12%Cr铁素体不锈钢的焊接热影响区组织特征
离散数学-第2章 习题课
谓词的概念与表示
解：a) a:小张 W(x): x是工人。 W(a)
b)S(x):x是田径运动员, B(x):x是球类运动员, h:他 S(h)B(h) c) C(x):x是聪明的，B(x):x是美丽的，a:小莉 C(a) B(a) d) O(x):x是奇数。 O(m) O(2m)
28
变元的约束
例15 如果论域是集合{a,b,c}，试消去下面公式 中的量词。 a) (x) P( x) P(a) P(b) P(c) b) (x) R( x) (x) S ( x)
R(a) R(b) R(c)S (a)S (b)S (c)
c) (x)( P( x) Q( x))
(x)( I ( x) ( R( x) N ( x)))
13
命题函数与量词
例5 令P(x)，L(x)，R(x,y,z)和E(x,y)分别表示 “x是一个点”，“x是一条直线”，“z通过x和 ”和“x=y”。符号化下面得句子。 对每两个点有且仅有一条直线通过该两点。 解：
(x)(y)(( P( x) P( y ) E ( x, y)) (! z )( L( z ) R( x, y, z )))
9
命题函数与量词
e) J(x): x是教练员, L(x): x是运动员。
(x)(L(x) J(x)) f) L(x): x是运动员, S(x): x是大学生,C(x):x是国家 选手。 (x)(S(x)L(x)C(x)) g) C(x):x是国家选手,V(x)：x是健壮的。 ( x)(C(x) V(x)) h) (x)(O(x) C(x) L(x))
14
谓词公式与翻译
例6 利用谓词公式翻译下列命题 a)如果有限个数的乘积等于零，那么至少有一个因 子等于零。 b)对于每一个实数x,存在一个更大的实数y。 c)存在实数x,y和z,使得x与y之和大于x与z之积。
a b c d e f g h i j k l m n o p q r s t u v w x y z
a b c d e f g h i j k l m n o p q r s t u v w x y z注：(1)r、v两个字母用来拼写普通话和外来语，拼写广州话时不用。
(2)广州话拼音字母有三个附加符号：ê、é、ü，其中é是和汉语拼音字母不同的。
这几个字母是e、u字母的变体，叫不列入表内。
二、声母表b波p婆m摸f科d多t拖n挪l罗g哥k卡ng我h何gu姑ku箍z左c初s梳j知q雌x思y也w华注：(1)z、c、s和j、q、x两组声母，广州话的读音没有区别，只是在拼写韵母时有不同，z、c、s拼写a、o、é及a、o、e、é、ê、u等字母开头的韵母，例如：za渣，ca茶，xa沙。
j、q、x拼写i、ü及i、ü字母开头的韵母，例如：ji知，qi次，xi思。
(2)gu姑、ku箍是圆唇的舌跟音，作为声母使用，不能单独注音，单独注音时是音节，不是声母。
(3)y也，w华拼音时作为声母使用，拼写出来的音节相当于汉语拼音方案的复韵母，但由于广州话当中这些韵母前面不再拼声母，因此只作为音节使用三、韵母表a呀o柯u乌i衣ū于ê(靴) é诶m唔n五ai挨 ei矮 oi哀 ui会éi(非)ao拗 eo欧 ou奥iu妖êu(去)am(监) em庵im淹an晏 en(恩) on安 un碗in烟ūn冤 ên(春)ang(横) eng莺 ong(康) ung瓮ing英êng(香) éng(镜)ab鸭 eb(急) ib叶ad押 ed(不) od(渴) ud活 id热ūd月 êd(律)ag(客) eg(德) og恶 ug屋 ig益êg(约) ég(尺)注：(1)例字外加( )号的，只取其韵母。
(2)i行的韵母，前面没有声母的时候，写成yi衣，yiu妖，yim淹，yin烟，ying 英，yib叶，yid热，yig益。
一年级带拼音阅读(全)
一年级阅读题1.大自然的邮票chūntiāndàzìrándeyóupiàoyīniánjíyuèdútí春天的树上，长出嫩嫩的芽瓣。
tiāndeshùshànɡɡuàmǎnféideyèpiàndeshùshànɡzhǎnɡchūnèndeyábàn夏天的树上，挂满肥肥的叶片。
秋天的树上，树叶xx鲜红和金huánɡqiūtiāndeshùshànɡshùyètúmǎnxiānhónɡhéjīnxià黄。
冬天的树下，树叶落地化成rǎnɡluòyèshìdàzìrándeyóupiàobǎyìdōnɡtiāndeshùxiàshùyèluòdìhuàchénɡ土壤。
落叶是大自然的邮票，把一niántú年四季寄给你，寄给我，寄给大jiāsìjìɡěinǐjìɡěiwǒjìɡěidà家。
（1）这一段话共有（）句；（2）填空:a、一年有( )、( )、( )、( )四个季节。
b、春天的树上，芽瓣是( )；chūntiāndeshùshànɡyábànshìsìɡèjìjiéyìniányǒutiánkònɡzhèyíduànhuàɡònɡyǒujù夏天的树上，叶片是( )；秋天的树叶颜色有( )和( )；冬天的树下，满地是( )。
离散数学期末试卷及部分答案 (2)
离散数学试题(A 卷及答案）一、证明题（10分）1)(⌝P ∧(⌝Q ∧R))∨(Q ∧R)∨(P ∧R)⇔R证明: 左端⇔(⌝P ∧⌝Q ∧R)∨((Q ∨P)∧R)⇔((⌝P ∧⌝Q)∧R))∨((Q ∨P)∧R)⇔(⌝(P ∨Q)∧R)∨((Q ∨P)∧R)⇔(⌝(P ∨Q)∨(Q ∨P))∧R ⇔(⌝(P ∨Q)∨(P ∨Q))∧R ⇔T ∧R(置换)⇔R2)∃x(A(x)→B(x))⇔ ∀xA(x)→∃xB(x)证明 ：∃x(A(x)→B(x))⇔∃x(⌝A(x)∨B(x))⇔∃x ⌝A(x)∨∃xB(x)⇔⌝∀xA(x)∨∃xB(x)⇔∀xA(x)→∃xB(x) 二、求命题公式(P ∨(Q ∧R))→(P ∧Q ∧R)的主析取范式和主合取范式（10分）证明：(P ∨(Q ∧R))→(P ∧Q ∧R)⇔⌝(P ∨(Q ∧R))∨(P ∧Q ∧R))⇔（⌝P ∧(⌝Q ∨⌝R)）∨(P ∧Q ∧R) ⇔(⌝P ∧⌝Q)∨(⌝P ∧⌝R))∨(P ∧Q ∧R)⇔(⌝P ∧⌝Q ∧R)∨(⌝P ∧⌝Q ∧⌝R)∨(⌝P ∧Q ∧⌝R))∨(⌝P ∧⌝Q ∧⌝R))∨(P ∧Q ∧R) ⇔m0∨m1∨m2∨m7 ⇔M3∨M4∨M5∨M6三、推理证明题（10分）1） C ∨D, (C ∨D)→ ⌝E, ⌝E →(A ∧⌝B), (A ∧⌝B)→(R ∨S)⇒R ∨S证明：(1) (C ∨D)→⌝E(2) ⌝E →(A ∧⌝B)(3) (C ∨D)→(A ∧⌝B) (4) (A ∧⌝B)→(R ∨S) (5) (C ∨D)→(R ∨S)(6) C ∨D(7) R ∨S2) ∀x(P(x)→Q(y)∧R(x))，∃xP(x)⇒Q(y)∧∃x(P(x)∧R(x))证明（1）∃xP(x) (2)P(a)(3)∀x(P(x)→Q(y)∧R(x)) (4)P(a)→Q(y)∧R(a) (5)Q(y)∧R(a) (6)Q(y) (7)R(a) (8)P(a) (9)P(a)∧R(a) (10)∃x(P(x)∧R(x)) (11)Q(y)∧∃x(P(x)∧R(x))四、设m 是一个取定的正整数，证明：在任取m ＋1个整数中，至少有两个整数，它们的差是m 的整数倍证明 设1a ，2a ，…，1+m a 为任取的m ＋1个整数，用m 去除它们所得余数只能是0，1，…，m －1，由抽屉原理可知，1a ，2a ，…，1+m a 这m ＋1个整数中至少存在两个数s a 和t a ，它们被m 除所得余数相同，因此s a 和t a 的差是m 的整数倍。
如果26个英文字母 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 分别等于
如果26个英文字母 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 分别等于
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 那么:
Knowledge（知识）K+N+O+W+L+E+D+G+E＝11+14+15+23+12+5+4+7+5=96%
Workhard （努力工作）W+O+R+K+H+A+R+D ＝23+15+18+11+8+1+18+4 =98%
也就是说知识和努力工作对我们人生的影响可以达到96％和98％Luck（好运）L+U+C+K＝12+21+3+11=47%
Love（爱情）L+O+V+E＝12+15+22+5=54%
看来，这些我们通常认为重要的东西却并没起到最重要的作用。
那么，什么可以决定我们100％的人生呢？
是Money（金钱）吗? M+O+N+E+Y=13+15+14+5+25=72%
看来也不是
是Leadership（领导能力）吗? L+E+A+D+E+R+S+H+I+P=12+5+1+4+5+18+19+9+16 =89%
还不是
金钱，权力也不能完全决定我们的生活。
那是什么呢？
其实，真正能使我们生活圆满的东西就在我们自己身上！ATTITUDE（心态）A+T+T+I+T+U+D+E＝1+20+20+9+20+21+4+5=100%
我们对待人生的态度才能够100％的影响我们的生活，或者说能够使我们的生活达到100%的圆满！用什么样的态度去看待人生，就会得到什么样的人生！。
法语综合教程1第12课后习题答案
