcome. magistrate n.地方行政官，地方法官，治安官 A: I am unable to read the small print in the book. B: It seems you need to magnify it. magnify vt.１．放大，扩大；２．夸大，夸张 A: That was a terrible storm. B: Indeed, but it is too early to determine the magnitude of the damage. magnitude n.１．重要性，重大；２．巨大，广大 A: A young fair maiden like you shouldn’t be single. B: That is because I am a young fair independent maiden. maiden n.少女，年轻姑娘，未婚女子 a.首次的，初次的 A: You look majestic sitting on that high chair. B: Yes, I am pretending to be the king! majestic a.雄伟的，壮丽的，庄严的，高贵的 A: Please cook me dinner now. B: Yes, your majesty, I’m at your service. majesty n.１．［Ｍ－］陛下（对帝王，王后的尊称）；２．雄伟，壮丽，庄严 A: Doctor, I traveled to Africa and I think I caught malaria. B: Did you take any medicine as a precaution? malaria n.疟疾 A: I hate you! B: Why are you so full of malice? malice n.恶意，怨恨 A: I’m afraid that the test results have come back and your lump is malignant. B: That means it’s serious, doesn’t it, doctor? malignant a.１．恶性的，致命的；２．恶意的，恶毒的 A: I’m going shopping in the mall this afternoon, want to join me? B: No, thanks, I have plans already. mall n.（由许多商店组成的）购物中心 A: That child looks very unhealthy. B: Yes, he does not have enough to eat. He is suffering from malnutrition.
通止规的用法及管理
通止规的用法及管理 令狐采学 1、止规 使用前：应经相关检验计量机构检验计量合格后，方可投入生产现场使用。 使用时：应注意被测螺纹公差等级及偏差代号与环规标识公差等级、偏差代号相同（如M24*1.56h与M24*1.55g两种环规外形相同，其螺纹公差带不相同，错用后将产生批量不合格品)。 检验测量过程：首先要清理干净被测螺纹油污及杂质，然后在环规与被测螺纹对正后，用大母指与食指转动环规，旋入螺纹长度在2个螺距之内为合格，否则判为不合格品。 2、通规 使用前：应经相关检验计量机构检验计量合格后，方可投入生
产现场使用。 使用时：应注意被测螺纹公差等级及偏差代号与环规标识的公差等级、偏差代号相同（如M24*1.56h与M24*1.55g两种环规外形相同，其螺纹公差带不相同，错用后将产生批量不合格品)。 检验测量过程：首先要清理干净被测螺纹塞规油污及杂质，然后在环规与被测螺纹对正后，用大母指与食指转动环规，使其在自由状态下旋合通过螺纹全部长度判定合格，否则以不通判定。 3、注意事项 在用量具应在每个工作日用校对塞规计量一次。经校对塞规计量超差或者达到计量器具周检期限的环规，由计量管理人员收回、标识隔离并作相应的处理措施。 可调节螺纹环规经调整后，测量部位会产生失圆，此现象由计量修复人员经螺纹磨削加工后再次计量鉴定，各尺寸合格后方
可投入使用。 报废环规应标识隔离并及时处理，不得流入生产现场。 4、维护与保养 量具（环规）使用完毕后，应及时清理干净测量部位附着物，存放在规定的量具盒内。生产现场在用量具应摆放在工艺定置位置，轻拿轻放，以防止磕碰而损坏测量表面。 严禁将量具作为切削工具强制旋入螺纹，避免造成早期磨损。可调节螺纹环规严禁非计量工作人员随意调整，确保量具的准确性。环规长时间不用，应交计量管理部门妥善保管。
base on的例句
意见应以事实为根据. 3 来自辞典例句 192. The bombers swooped ( down ) onthe air base. 轰炸机 突袭 空军基地. 来自辞典例句 193. He mounted their engines on a rubber base. 他把他们的发动机装在一个橡胶垫座上. 14 来自辞典例句 194. The column stands on a narrow base. 柱子竖立在狭窄的地基上. 14 来自辞典例句 195. When one stretched it, it looked like grey flakes on the carvas base. 你要是把它摊直, 看上去就象好一些灰色的粉片落在帆布底子上. 18 来自辞典例句 196. Economic growth and human well - being depend on the natural resource base that supports all living systems. 经济增长和人类的福利依赖于支持所有生命系统的自然资源. 12 1 来自辞典例句 197. The base was just a smudge onthe untouched hundred - mile coast of Manila Bay. 那基地只是马尼拉湾一百英里长安然无恙的海岸线上一个硝烟滚滚的污点. 6 来自辞典例句 198. You can't base an operation on the presumption that miracles are going to happen. 你不能把行动计划建筑在可能出现奇迹的假想基础上.