欢迎阅读Le?on 12Les occupations du matinDialogueC ompréhension du texteI. Vrai ou faux（对或错）?1. Faux2. Faux3. Faux4. VraiRelisez le dialogue et répondez（读课文回答问题）?:?a dépend.S’il a cours,il se lève à six heures et demie. S’il n’a pas cou rs, il ne se lève pas avant sept heures.Il va dans la salle de bains. Il se brosse les dents, il se lave le visage et les mains en vitesse. Et il se regarde dans la glace pour se peigner. Et puis, il s’habille.Il met son stylo, ses livres et ses cahiers.Non.Il va à la cantine pour prendre le petit déjeuner.TexteC ompréhension du texte zI. Relisez le texte et répondez（读课文回答问题）?:1.Oui, il dort bien.2.Il se réveille de bon matin.3.Il se regarde pour se peigner.4.Il s’habille.5.Ses chaussettes sont grises.II．Choisissez（选择正确答案）:1. dort2. se lève3. s’essuie4. se regarde5. metE xercices de grammaireII. Mettez les phrases suivantes à la forme négative?（将下列句子改为否定形式）:1. Marc ne se réveille pas t?t.2. Philippe ne se lève pas avant sept heures.3. Je ne me brosse pas les dents en vitesse.4. Nous ne nous habillons pas en deux minutes.5. Tu ne te laves pas vite.6. Quand vous vous réveillez, vous ne vous levez pas aussit?t.7. Elle ne se regarde pas dans la glace pour se peigner.8. Elles ne se lavent pas avec de l’eau chaude.9. Nathalie ne se promène pas après le d?ner.10. Les enfants ne se lavent pas les mains.III. Transformez les phrases selon le modèle （根据范例改写下列句子）?:1.Réveille-toi.2.Couchez-vous à onze heures.3.Dépêchons-nous.4.Habille-toi vite.5.Brosse-toi les dents en cinq minutes.vez-vous seulement avec de l’eau froide.7.Téléphonons-nous tous les soirs.ve-toi les mains.9.Promenez-vous jusqu’à 6 heures.10.Essuie-toi avec la serviette blanche.?:1.Oui, ils y pensent./ Non, ils n’y pensent pas.2.Oui, il m’en parle./ Non, il ne m’en parle pas.3.Oui, je peux y garer ma bicyclette./ Non, je ne peux pas y garer ma bicyclette.4.Oui, j’en ai./ Non, je n’en ai pas.5.Oui, il en vient./ Non, il n’en vient pas.6.Oui, j’y cherche mon ami./ Non, je n’y cherche pas mon ami.7.Oui, nous y allons souvent./ Non, nous n’y allons pas souvent.8.Oui, ils y sont à vingt-deux heures./ Non, ils n’y sont pas à vingt-deux heures.9.Oui, nous y rentrons tous le week-end./ Non, nous n’y rentrons pas tous le week-end.10.Oui, ils m’y attendent./ Non, ils ne m’y attendent pas.III. Transformez selon le modèle les phrases suivantes à la forme impérative?（根据范例将下列句子改为命令式）:a)Penses-y encore.b)Allons-y.c)Restez-y.d)Réponds-y.e)Vas-y.f)Arrives-y t?t.g)Entrez-y à minuit.h)Répondons-y tout de suite.i)Manges-y.?:1. D’, de2. au3. dans, pour4. avec5. dans, pour6. Après7. à, pour8. Après, enV. Dites les chiffres en fran?ais（用法语说出下列数字）?:101 cent un 116 cent seize 119 cent dix-neuf 200 deux cents201 deux cent un 300 trois cents 450 quatre cent cinquante586 cinq cent quatre-vingt-six 900 neuf cents999 neuf cent quatre-vingt-dix-neufE xercices de structureI. Posez des questions?selon la partie soulignée （对划线部分提问）:1. A quelle heure vous réveillez-vous??2. Comment se montre le soleil?3. Avec quoi vous lavez-vous?4. En combien de temps vous brossez-vous les dents?5. Comment vous habillez-vous?6. Pourquoi vous regardez-vous dans la glace?II. Mettez les phrases suivantes aux formes affirmative et négative de l’impératif（将下列句子改为肯定和否定的命令式）?:1. Levez-vous.2. Lè3.4.5.6.7.8.A.5. Je déjeune à midi.6. Les cours finissent à quatre heures de l’après-midi.7. Je fais mes devoirs à sept heures du soir.8. Je vais au lit à onze heures.B.1. Nous nous regardons dans la glace pour nous peigner.2. J’ouvre l e robinet pour me laver les mains.3. Tu remontes ton réveil pour te réveiller à l’heure.IV. Remettez les phrases suivantes dans un ordre logique?（按照逻辑顺序排列句子）:(1) ........c............. (2)..........f............. (3)..........d.............(4)...........a............(5).........b..............(6)..........g.............(7)..........e............. (8)..........h..............E xercices audio-orauxI. écoutez et remplissez les blancs（听录音并填空）?: me lève, t?t, du matin,petit déjeuner, ma voiture,cette heure-là, présente, libre, repas,jusqu’, au bureau, vers, fais, d’enfants,rentre, ma femme, de la gymnastiqueII. Choisissez la bonne réponse （选择正确的答案）: 1. a 2. c 3. a 4. a 5. c 6. b 7. b 8. b 9. bE xercices de traduction qI. Traduisez les mots et locutions? （翻译词组）:通常d’habitude有课avoir cours 然后puis?/ ensuite迅速地 en vitesse 照镜子se regarder dans la glace一清早 de bon matin?/de bonne heure 打开水龙头ouvrir le robinet穿上一件男式衬衫mettre une chemise 即刻tout de suite 擦干s’essuyerII. Rendez les phrases en fran?ais（翻译句子）?:1．- 你睡眠好吗？- 很好。
四年级上册英语lesson12 Let's talk
Q:What’s that in English? E:It’s a horse. Q:Who’s on the horse? E:My uncle. Q:Is he a worker or a farmer? E:He’s a farmer. Q:Can you see any sheep? Q:Sheep?Where are they? E:They’re near the house Q:Oh,yes. E:How many sheep can you see? Q:I can see fifteen. E:What’s the time,please? Q:It’s twelve o’clock. E:I have to go now.Goodbye. Q:Bye-bye.
Let’s act
Homework
课文一英一汉
你能看到多少只羊？ 2. Who’s on the horse? 谁在马上 3.现在几点了？ E:What’s the time,please? 4.他们在房子附近 E:They’re near the house 5.他是工人还是农民？ Is he a worker or a farmer?
1.What’s that in English? 2.Who’s on the horse? 3.Is he a worker or a farmer?
Lesson 12 Let’s talk
Q:What’s that in English? E:It’s a horse. Q:Who’s on the horse? E:My uncle. Q:Is he a worker or a farmer? E:He’s a farmer. Q:Can you see any sheep? Q:Sheep?Where are they? E:They’re near the house.
给水管网平差结果
给水管网平差一、平差基本数据1、平差类型：反算水源压力。
2、计算公式：柯尔－勃洛克公式I=λ*V^2/(2.0*g*D)1.0/λ^0.5=-2.0*lg[k/(3.7*D)+2.5/(Re*λ^0.5)]Re=V*D/ν计算温度：10 ，ν=0.0000013、局部损失系数：1.204、水源点水泵参数：水源点水泵杨程单位(m)，水源点水泵流量单位:(立方米/小时)水源节点编号流量1 扬程1 流量2 扬程2 流量3 扬程3二、节点参数节点编号流量(L/s) 地面标高(m) 节点水压(m) 自由水头(m)1 0.521 140.000 170.322 30.3222 -115.740 140.000 171.497 31.4973 6.544 140.000 170.342 30.3424 5.746 140.000 171.120 31.1205 1.389 140.000 169.777 29.7776 10.743 140.000 170.067 30.0677 11.814 140.000 169.717 29.7178 1.505 140.000 169.160 29.1609 6.544 140.000 169.522 29.52210 1.853 140.000 169.072 29.07211 8.165 140.000 169.243 29.24312 10.192 140.000 169.242 29.24213 2.345 140.000 168.000 28.00014 0.579 136.000 168.985 32.98515 8.893 136.000 169.011 33.01116 6.023 136.000 169.013 33.01317 11.962 136.000 168.897 32.89718 1.476 136.000 168.554 32.55419 12.498 136.000 168.893 32.89320 1.389 136.000 168.602 32.60221 2.316 136.000 167.692 31.69222 3.243 136.000 165.822 29.822三、管道参数管道编号管径(mm) 管长(m) 流量(L/s) 流速(m/s) 千米损失(m) 管道损失(m)1-3 100 90.0 0.521 0.092 0.218 0.0202-4 315 46.1 115.740 1.637 8.172 0.3773-7 315 540.0 40.102 0.567 1.157 0.625 3-4 315 500.0 47.167 0.667 1.556 0.778 4-6 315 400.0 62.827 0.889 2.633 1.053 5-6 100 240.0 1.389 0.245 1.209 0.290 6-7 225 725.0 11.452 0.288 0.482 0.350 6-9 315 490.0 39.242 0.555 1.112 0.545 7-12 315 455.0 37.888 0.536 1.043 0.475 8-9 100 260.0 1.505 0.265 1.394 0.362 9-11 315 380.0 31.193 0.441 0.733 0.278 10-7 100 320.0 1.853 0.327 2.016 0.645 11-12 225 460.0 0.492 0.012 0.002 0.001 11-15 315 570.0 22.536 0.319 0.407 0.232 12-13 100 405.0 2.345 0.413 3.068 1.242 12-16 315 440.0 25.843 0.366 0.521 0.229 14-15 100 100.0 0.579 0.102 0.262 0.026 15-16 225 200.0 1.174 0.030 0.009 0.002 15-19 315 665.0 14.237 0.201 0.179 0.119 16-17 315 400.0 18.647 0.264 0.290 0.116 17-22 100 560.0 3.243 0.572 5.491 3.075 18-17 100 255.0 1.476 0.260 1.346 0.343 19-21 100 400.0 2.316 0.408 3.000 1.200 19-17 315 850.0 1.966 0.028 0.006 0.005 20-19 100 240.0 1.389 0.245 1.209 0.290 四、管网平差结果特征参数水源点2: 节点流量(L/s):-115.740 节点压力(m):171.50最大管径(mm):315.00 最小管径(mm):100.00最大流速(m/s):1.637 最小流速(m/s):0.012水压最低点22, 压力(m):165.82 自由水头最低13, 自由水头(m):28.00第六章给水管网设计（一）教学要求1、了解相关的基本概念；2、熟练掌握给水管网的设计计算方法和步骤；（二）教学内容1、沿线流量和节点流量计算2、管段流量分配3、初拟管径4、平差计算5、泵站扬程与水塔高度设计；6、管网校核；（三）重点：沿线流量和节点流量计算，环状管网设计计算的理论、步骤及平差方法和管网校核。
补充：应力函数求解
Axy Bx y
3
xy -q A
4
q
10
在y 0 边界上
b/2
-b/2 b/2
y dx 0
满足; y xdx 0满足
sin 2Cx 6 Dx tan cos 2Cx tan 0 sin 2Cy cosgy 0
2C g cot 2 6 D g cot
sin 2C 6 D tan cos 2C tan 0 sin 2C cosg 0
3
h 2 h 2
x
x
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汉语拼音知识点整理[1]
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汉语拼音知识点整理一、音节1.汉语的一个汉字的读音就是一个音节。
例题：“我爱爸爸妈妈。
”这句话有几个音节？答：“wǒài bàba māma”六个音节。
2. 音节由声母、韵母和声调组成。
3. 有些音节开头没有声母，如en、ou、er，这些音节的声母是零，因此就叫做“零声母”。
二、声母1. 23个声母：b p m f d t n l ɡk h j q x zc s zh ch sh r y w由于i、u、ü等韵母可以自成音节，如chuānyī（穿衣）、tānwán（贪玩），如果不用y、w隔开，就成了分不清的chuāiī、tānu án，所以起隔音作用的y、w在小学语文课本中也被当作声母来学。
2. 声母儿歌：右下半圆b b b，右上半圆ppp。
两个门洞mmm，一根拐杖f f f。
左下半圆d d d，伞把朝下t t t。
一个门洞n n n，小小木棍l l l。
9字加弯ɡɡɡ，小鸟展翅k k k。
一把椅子h h h，一只小鸡j j j。
左上半圆q q q，一个大叉xxx。
像个2字z z z，半个圆圈c c c。
半个8字s s s，小芽出土r r r。
一个树杈y y y，小屋倒影www。
3. 书写规范：四线三格要分清，声母兄弟住其中。
胳膊要在上格住，尾巴就往下格请。
书写规范不能忘，我写的拼音最漂亮。
例题1：默写声母表注意点：不要把y、w给漏了4. 平翘舌音记忆法①声韵配合规律记忆法ua，uai，uang可与zh，ch，sh相拼，不与z，c，s相拼。
ong可与平舌音s相拼，不与sh相拼。
②典型字或偏旁类推法汉字百分之八十以上是形声字，就有规律可循：如“召（zhāo）”，“召”旁的字都是翘舌音，例：招、昭、超、照；如“主（zhù）”，例：住，驻，柱，注；如“占（zhàn）”，例：沾，战，站，粘，毡；如“子（zǐ）”，例：字，仔，籽；如“澡（zǎo）”，例：燥，躁，操，噪。
离散数学复习资料
1.证明永真公式Q14,Q15,Q16,Q17和Q18。
2.证明P(x)∧任意xQ(x)==>存在x(P(x)∧Q(x))3.设论述域是{a1,a2,a3,…an},试证明下列关系式。
(a) 任意xA(x)∧P<==>任意x(A(x)∧P)(b) 任意x(A(x)∧B(x))<==>任意xA(x)∧任意xB(x)(c) 存在x(A(x)∧B(x))<==>存在xA(x)∧存在xB(x)4.证明下列关系式(a) 任意x任意y(P(x)∨P(y))<==>任意xP(x)∨任意yP(y)(b) 存在x存在y(P(x)∧Q(y))==>存在xP(x)(c) 任意x任意y(P(x)∧Q(y))<==>任意xP(x)∧任意yQ(y)(d) 存在x存在y(P(x)－＞P(y)) <==>任意xP(x)－＞存在yP(y)(e) 任意x任意y(P(x) －＞Q(y)) <==>(存在xP(x)－＞任意yQ(y))5.写出limf(x)=k的定义的符号形式，并用形成定理两边的否定的方法，找出limf(x)不等x->c x->c于k的条件。
6.给定自然数集合N的下列子集：A={1,2,7,8}B={i|i平方<50}C={i|i可被30整除}D={i|i=2的k次方∧k∈I∧0≤k≤6}求下列集合(a)A∪(B∪(C∪D))(b)A∩(B∩(C∩D))(c)B-(A∪C)(d)(非A∩B) ∪D7.假定A≠空集和A∪B=A∪C，证明这不能得出B=C，假设中增加A∩B=A∩C，你能得出B=C吗？8．(a)证明“相对补”不是一个可交换运算，即证明存在一个论述域包含集合A和B，使A-B≠B-A。
(b)A-B=B-A可能吗？刻划上式出现的全部条件。
(c)“相对补”是一个可结合的运算马？证明你的断言。
9.证明下列恒等式(a)A∪(A∩B)=A(b)A∩(A∪B)=A(c)A-B=A∩非B(d)A∪(非A∩B)=A∪B(e)A∩(非A∪B)=A∩B10.设Sn={a0,a1,…,an}和Sn+1={a0,a1, …,an,an+1},试用p(Sn)和an+1表达出p(Sn+1)。
英语字母密码记忆法
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基本常用指令
一．RO 航班的读出显示某一航班的具体信息格式：RO/航班号/日期或RO：航班号/日期或RO航班号/日期RO指令是对于指定航班的航班所有现在状态的显示读出。
以下指令：>RO：zh841/23MAY<xmit>显示结果请参考：以下分别介绍：表斗部分ZH9801 12MAR D 1 74E FA/CD/YSHKMTGXQZV CONTROL PEK101 LEG航班控制部门舱位布局航节可利用航班标识●LEG航节部分还可销售数锁订座位数座位布局表号T 航节最大开放数团体限制表号G 限制销售表号L AVS表号V已订妥座数团体座位开放数G 还可销售数状态电报表号M 舱位状态布局数订妥团体座位数 PCF表号PC LEG AV OPN MAX CAP T/B GT GRO GRS BLK LT LSS PT AT CT SMT INDF/ASHA AS 12 18 18 6 0 0 0 0 0 1 0 0 37 RDFPEK CR 5 18 18 13 0 0 0 0 0 1 0 0 37 CRC/DSHA AS 20 35 35 15 0 0 0 0 0 1 0 0 37 RDFPEK AS 12 35 35 23 0 0 0 0 0 1 0 0 37 CRY/SHKMTGXQZVSHA AS 72 243 243 171 0 0 41 0 0 1 0 0 37 RDFPEK AS 27 243 243 216 0 0 85 0 0 1 0 0 37 CRLEG中的IND项说明：R——已拍发完整的旅客名单报（IM：R）D——一次性拍发旅客增减报（IM：AC）F——按特殊表的定义拍发旅客增减报C——使用混合等级（IM：C）X——城市被取消（IM：X）E——航班已从该城市出发N——夜航航班L——紧急锁定（IM：E）A——航班特定修改（AH）●SEGMENT航段部分限制销售组合后，还可销售数已订妥座位数限制销售座位数团体订座数候补座位数限制销售表号航段舱位锁订座位数状态电报地址表号SEG CLS BKD GRS BLK WL LSV LSS LT SMT IND SHAFRA F 0 0 0 0 - - - AK A# 0 0 0 0 2 2 - AK C 3 0 0 0 - - - AK D# 0 0 0 0 2 2 - AK Y 0 0 0 0 - - - AK S 0 0 0 0 - - - AK H 3 0 0 0 50 466 - LAK K 2 0 0 0 70 419 - LAK M 0 0 0 0 180 327 - LAK T 27 0 0 4 180 152 - LAK G# 0 0 0 0 13 18 - LAK X# 0 0 0 0 5 5 - LAKQ 0 0 0 0 5 5 - AKSEGMENT项中的IND项的说明：A——告知航班更改标识（IM：A）K——禁止候补自动证实（IM：W）L——该级别为限制销售组合等级（IM：I）N——NOOP（IM：U）R——释放旅客信息（IM：R）P——永久申请航段（IM：N）M——该航段上有市场航线限制O——存在超订PNRC——等级被取消（IM：D）S——无效航段I——不规则运营航班二．AV/FV/SK 航班查询指令格式：AV:航段/日期/（航空公司）---查询航班座位情况FV:航段/日期---查询有座位最早航班SK:航段/日期/（航空公司）查询航班班期情况AV例子：Av:航段/日期/航空公司：只查询该航空公司该航段的所有的班期的所有舱位的的座位情况av:szxhfe/+/zh 20AUG(TUE) SZXHFE VIA ZH 1- ZH9991 SZXHFE 0850 1035 738 0^ EFL PL AL OL DX<B --> YL BQ MQ HQ KQ LQ JQ QQ ZQ GQ VQ WQ EQ TQ UL SL XL NL 2 ZH9971 SZXHFE 1210 1400 738 0^ EF1 P1 AS OS DX<B -->YA BQ MQ HQ KQ LQ JQ QQ ZQ GQ VQ WQ EQ TQ US SS XS NS 3 ZH9989 SZXHFE 1520 1710 319 0^ EF5 P3 AS O1 DX<B --> Y6 BQ MQ HQ KQ LQ JQ QQ ZQ GQ VQ WQ EQ TQ U6 SS X1 NS 4+ ZH9785 SZXHFE 1905 2050 738 0^ EF6 P1 A2 O2 DX<B --> YA BQ MQ HQ KQ LQ JQ QQ ZQ GQ VQ WQ EQ TQ UA SS X3 NS ** ** **PLEASE CHECK IN 40 MINUTES BEFORE DEPARTURE AT SZX Av:航段/日期：查询该航段上的所有公司的航班班期的座位情况av:szxhfe/+ 20AUG(TUE) SZXHFE 1- ZH9991 SZXHFE 0850 1035 738 0^ EFL PL AL OL DX<B --> YL BQ MQ HQ KQ LQ JQ QQ ZQ GQ VQ WQ EQ TQ UL SL XL NL 2 *CA3513 SZXHFE 0850 1035 738 0^ EFL YL BQ MQ HQ<B --> ZH9991 KQ LQ QQ GQ VQ EQ TQ UL SL 3 HU7745 SZXHFE 1055 1245 738 0^L EF1 ZQ PQ AQ YL BQ HQ KQ LQ MQ QQ XQ UQ EQ TQ VL WQ GQ OQ SQ 4 ZH9971 SZXHFE 1210 1400 738 0^ EF1 P1 AS OS DX<B --> YA BQ MQ HQ KQ LQ JQ QQ ZQ GQ VQ WQ EQ TQ US SS XS NS 5+ *CA3753 SZXHFE 1210 1400 738 0^ EF1 YA BQ MQ HQ<B --> ZH9971 KQ LQ QQ GQ VQ EQ TQ US SS 其中：0^：代表直飞，1^：代表甩飞。