英语造句大全
英语造句大全English sentence 在句子中，更好的记忆单词！ 1、(1)、able adj. 能 句子：We are able to live under the sea in the future. (2)、ability n. 能力 句子：Most school care for children of different abilities. (3)、enable v. 使。。。能句子：This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的句子：We must have the accurate calculation. (2)、accurately adv. 精确地 句子：His calculation is accurately. 3、(1)、act v. 扮演 句子：He act the interesting character. （2）、actor n. 演员 句子：He was a famous actor. (3)、actress n. 女演员 句子：She was a famous actress. (4)、active adj. 积极的 句子：He is an active boy. 4、add v. 加 句子：He adds a little sugar in the milk. 5、advantage n. 优势 句子：His advantage is fight. 6、age 年龄n. 句子：His age is 15. 7、amusing 娱人的adj. 句子：This story is amusing. 8、angry 生气的adj. 句子：He is angry. 9、America 美国n.
(完整版)主谓造句
主语+谓语 1. 理解主谓结构 1) The students arrived. The students arrived at the park. 2) They are listening. They are listening to the music. 3) The disaster happened. 2．体会状语的位置 1) Tom always works hard. 2) Sometimes I go to the park at weekends.. 3) The girl cries very often. 4) We seldom come here. The disaster happened to the poor family. 3. 多个状语的排列次序 1) He works. 2) He works hard. 3) He always works hard. 4) He always works hard in the company. 5) He always works hard in the company recently. 6) He always works hard in the company recently because he wants to get promoted. 4. 写作常用不及物动词 1. ache My head aches. I’m aching all over. 2. agree agree with sb. about sth. agree to do sth. 3. apologize to sb. for sth. 4. appear (at the meeting, on the screen) 5. arrive at / in 6. belong to 7. chat with sb. about sth. 8. come (to …) 9. cry 10. dance 11. depend on /upon 12. die 13. fall 14. go to … 15. graduate from 16. … happen 17. laugh 18. listen to... 19. live 20. rise 21. sit 22. smile 23. swim 24. stay (at home / in a hotel) 25. work 26. wait for 汉译英： 1.昨天我去了电影院。 2.我能用英语跟外国人自由交谈。 3.晚上7点我们到达了机场。 4.暑假就要到了。 5.现在很多老人独自居住。 6.老师同意了。 7.刚才发生了一场车祸。 8.课上我们应该认真听讲。9. 我们的态度很重要。 10. 能否成功取决于你的态度。 11. 能取得多大进步取决于你付出多少努力。 12. 这个木桶能盛多少水取决于最短的一块板子的长度。
通止规的用法及管理修订稿
通止规的用法及管理 WEIHUA system office room 【WEIHUA 16H-WEIHUA WEIHUA8Q8-
通止规的用法及管理 1、止规 使用前：应经相关检验计量机构检验计量合格后，方可投入生产现场使用。 使用时：应注意被测螺纹公差等级及偏差代号与环规标识公差等级、偏差代号相同（如M24*与M24*两种环规外形相同，其螺纹公差带不相同，错用后将产生批量不合格品)。 检验测量过程：首先要清理干净被测螺纹油污及杂质，然后在环规与被测螺纹对正后，用大母指与食指转动环规，旋入螺纹长度在2个螺距之内为合格，否则判为不合格品。 2、通规 使用前：应经相关检验计量机构检验计量合格后，方可投入生产现场使用。 使用时：应注意被测螺纹公差等级及偏差代号与环规标识的公差等级、偏差代号相同（如M24*与M24*两种环规外形相同，其螺纹公差带不相同，错用后将产生批量不合格品)。 检验测量过程：首先要清理干净被测螺纹塞规油污及杂质，然后在环规与被测螺纹对正后，用大母指与食指转动环规，使其在自由状态下旋合通过螺纹全部长度判定合格，否则以不通判定。 3、注意事项
在用量具应在每个工作日用校对塞规计量一次。经校对塞规计量超差或者达到计量器具周检期限的环规，由计量管理人员收回、标识隔离并作相应的处理措施。 可调节螺纹环规经调整后，测量部位会产生失圆，此现象由计量修复人员经螺纹磨削加工后再次计量鉴定，各尺寸合格后方可投入使用。 报废环规应标识隔离并及时处理，不得流入生产现场。 4、维护与保养 量具（环规）使用完毕后，应及时清理干净测量部位附着物，存放在规定的量具盒内。生产现场在用量具应摆放在工艺定置位置，轻拿轻放，以防止磕碰而损坏测量表面。 严禁将量具作为切削工具强制旋入螺纹，避免造成早期磨损。可调节螺纹环规严禁非计量工作人员随意调整，确保量具的准确性。环规长时间不用，应交计量管理部门妥善保管。
初中英语造句