部编版三年级语文上册生字(附音序、部首、组词带拼音)
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煤 M 火 9 煤油灯
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gào sù
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低洼 zēng chǎn
增加
增产
岩土常用土的本构模型
应力状态的描述 弹性模型 塑性模型 算例分析
4.1
应力状态的描述
本书并不试图从原理上介绍本构模型， 而是重点讨论 ABAQUS 如何应用这些模型。 因此， 读者最好掌握一些力学基本知识。为方便起见，这里简要介绍一些涉及到的名词。 4.1.1 应力张量 土体中一点的应力状态可以由应力分量来表示： 11 12 13 x σ σ ij 21 22 23 yx 31 32 33 zx 4.1.2 应力张量的分解 可将应力分量分解为偏应力 s 和平均应力 p ：
注意：由于 ABAQUS 以拉为正，而岩土工程常受到压应力，因此为方便起见 ABAQUS 1 令 p trac(σ) 。 3 4.1.3 应力张量不变量和偏应力不变量 应力张量三个不变量为： I1 x y z 1 2 3
I2
2 x y y z z x xy 2 yz 2 zx
1 在这些不变量中，最常用到的有两个，一个是 I1 ，即前面提到的平均应力 p trac(σ) ； 3 另外一个是 J 2 ，读者可能更熟悉 q 3J 2 的形式，即岩土工程中常说的偏应力，在 ABAQUS
中称为等效 Mises 偏应力（Mises equivalent stress） 。 4.1.4 应力空间 应力空间是一种物理空间，它是以 1 ， 2 ， 3 作为坐标轴而形成的三维空间，空间中的 每一个点表达了一种应力状态， 因而屈服面就可用应力空间中的曲面图形来表达。 通常将三维 空间转到两个特殊平面中进行分析： 1 等斜面：又称 平面，该平面通过原点，其法线的三个方向的余弦都是 ，即与三 3
特殊字符大全
特殊字符大全汉字大全(1 2 3 4) 按部首查询字符大全! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~ •￠￡¤ ￥| § ¨ a - ˉ ° ± 2 3 ′ μ · 1 o à á è é ê ì í D ò ó × ù ú ü Y T à á a è é ê ì í e ò ó ÷ ù ú ü y t ā ā ē ē ě ě ī ī ń ň ō ō ū ū ∥ ǎ ǎ ǐ ǐ ǒ ǒ ǔ ǔ ǖ ǖ ǘ ǘ ǚ ǚ ǜ ǜ ɑ ɡ ˇ ˉ ˊ ˋ ˙ Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω Ё А Б В Г Д Е Ж З И Й К Л М Н О П Р С Т У Ф Х Ц Ч Ш Щ Ъ Ы Ь Э Ю Я а б в г д е ж з и й к л м н о п р с т у ф х ц ч ш щ ъ ы ь э ю я ё‐ –—― ‖‘ ’ “ ” ‥ … ‰ ′ ″ ‵ ※ ￣€ ℃ ℅ ℉ № ℡ Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ Ⅻ ⅰ ⅱ ⅲ ⅳ ⅴ ⅵ ⅶ ⅷ ⅸ ⅹ ← ↑ → ↓ ↖ ↗ ↘ ↙ ∈ ∏ ∑ ∕ ° √ ∝ ∞ ∟ ∠ ∣ ∥ ∧ ∨ ∩ ∪ ∫ ∮ ∴ ∵ ∶ ∷ ～∽ ≈ ≌ ≒ ≠ ≡ ≤ ≥ ≦ ≧ ≮ ≯ ⊕ ⊙ ⊥ ⊿ ⌒ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑴ ⑵ ⑶ ⑷ ⑸ ⑹ ⑺ ⑻ ⑼ ⑽ ⑾ ⑿ ⒀ ⒁ ⒂ ⒃ ⒄ ⒅ ⒆ ⒇ ⒈ ⒉ ⒊ ⒋ ⒌ ⒍ ⒎ ⒏ ⒐ ⒑⒒ ⒓ ⒔ ⒕ ⒖ ⒗ ⒘ ⒙ ⒚ ⒛ ─ ━ │ ┃ ┄ ┅ ┆ ┇ ┈ ┉ ┊ ┋ ┌ ┍ ┎ ┏ ┐ ┑ ┒ ┓ └ ┕ ┖ ┗ ┘ ┙ ┚ ┛ ├ ┝ ┞ ┟ ┠ ┡ ┢ ┣ ┤ ┥ ┦ ┧ ┨ ┩ ┪ ┫ ┬ ┭ ┮ ┯ ┰ ┱ ┲ ┳ ┴ ┵ ┶ ┷ ┸ ┹ ┺ ┻ ┼ ┽ ┾ ┿ ╀ ╁ ╂ ╃ ╄ ╅ ╆ ╇ ╈ ╉ ╊ ╋ ═ ║ ╒ ╓ ╔ ╕ ╖ ╗ ╘ ╙ ╚ ╛ ╜ ╝ ╞ ╟ ╠ ╡ ╢ ╣ ╤ ╥ ╦ ╧ ╨ ╩ ╪ ╫ ╬ ╭ ╮ ╯ ╰ ╱ ╲ ╳ ▁ ▂ ▃ ▄ ▅ ▆▇ █ ▉ ▊ ▋ ▌ ▍ ▎ ▏ ▓ ▔ ▕ ■ □ ▲ △ ▼ ▽ ◆ ◇ ○ ◎ ● ◢ ◣ ◤ ◥ ★ ☆ ☉ ♀♂、。
N=4 Super-Yang-Mills Theory, QCD and Collider Physics
a rXiv:h ep-th/04121v12O ct24SLAC–PUB–10739,IPPP/04/59,DCPT/04/118,UCLA/04/TEP/40Saclay/SPhT–T04/116,hep-th/0410021October,2004N =4Super-Yang-Mills Theory,QCD and Collider Physics Z.Bern a L.J.Dixon b 1 D.A.Kosower c a Department of Physics &Astronomy,UCLA,Los Angeles,CA 90095-1547,USA b SLAC,Stanford University,Stanford,CA 94309,USA,and IPPP,University of Durham,Durham DH13LE,England c Service de Physique Th´e orique,CEA–Saclay,F-91191Gif-sur-Yvette cedex,France1Introduction and Collider Physics MotivationMaximally supersymmetric (N =4)Yang-Mills theory (MSYM)is unique in many ways.Its properties are uniquely specified by the gauge group,say SU(N c ),and the value of the gauge coupling g .It is conformally invariant for any value of g .Although gravity is not present in its usual formulation,MSYMis connected to gravity and string theory through the AdS/CFT correspon-dence[1].Because this correspondence is a weak-strong coupling duality,it is difficult to verify quantitatively for general observables.On the other hand, such checks are possible and have been remarkably successful for quantities protected by supersymmetry such as BPS operators[2],or when an additional expansion parameter is available,such as the number offields in sequences of composite,large R-charge operators[3,4,5,6,7,8].It is interesting to study even more observables in perturbative MSYM,in order to see how the simplicity of the strong coupling limit is reflected in the structure of the weak coupling expansion.The strong coupling limit should be even simpler when the large-N c limit is taken simultaneously,as it corresponds to a weakly-coupled supergravity theory in a background with a large radius of curvature.There are different ways to study perturbative MSYM.One approach is via computation of the anomalous dimensions of composite,gauge invariant operators[1,3,4,5,6,7,8].Another possibility[9],discussed here,is to study the scattering amplitudes for(regulated)plane-wave elementaryfield excitations such as gluons and gluinos.One of the virtues of the latter approach is that perturbative MSYM scat-tering amplitudes share many qualitative properties with QCD amplitudes in the regime probed at high-energy colliders.Yet the results and the computa-tions(when organized in the right way)are typically significantly simpler.In this way,MSYM serves as a testing ground for many aspects of perturbative QCD.MSYM loop amplitudes can be considered as components of QCD loop amplitudes.Depending on one’s point of view,they can be considered either “the simplest pieces”(in terms of the rank of the loop momentum tensors in the numerator of the amplitude)[10,11],or“the most complicated pieces”in terms of the degree of transcendentality(see section6)of the special functions entering thefinal results[12].As discussed in section6,the latter interpreta-tion links recent three-loop anomalous dimension results in QCD[13]to those in the spin-chain approach to MSYM[5].The most direct experimental probes of short-distance physics are collider experiments at the energy frontier.For the next decade,that frontier is at hadron colliders—Run II of the Fermilab Tevatron now,followed by startup of the CERN Large Hadron Collider in2007.New physics at colliders always contends with Standard Model backgrounds.At hadron colliders,all physics processes—signals and backgrounds—are inherently QCD processes.Hence it is important to be able to predict them theoretically as precisely as possi-ble.The cross section for a“hard,”or short-distance-dominated processes,can be factorized[14]into a partonic cross section,which can be computed order by order in perturbative QCD,convoluted with nonperturbative but measur-able parton distribution functions(pdfs).For example,the cross section for producing a pair of jets(plus anything else)in a p¯p collision is given byσp¯p→jjX(s)= a,b1 0dx1dx2f a(x1;µF)¯f b(x2;µF)׈σab→jjX(sx1x2;µF,µR;αs(µR)),(1)where s is the squared center-of-mass energy,x1,2are the longitudinal(light-cone)fractions of the p,¯p momentum carried by partons a,b,which may be quarks,anti-quarks or gluons.The experimental definition of a jet is an in-volved one which need not concern us here.The pdf f a(x,µF)gives the prob-ability forfinding parton a with momentum fraction x inside the proton; similarly¯f b is the probability forfinding parton b in the antiproton.The pdfs depend logarithmically on the factorization scaleµF,or transverse resolution with which the proton is examined.The Mellin moments of f a(x,µF)are for-ward matrix elements of leading-twist operators in the proton,renormalized at the scaleµF.The quark distribution function q(x,µ),for example,obeys 10dx x j q(x,µ)= p|[¯qγ+∂j+q](µ)|p .2Ingredients for a NNLO CalculationMany hadron collider measurements can benefit from predictions that are accurate to next-to-next-to-leading order(NNLO)in QCD.Three separate ingredients enter such an NNLO computation;only the third depends on the process:(1)The experimental value of the QCD couplingαs(µR)must be determinedat one value of the renormalization scaleµR(for example m Z),and its evolution inµR computed using the3-loopβ-function,which has been known since1980[15].(2)The experimental values for the pdfs f a(x,µF)must be determined,ide-ally using predictions at the NNLO level,as are available for deep-inelastic scattering[16]and more recently Drell-Yan production[17].The evolu-tion of pdfs inµF to NNLO accuracy has very recently been completed, after a multi-year effort by Moch,Vermaseren and Vogt[13](previously, approximations to the NNLO kernel were available[18]).(3)The NNLO terms in the expansion of the partonic cross sections must becomputed for the hadronic process in question.For example,the parton cross sections for jet production has the expansion,ˆσab→jjX=α2s(A+αs B+α2s C+...).(2)The quantities A and B have been known for over a decade[19],but C has not yet been computed.Figure 1.LHC Z production [22].•real ×real:וvirtual ×real:וvirtual ×virtual:וdoubly-virtual ×real:×Figure 2.Purely gluonic contributionsto ˆσgg →jjX at NNLO.Indeed,the NNLO terms are unknown for all but a handful of collider puting a wide range of processes at NNLO is the goal of a large amount of recent effort in perturbative QCD [20].As an example of the im-proved precision that could result from this program,consider the production of a virtual photon,W or Z boson via the Drell-Yan process at the Tevatron or LHC.The total cross section for this process was first computed at NNLO in 1991[21].Last year,the rapidity distribution of the vector boson also be-came available at this order [17,22],as shown in fig.1.The rapidity is defined in terms of the energy E and longitudinal momentum p z of the vector boson in the center-of-mass frame,Y ≡1E −p z .It determines where the vector boson decays within the detector,or outside its acceptance.The rapidity is sensitive to the x values of the incoming partons.At leading order in QCD,x 1=e Y m V /√s ,where m V is the vector boson mass.The LHC will produce roughly 100million W s and 10million Z s per year in detectable (leptonic)decay modes.LHC experiments will be able to map out the curve in fig.1with exquisite precision,and use it to constrain the parton distributions —in the same detectors that are being used to search for new physics in other channels,often with similar q ¯q initial states.By taking ratios of the other processes to the “calibration”processes of single W and Z production,many experimental uncertainties,including those associated with the initial state parton distributions,drop out.Thus fig.1plays a role as a “partonic luminosity monitor”[23].To get the full benefit of the remarkable experimental precision,though,the theory uncertainty must approach the 1%level.As seen from the uncertainty bands in the figure,this precision is only achievable at NNLO.The bands are estimated by varying the arbitrary renormalization and factorization scales µR and µF (set to a common value µ)from m V /2to 2m V .A computation to all orders in αs would have no dependence on µ.Hence the µ-dependence of a fixed order computation is related to the size of the missing higher-order terms in the series.Althoughsub-1%uncertainties may be special to W and Z production at the LHC, similar qualitative improvements in precision will be achieved for many other processes,such as di-jet production,as the NNLO terms are completed.Even within the NNLO terms in the partonic cross section,there are several types of ingredients.This feature is illustrated infig.2for the purely gluonic contributions to di-jet production,ˆσgg→jjX.In thefigure,individual Feynman graphs stand for full amplitudes interfered(×)with other amplitudes,in order to produce contributions to a cross section.There may be2,3,or4partons in thefinal state.Just as in QED it is impossible to define an outgoing electron with no accompanying cloud of soft photons,also in QCD sensible observables require sums overfinal states with different numbers of partons.Jets,for example,are defined by a certain amount of energy into a certain conical region.At leading order,that energy typically comes from a single parton, but at NLO there may be two partons,and at NNLO three partons,within the jet cone.Each line infig.2results in a cross-section contribution containing severe infrared divergences,which are traditionally regulated by dimensional regula-tion with D=4−2ǫ.Note that this regulation breaks the classical conformal invariance of QCD,and the classical and quantum conformal invariance of N=4super-Yang-Mills theory.Each contribution contains poles inǫranging from1/ǫ4to1/ǫ.The poles in the real contributions come from regions ofphase-space where the emitted gluons are soft and/or collinear.The poles in the virtual contributions come from similar regions of virtual loop integra-tion.The virtual×real contribution obviously has a mixture of the two.The Kinoshita-Lee-Nauenberg theorem[24]guarantees that the poles all cancel in the sum,for properly-defined,short-distance observables,after renormal-izing the coupling constant and removing initial-state collinear singularities associated with renormalization of the pdfs.A critical ingredient in any NNLO prediction is the set of two-loop ampli-tudes,which enter the doubly-virtual×real interference infig.2.Such ampli-tudes require dimensionally-regulated all-massless two-loop integrals depend-ing on at least one dimensionless ratio,which were only computed beginning in 1999[25,26,27].They also receive contributions from many Feynman diagrams, with lots of gauge-dependent cancellations between them.It is of interest to develop more efficient,manifestly gauge-invariant methods for combining di-agrams,such as the unitarity or cut-based method successfully applied at one loop[10]and in the initial two-loop computations[28].i,ij+ i iFigure3.Illustration of soft-collinear(left)and pure-collinear(right)one-loop di-vergences.3N=4Super-Yang-Mills Theory as a Testing Ground for QCDN=4super-Yang-Mills theory serves an excellent testing ground for pertur-bative QCD methods.For n-gluon scattering at tree level,the two theories in fact give identical predictions.(The extra fermions and scalars of MSYM can only be produced in pairs;hence they only appear in an n-gluon ampli-tude at loop level.)Therefore any consequence of N=4supersymmetry,such as Ward identities among scattering amplitudes[29],automatically applies to tree-level gluonic scattering in QCD[30].Similarly,at tree level Witten’s topological string[31]produces MSYM,but implies twistor-space localization properties for QCD tree amplitudes.