【it's time to和it's time for】 ——————这其实是一个句型,只不过后面要跟不同的东西. ——————It's time to跟的是不定式（to do）.也就是说,要跟一个动词,意思是“到做某事的时候了”.如： It's time to go home. It's time to tell him the truth. ——————It's time for 跟的是名词.也就是说,不能跟动词.如： It's time for lunch.(没必要说It's time to have lunch) It's time for class.(没必要说It's time to begin the class.) They can't wait to see you Please ask liming to study tonight. Please ask liming not to play computer games tonight. Don’t make/let me to smoke I can hear/see you dance at the stage You had better go to bed early. You had better not watch tv It’s better to go to bed early It’s best to run in the morning I am enjoy running with music. With 表伴随听音乐 I already finish studying You should keep working. You should keep on studying English Keep calm and carry on 保持冷静继续前行二战开始前英国皇家政府制造的海报名字 I have to go on studying I feel like I am flying I have to stop playing computer games and stop to go home now I forget/remember to finish my homework. I forget/remember cleaning the classroom We keep/percent/stop him from eating more chips I prefer orange to apple I prefer to walk rather than run I used to sing when I was young What’s wrong with you There have nothing to do with you I am so busy studying You are too young to na?ve I am so tired that I have to go to bed early
螺纹规使用方法
螺纹规使用方法 一、目的 规范塞规、环规使用的操作方法，保证测量结果的准确性。螺纹塞规使用者应根据操作规范要求，确保操作过程正确，并负责仪器的维护和保养。 二、说明 螺纹规又称螺纹通止规、螺纹量规，通常用来检验判定螺纹的尺寸是否合格。 螺纹规根据所检验内外螺纹分为螺纹塞规和螺纹环规，目前我们所使用的只有螺纹塞规。 图1 三、使用方法 1、选择螺纹规时，应选择与被测螺纹相匹配的规格。 2、使用前，先清理干净螺纹规和被测螺纹表面的油污、杂质等。 3、使用时，使螺纹规的通端（止端）与被测螺纹对正后，用大拇指与食指转动螺纹规或被 测零件，使其在自由状态下旋转。通常情况下（无被测零件的螺纹的图示说明时），螺纹 规（通端）的通规可以在被测螺纹的任意位置转动,通过全部螺纹长度则判定为合格，否 则为不合格品;在螺纹规（止端）的止规与被测螺纹对正后，旋入螺纹长度在2个螺距之 内止住为合格，不可强行用力通过，否则判为不合格品。（有被测零件的图示说明时，应 按照图示说明做判定。） 图2 图3 图中英文字母“GO”或“T”:表 示螺纹塞规的通端。 图中“G 3/8-19”或“M3 6H” 表示该螺纹规规格. 图中英文字母“NO GO”或“Z”: 表示螺纹塞规的止端。 螺纹塞规
4、检验工件时旋转螺纹规不能用力拧，用三只手指自然顺畅地旋转，止住即可，螺纹规退 出工件最后一圈时也要自然退出，不能用力拔出螺纹规,否则会影响产品检验结果的误差,螺纹规的损坏。 图4 图5 如上图4操作方法是正确的，图5是错误的，无需手握。 5、使用完毕后，及时清理干净螺纹规的通端（止端）的表面附着物，并存放在工具柜的量 具盒内。 四、注意事项 1、被测件螺纹公差等级及偏差代号必须与塞规标识公差等级、偏差代号相同，才可使用。 2、只有当通规和止规联合使用，并分别检验合格，才表示被测螺纹合格。 3、应避免与坚硬物品相互碰撞，轻拿轻放，以防止磕碰而损坏测量表面。 4、严禁将螺纹规作为切削工具强制旋入螺纹，避免造成早期磨损。 5、螺纹规使用完毕后，应及时清理干净测量部位附着物，存放在规定的量具盒内。 五、维护和保养 1、每月定期涂抹防锈油，以保证表面无锈蚀、无杂质（我们的螺纹规使用频繁且所 处环境干净无需上油保护）。 2、所有的螺纹规必须经计量校验机构校验合格后并在校验有效期内，方可使用。 3、损坏或报废的螺纹规应及时反馈处理，不得继续使用。 4、经校对的螺纹规计量超差或者达到计量器具周检期的螺纹规，由计量管理人员收回 并做相应的处理。
The Kite Runner-美句摘抄及造句
《The Kite Runner》追风筝的人--------------------------------美句摘抄 1.I can still see Hassan up on that tree, sunlight flickering through the leaves on his almost perfectly round face, a face like a Chinese doll chiseled from hardwood: his flat, broad nose and slanting, narrow eyes like bamboo leaves, eyes that looked, depending on the light, gold, green even sapphire 翻译：我依然能记得哈桑坐在树上的样子，阳光穿过叶子，照着他那浑圆的脸庞。他的脸很像木头刻成的中国娃娃，鼻子大而扁平，双眼眯斜如同竹叶，在不同光线下会显现出金色、绿色，甚至是宝石蓝。 E.g.: A shadow of disquiet flickering over his face. 2.Never told that the mirror, like shooting walnuts at the neighbor's dog, was always my idea. 翻译：从来不提镜子、用胡桃射狗其实都是我的鬼主意。E.g.:His secret died with him, for he never told anyone. 3.We would sit across from each other on a pair of high