(Amplitudes with quarks can be related to supersymmetric amplitudes with gluinos using simple color manipulations.)3.1Pole Structure at One and Two LoopsAt the loop-level,MSYM becomes progressively more removed from QCD. However,it can still illuminate general properties of scattering amplitudes,in a calculationally simpler arena.Consider the infrared singularities of one-loop massless gauge theory amplitudes.In dimensional regularization,the leading singularity is1/ǫ2,arising from virtual gluons which are both soft and collinear with respect to a second gluon or another massless particle.It can be char-acterized by attaching a gluon to any pair of external legs of the tree-level amplitude,as in the left graph infig.3.Up to color factors,this leading diver-gence is the same for MSYM and QCD.There are also purely collinear terms associated with individual external lines,as shown in the right graph infig.3. The pure-collinear terms have a simpler form than the soft terms,because there is less tangling of color indices,but they do differ from theory to theory.The full result for one-loop divergences can be expressed as an operator I(1)(ǫ) which acts on the color indices of the tree amplitude[32].Treating the L-loop amplitude as a vector in color space,|A(L)n ,the one-loop result is|A(1)n =I(1)(ǫ)|A(0)n +|A(1),finn ,(3)where |A (1),fin nis finite as ǫ→0,and I (1)(ǫ)=1Γ(1−ǫ)n i =1n j =i T i ·T j 1T 2i 1−s ij ǫ,(4)where γis Euler’s constant and s ij =(k i +k j )2is a Mandelstam invariant.The color operator T i ·T j =T a i T a j and factor of (µ2R /(−s ij ))ǫarise from softgluons exchanged between legs i and j ,as in the left graph in fig.3.The pure 1/ǫpoles terms proportional to γi have been written in a symmetric fashion,which slightly obscures the fact that the color structure is actually simpler.We can use the equation which represents color conservation in the color-space notation, n j =1T j =0,to simplify the result.At order 1/ǫwe may neglect the (µ2R /(−s ij ))ǫfactor in the γi terms,and we have n j =i T i ·T j γi /T 2i =−γi .So the color structure of the pure 1/ǫterm is actually trivial.For an n -gluon amplitude,the factor γi is set equal to its value for gluons,which turns out to be γg =b 0,the one-loop coefficient in the β-function.Hence the pure-collinear contribution vanishes for MSYM,but not for QCD.The divergences of two-loop amplitudes can be described in the same for-malism [32].The relation to soft-collinear factorization has been made more transparent by Sterman and Tejeda-Yeomans,who also predicted the three-loop behavior [33].Decompose the two-loop amplitude |A (2)n as|A (2)n =I (2)(ǫ)|A (0)n +I (1)(ǫ)|A (1)n +|A (2),fin n,(5)where |A (2),fin n is finite as ǫ→0and I (2)(ǫ)=−1ǫ+e −ǫγΓ(1−2ǫ)ǫ+K I (1)(2ǫ)+e ǫγT 2i µ22C 2A ,(8)where C A =N c is the adjoint Casimir value.The quantity ˆH(2)has non-trivial,but purely subleading-in-N c ,color structure.It is associated with soft,rather than collinear,momenta [37,33],so it is theory-independent,up to color factors.An ansatz for it for general n has been presented recently [38].3.2Recycling Cuts in MSYMAn efficient way to compute loop amplitudes,particularly in theories with a great deal of supersymmetry,is to use unitarity and reconstruct the am-plitude from its cuts [10,38].For the four-gluon amplitude in MSYM,the two-loop structure,and much of the higher-loop structure,follows from a sim-ple property of the one-loop two-particle cut in this theory.For simplicity,we strip the color indices offof the four-point amplitude A (0)4,by decomposing it into color-ordered amplitudes A (0)4,whose coefficients are traces of SU(N c )generator matrices (Chan-Paton factors),A (0)4(k 1,a 1;k 2,a 2;k 3,a 3;k 4,a 4)=g 2 ρ∈S 4/Z 4Tr(T a ρ(1)T a ρ(2)T a ρ(3)T a ρ(4))×A (0)4(k ρ(1),k ρ(2),k ρ(3),k ρ(4)).(9)The two-particle cut can be written as a product of two four-point color-ordered amplitudes,summed over the pair of intermediate N =4states S,S ′crossing the cut,which evaluates toS,S ′∈N =4A (0)4(k 1,k 2,ℓS ,−ℓ′S ′)×A (0)4(ℓ′S ′,−ℓS ,k 3,k 4)=is 12s 23A (0)4(k 1,k 2,k 3,k 4)×1(ℓ−k 3)2,(10)where ℓ′=ℓ−k 1−k 2.This equation is also shown in fig.4.The scalar propagator factors in eq.(10)are depicted as solid vertical lines in the figure.The dashed line indicates the cut.Thus the cut reduces to the cut of a scalar box integral,defined byI D =4−2ǫ4≡ d 4−2ǫℓℓ2(ℓ−k 1)2(ℓ−k 1−k 2)2(ℓ+k 4)2.(11)One of the virtues of eq.(10)is that it is valid for arbitrary external states in the N =4multiplet,although only external gluons are shown in fig.4.Therefore it can be re-used at higher loop order,for example by attaching yet another tree to the left.N =41234=i s 12s 231234Figure 4.The one-loop two-particle cuts for the four-point amplitude in MSYM reduce to the tree amplitude multiplied by a cut scalar box integral (for any set of four external states).i 2s 12s121234+s 121234+perms Figure 5.The two-loop gg →gg amplitude in MSYM [11,39].The blob on theright represents the color-ordered tree amplitude A (0)4.(The quantity s 12s 23A (0)4transforms symmetrically under gluon interchange.)In the the brackets,black linesare kinematic 1/p 2propagators,with scalar (φ3)vertices.Green lines are color δab propagators,with structure constant (f abc )vertices.The permutation sum is over the three cyclic permutations of legs 2,3,4,and makes the amplitude Bose symmetric.At two loops,the simplicity of eq.(10)made it possible to compute the two-loop gg →gg scattering amplitude in that theory (in terms of specific loop integrals)in 1997[11],four years before the analogous computations in QCD [36,37].All of the loop momenta in the numerators of the Feynman di-agrams can be factored out,and only two independent loop integrals appear,the planar and nonplanar scalar double box integrals.The result can be writ-ten in an appealing diagrammatic form,fig.5,where the color algebra has the same form as the kinematics of the loop integrals [39].At higher loops,eq.(10)leads to a “rung rule”[11]for generating a class of (L +1)-loop contributions from L -loop contributions.The rule states that one can insert into a L -loop contribution a rung,i.e.a scalar propagator,transverse to two parallel lines carrying momentum ℓ1+ℓ2,along with a factor of i (ℓ1+ℓ2)2in the numerator,as shown in fiing this rule,one can construct recursively the external and loop-momentum-containing numerators factors associated with every φ3-type diagram that can be reduced to trees by a sequence of two-particle cuts,such as the diagram in fig.7a .Such diagrams can be termed “iterated 2-particle cut-constructible,”although a more compact notation might be ‘Mondrian’diagrams,given their resemblance to Mondrian’s paintings.Not all diagrams can be computed in this way.The diagram in fig.7b is not in the ‘Mondrian’class,so it cannot be determined from two-particle cuts.Instead,evaluation of the three-particle cuts shows that it appears with a non-vanishing coefficient in the subleading-color contributions to the three-loop MSYM amplitude.ℓ1ℓ2−→i (ℓ1+ℓ2)2ℓ1ℓ2Figure 6.The rung rule for MSYM.(a)(b)Figure 7.(a)Example of a ‘Mondrian’diagram which can be determined re-cursively from the rung rule.(b)Thefirst non-vanishing,non-Mondrian dia-grams appear at three loops in nonplanar,subleading-color contributions.4Iterative Relation in N =4Super-Yang-Mills TheoryAlthough the two-loop gg →gg amplitude in MSYM was expressed in terms of scalar integrals in 1997[11],and the integrals themselves were computed as a Laurent expansion about D =4in 1999[25,26],the expansion of the N =4amplitude was not inspected until last fall [9],considerably after similar investigations for QCD and N =1super-Yang-Mills theory [36,37].It was found to have a quite interesting “iterative”relation,when expressed in terms of the one-loop amplitude and its square.At leading color,the L -loop gg →gg amplitude has the same single-trace color decomposition as the tree amplitude,eq.(9).Let M (L )4be the ratio of this leading-color,color-ordered amplitude to the corresponding tree amplitude,omitting also several conventional factors,A (L ),N =4planar 4= 2e −ǫγg 2N c2 M (1)4(ǫ) 2+f (ǫ)M (1)4(2ǫ)−12(ζ2)2is replaced by approximately sixpages of formulas (!),including a plethora of polylogarithms,logarithms and=+f(ǫ)−12(ζ2)2+O(ǫ)f(ǫ)=−(ζ2+ǫζ3+ǫ2ζ4+...)Figure8.Schematic depiction of the iterative relation(13)between two-loop and one-loop MSYM amplitudes.polynomials in ratios of invariants s/t,s/u and t/u[37].The polylogarithm is defined byLi m(x)=∞i=1x i t Li m−1(t),Li1(x)=−ln(1−x).(14)It appears with degree m up to4at thefinite,orderǫ0,level;and up to degree4−i in the O(ǫ−i)terms.In the case of MSYM,identities relating these polylogarithms are needed to establish eq.(13).Although the O(ǫ0)term in eq.(13)is miraculously simple,as noted above the behavior of the pole terms is not a miracle.It is dictated in general terms by the cancellation of infrared divergences between virtual corrections and real emission[24].Roughly speaking,for this cancellation to take place,the virtual terms must resemble lower-loop amplitudes,and the real terms must resemble lower-point amplitudes,in the soft and collinear regions of loop or phase-space integration.At the level of thefinite terms,the iterative relation(13)can be understood in the Regge/BFKL limit where s≫t,because it then corresponds to expo-nentiation of large logarithms of s/t[40].For general values of s/t,however, there is no such argument.The relation is special to D=4,where the theory is conformally invariant. That is,the O(ǫ1)remainder terms cannot be simplified significantly.For ex-ample,the two-loop amplitude M(2)4(ǫ)contains at O(ǫ1)all three independent Li5functions,Li5(−s/u),Li5(−t/u)and Li5(−s/t),yet[M(1)4(ǫ)]2has only the first two of these[9].The relation is also special to the planar,leading-color limit.The subleading color-components of thefinite remainder|A(2),finn defined by eq.(5)show no significant simplification at all.For planar amplitudes in the D→4limit,however,there is evidence that an identical relation also holds for an arbitrary number n of external legs, at least for certain“maximally helicity-violating”(MHV)helicity amplitudes. This evidence comes from studying the limits of two-loop amplitudes as two of the n gluon momenta become collinear[9,38,41].(Indeed,it was by analyzing these limits that the relation for n=4wasfirst uncovered.)The collinear limits turn out to be consistent with the same eq.(13)with M4replaced by M n everywhere[9],i.e.M(2)n(ǫ)=12(ζ2)2+O(ǫ).(15)The collinear consistency does not constitute a proof of eq.(15),but in light of the remarkable properties of MSYM,it would be surprising if it were not true in the MHV case.Because the direct computation of two-loop amplitudes for n>4seems rather difficult,it would be quite interesting to try to examine the twistor-space properties of eq.(15),along the lines of refs.[31,42].(The right-hand-side of eq.(15)is not completely specified at order1/ǫandǫ0for n>4.The reason is that the orderǫandǫ2terms in M(1)n(ǫ),which contribute to thefirst term in eq.(15)at order1/ǫandǫ0,contain the D=6−2ǫpentagon integral[43],which is not known in closed form.On the other hand, the differential equations this integral satisfies may suffice to test the twistor-space behavior.Or one may examine just thefinite remainder M(L),finn definedvia eq.(5).)It may soon be possible to test whether an iterative relation for planar MSYM amplitudes extends to three loops.An ansatz for the three-loop planar gg→gg amplitude,shown infig.9,was provided at the same time as the two-loop re-sult,in1997[11].The ansatz is based on the“rung-rule”evaluation of the iterated2-particle cuts,plus the3-particle cuts with intermediate states in D=4;the4-particle cuts have not yet been verified.Two integrals,each be-ginning at O(ǫ−6),are required to evaluate the ansatz in a Laurent expansion about D=4.(The other two integrals are related by s↔t.)The triple ladder integral on the top line offig.9was evaluated last year by Smirnov,all the way through O(ǫ0)[44].Evaluation of the remaining integral,which contains a factor of(ℓ+k4)2in the numerator,is in progress[45];all the terms through O(ǫ−2)agree with predictions[33],up to a couple of minor corrections.5Significance of Iterative Behavior?It is not yet entirely clear why the two-loop four-point amplitude,and prob-ably also the n-point amplitudes,have the iterative structure(15).However, one can speculate that it is from the need for the perturbative series to=i3s12s212+s223+2s12(ℓ+k4)+2s23(ℓ+k1)21Figure9.Graphical representation of the three-loop amplitude for MSYM in the planar limit.be summable into something which becomes“simple”in the planar strong-coupling limit,since that corresponds,via AdS/CFT,to a weakly-coupled supergravity theory.The fact that the relation is special to the conformal limit D→4,and to the planar limit,backs up this speculation.Obviously it would be nice to have some more information at three loops.There have been other hints of an iterative structure in the four-point correlation func-tions of chiral primary(BPS)composite operators[46],but here also the exact structure is not yet clear.Integrability has played a key role in recent higher-loop computations of non-BPS spin-chain anomalous dimensions[4,5,6,8].By imposing regularity of the BMN‘continuum’limit[3],a piece of the anoma-lous dimension matrix has even been summed to all orders in g2N c in terms of hypergeometric functions[7].The quantities we considered here—gauge-invariant,but dimensionally regularized,scattering amplitudes of color non-singlet states—are quite different from the composite color-singlet operators usually treated.Yet there should be some underlying connection between the different perturbative series.6Aside:Anomalous Dimensions in QCD and MSYMAs mentioned previously,the set of anomalous dimensions for leading-twist operators was recently computed at NNLO in QCD,as the culmination of a multi-year effort[13]which is central to performing precise computations of hadron collider cross sections.Shortly after the Moch,Vermaseren and Vogt computation,the anomalous dimensions in MSYM were extracted from this result by Kotikov,Lipatov,Onishchenko and Velizhanin[12].(The MSYM anomalous dimensions are universal;supersymmetry implies that there is only one independent one for each Mellin moment j.)This extraction was non-trivial,because MSYM contains scalars,interacting through both gauge and Yukawa interactions,whereas QCD does not.However,Kotikov et al.noticed, from comparing NLO computations in both leading-twist anomalous dimen-sions and BFKL evolution,that the“most complicated terms”in the QCDcomputation always coincide with the MSYM result,once the gauge group representation of the fermions is shifted from the fundamental to the adjoint representation.One can define the“most complicated terms”in the x-space representation of the anomalous dimensions—i.e.the splitting kernels—as follows:Assign a logarithm or factor ofπa transcendentality of1,and a polylogarithm Li m or factor ofζm=Li m(1)a transcendentality of m.Then the most complicated terms are those with leading transcendentality.For the NNLO anomalous dimensions,this turns out to be transcendentality4.(This rule for extracting the MSYM terms from QCD has also been found to hold directly at NNLO,for the doubly-virtual contributions[38].)Strikingly,the NNLO MSYM anomalous dimension obtained for j=4by this procedure agrees with a previous result derived by assuming an integrable structure for the planar three-loop contribution to the dilatation operator[5].7Conclusions and OutlookN=4super-Yang-Mills theory is an excellent testing ground for techniques for computing,and understanding the structure of,QCD scattering amplitudes which are needed for precise theoretical predictions at high-energy colliders. One can even learn something about the structure of N=4super-Yang-Mills theory in the process,although clearly there is much more to be understood. Some open questions include:Is there any AdS/CFT“dictionary”for color non-singlet states,like plane-wave gluons?Can one recover composite operator correlation functions from any limits of multi-point scattering amplitudes?Is there a better way to infrared regulate N=4supersymmetric scattering amplitudes,that might be more convenient for approaching the AdS/CFT correspondence,such as compactification on a three-sphere,use of twistor-space,or use of coherent external states?Further investigations of this arena will surely be fruitful.AcknowledgementsWe are grateful to the organizers of Strings04for putting together such a stim-ulating meeting.This research was supported by the US Department of En-ergy under contracts DE-FG03-91ER40662(Z.B.)and DE-AC02-76SF00515 (L.J.D.),and by the Direction des Sciences de la Mati`e re of the Commissariat `a l’Energie Atomique of France(D.A.K.).。
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要达到满意的数码扩印效果照片规格(英寸) （厘米）(像素) 数码相机类型1寸2.5*3.5cm 413*295身份证大头照3.3*2.2 390*2602寸3.5*5.3cm 626*413小2寸（护照）4.8*3.3cm 567*3905 寸5x3.5 12.7*8.9 1200x840以上100万像素6 寸6x4 15.2*10.2 1440x960以上130万像素7寸7x5 17.8*12.7 1680x1200以上200万像素8寸8x6 20.3*15.2 1920x1440以上300万像素10寸10x8 25.4*20.3 2400x1920以上400万像素12寸12x10 30.5*20.3 2500x2000以上500万像素15寸15x10 38.1*25.4 3000x2000 600万像素19寸15x19 38.1*48.26 3000x4000 1200万像素另外，数码的片子别管像素是几百万，只看长边的像素数，1200出5寸1400出6寸，1700出7寸，类推。
1寸（是指英寸）=2.54cm我们说的x寸是指照片的长边，如5寸就是照片长2.54x5=12.7cm12寸就是2.54x12=30.5cm ,8x12就是长边2.54x12=30.5cm ，短边2.54x8=20.3cm3R指纸，3R为89MM，5R为127MM通常3R指3*5就是5寸5R指5*7就是7寸R的意思是长方型(英文是Rectangle),都以最短边耒算.像135机拍的相片大都洗成3R,4R或5R以上,如果120机的6X7底洗成3R相片,那它就没"3寸X 5寸"了,它按照比例出片是"3寸x 3.5寸"了,这也算是3R相片,还有3寸一定要足够.又像120哈苏6X6底出的相片,因它的底片是正四方型,如果要出正四方的相片,如"3寸X 3寸", "5寸X 5寸",在这种情行我们不叫3R,而是3S或5S,S代表正四方型(英文是Square).数码相机拍摄的照片一般是4：3的比例（与我们的显示器的比例一致），而扩印的照片的比例一般是3：2左右的（与胶卷负片的长宽比例一致），所以，讲数码相机的照片扩印出来一般要把照片的比例剪裁成3：2左右的，这样扩印出来的照片才是正好充满整张相纸。
several的同义词
several的同义词several表几个的; 专有的意思，那么你知道several的同义词有哪些吗?接下来小编为大家整理了several的同义词，希望对你有帮助哦!several的同义词辨析：little, few, several这几个词用作形容词时均含"少量的"之意。
little ：只修饰不可数名词，含否定意义。
few ：只修饰可数名词的复数形式，侧重指数量非常少，给人一种模糊概念，含否定意义。
several ：修饰可数名词的复数形式，指至少有3个，但不会超过5、6个。
词组习语：in little1. (古)小规模的，微缩的little or nothing1. 几乎没有make little of1. 没当回事他们没把与王室的关系当回事儿。
they made little of their royal connection.no little1. 不小，很大很重要的因素。
a factor of no little importance.not a little1. 不小，很多造成了不小的恐慌。
not a little consternation was caused.quite a little1. 很多，大量有些人大讲英语。
some spoke quite a little English.quite the little —1. [用以表示不情愿地或讽刺地承认某人具备能力或取得了成就]的确，真正你现在确实已成为女骑师了。
you've become quite the little horsewoman.a little1. 一点儿感觉好了一点felt a little better.little by little1. 逐渐地：慢慢地或逐渐增长地;渐渐地every few1. (尤指时间单位)每隔几…一次她每隔几周探望一次。
she visits every few weeks.few and far between1. 稀少，罕有;稀疏我难得有灵感。
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Ｍｉ ｃ ｒ ｏ ｓ ｔ ｒ ｕ ｃ ｔ ｕ ｒ ｅ ｓ ０ ｆ １ ２％ Ｃｒ Ｆｅ ｒ ｒ ｉ ｔ ｉ ｃ Ｓ ｔ ａ ｉ ｎ ｌ ｅ ｓ ｓ Ｓ ｔ ｅ ｅ ｌ ｉ ｎ Ｗ ｅ ｌ ｄ ｉ ｎ ｇ Ｈｅ ａ ｔ ． ａ ｆ ｆ ｅ ｃ ｔ ｅ ｄ Ｚｏｎ ｅ
维普资讯
７ ０
宝
钢
技
术
２ ０ ０ ７年第 ３期
１ ２ ％Ｃ ｒ 铁 素体 不 锈 钢 的焊 接 热 影 响 区组 织特 征
王 宝森 ， 马 （ １ ． 宝钢研 究院 ， 上海 立 ， 叶晓 宁 ， 田劲松 ２ ０ ０ ４ ３ １ ） ２ ０ １ ９ ０ ０ ； ２ ． 不锈 钢分 公 司 ， 上海
ｓ ｔ ｒ ａ ｉ ｎ ｒａ ｇ ｉ ｎ ｇ ｒ ｏ ｗｔ ｈ ｉ ｎ ｔ ｈ ｅ Ｃ Ｏ ａ ｌ ＇ ｓ ｅ ｒａ ｇ ｉ ｎ ｚ ｏ ｎ ｅ． ｈ ｅ Ｔ ｒ ｅ ｓ ｔ ｒ ａ ｉ ｎ ｔ ｅ ｆｅ ｃ ｔ ｏ ｆ Ｔｉ ｏ ｎ ｔ ｈ ｅ ｇ ｒ ａ ｉ ｎ ｇ ｒ ｏ ｔｈ ｗ ｉ ｓ ｂ ｅ ｔ ｔ ｅ ｒ ｔ ｈ ａ ｎ ｔ ｈ ａ ｔ ｏ ｆ Ｎｂ． Ｋｅ ｙｗｏ ｒ ｄｓ：ｆ ｅ ｒ ｒ ｉ ｔ ｉ ｃ ｓ ｔ ａ ｉ ｎｌ ｅ ｓ ｓ ｓ ｔ ｅ ｅｌ ；ｈ ｅ ａ ｔ ａ ｆ ｆ ｅ ｃ ｔ ｅ ｄ ｚ ｏ ｎｅ；ｍ ｉ ｃ ｏａ ｒ ｌｌ ｏ ｙ ｉ ｎ ｇ
善铁 素体不锈钢焊接接 头热影响 区韧性 的建议 ， 即焊接热 影响粗 晶区存在适 量的马 氏体 ； 钢 中添加微 量元 素
Ｔ ｉ 可抑 制粗 晶 区 晶 粒 长 大 ， 其 作 用优 于 Ｎ ｂ 。
关键词 ： 铁 素体 不锈 钢 ； Ｈ Ａ Ｚ ； 微 合 金 化 中图分类号 ： Ｔ Ｇ ４ ５ ７ ． １ １ 文献标识码 ： Ｂ 文章编号 ： １ ０ ０ ８—０ ７ １ ６ （ ２ ０ ０ ７ ｌ ０ ３— ０ ０ ７ ０— ０ ４
Ａｂｓ ｔ ｒ ａｃ ｔ ： Ｍｉ ｃ ｏｓ ｒ ｔ ｒ ｕ ｃ ｔ ａ ｉ ｎｌ ｅ ｓ ｓ ｓ ｔ ｅ ｅ ｌ ｕｎ ｄｅ ｒ ｄｉ ｆｅ ｒ ｅ ｎ ｔ ｗｅ ｌ ｄｉ ｎ ｇ ｈ ｅ ａ ｔ ｉ ｎ ｐｕ ｔ ｃ ｏ ｎｄ ｉ ｔ ｉ ｏ ｎｓ ｗｅ ｒ ｅ ｏ ｂ —
Ｗａ ｎ ｇ Ｂａ ｏ ｓ ｅ ｎ ， Ｍａ Ｌ ｉ ，Ｙ ｅ Ｘｉ ａ ｏ ｎ ｉ ｎ ｇ ，Ｔ ｉ ａ ｎ Ｊ ｉ ｎ ｓ ｏ ｎ ｇ
（ １ ．Ｂ ａ ｏ ｓ ｔ ｅ ｅ ｌ Ｒｅ ｓ ｅ ａ ｒ ｃ ｈ Ｉ ｎ ｓ ｔ ｉ ｔ ｕ ｔ ｅ ， Ｓ ｈ ａ ｎ ｇ ｈ ａ ｉ ２ ０ １ ９ ０ ０， Ｃｈ ｉ ｎ ａ ； ２ ．Ｓ ｔ ａ ｉ ｎ ｌ ｅ ｓ ｓ Ｓ ｔ ｅ ｅ ｌ Ｂ ｒ ａ ｎ ｃ ｈ ，Ｓ ｈ ａ ｎ ｈａ ｇ ｉ ２ ０ ０ ４ ３ １ ， Ｃ ｈ ｉ ｎ ａ ）
ｔ ｅ ｍｉ ｒ ｎ ｅ ｄ ｂ ｙ Ｓ ｏ ｔ ｆ ｗ ａ ｒ ｅ ｈｅ Ｔ ｍ ａ ｒ ｌ— ｃ ａ ｌ ，ｔ ｏ ｇ ｅ ｔ ｈ ｅ ｒ ｗ ｉ ｔ ｈ ｐ ｒ ｅ ｃ ｉ ｐ ｉ ｔ ａ ｔ ｅ ｐ ｈ ｓｅ ａ ｄ ｉ ａ ｇ ｒ ａ ｍｓ ｏ ｆ ｍｉ ｃ ｏａ ｒ ｌｌ ｏ ｙ ｓ Ｔｉ ａ ｎ ｄ Ｎｂ ．Ｓ ｕ ｇ ｇ ｅ ｓ ｔ ｉ ｏ ｎ ｓ ｏ ｆ
ｓ ｅ ￣ｅ ｄ ｂ ｙ ｏ ｐ ｔ ｉ ｃ ｌ ａ ｍ ｉ ｃ ｒ ｏ ｓ ｃ ｏ ｐ ｅ ａ ｎ ｄ ｓ ｃ ａ ｎ ｎ ｉ ｎ ｇ ｅ ｌ ｅ ｃ ｔ ｒ ｏ ｎ ｍ ｉ ｃ ｏｓ ｒ ｃ ｏ ｐ ｅ（ Ｓ Ｅ Ｍ） ．Ｔ ｈ ｅ ｃ ｈ ａ ｎ ｇ ｅ ｏｌ ｒ ｅ ｓ ｏ ｆ ｔ ｈ ｅ ｓ ｔ ｅ ｅ ｌ ｉ ｎ ｃ ｏ ａ ｒ ｓ ｅ ｇ ｒ ａ ｉ ｎ ｅ ｄ ｈ ｅ ａ ｔ — ａ ｆ ｅ ｃ ｔ ｅ ｄ ｚ ｏ ｎ ｅ（ Ｃ Ｇ ＨＡ Ｚ ）ｗ ｅ ｒ ｅ ｏ ｂ ｔ ａ ｉ ｎ ｅ ｄ ．Ｔ ｈ ｅ ｔ ｅ ｍ ｅｒ ｐ ａ ｔ ｕ ｒ ｅ ｒ ａ ｎ ｇ ｅ ｗ ｈ ｅ ｒ ｅ ｐ ｈ ａ ｓ ｅ ｃ ｈ ｎｇ ａ ｅ ｓ ｔ ｏ ｏ ｋ ｐ ｌ ａ ｃ ｅ Ｗ ｓ ａ ｄ ｅ —
摘要： ： 针对 １ ２ ％Ｃ ｒ 铁 素体 不锈钢 ， 利 用光 学显微镜 、 扫描 电镜 ， 对在 不同焊接 热输入 条件 下的显微 组 织
种类进行观察 ， 得 出热影 响粗 晶 区 的 组 织 变化 规 律 ； 应用 Ｔ ｈ ｅ ｒ ｍ ａ ｌ — ｃ ｌ软件 ， ａ 确定了 １ ２ ％Ｃ ｒ 铁 素 体 不锈 钢 在 焊 接 热 循 环 条 件 下 发 生 相 变 的温 度 区 间 ， 以及 微 合 金 元 素 Ｔ ｊ 和 Ｎ ｂ的析 出相 图 。 给 出在 焊 接 热 循 环 作 用 下 ， 改
ｉ ｍ ｐ ｏｖ ｒ ｉ ｎ ｇ ｆ ｅ ｒ ｒ ｉ ｔ ｉ ｃ ｓ ｔ ａ ｉ ｎ ｌ ｅ ｓ ｓ ｓ ｔ ｅ ｅ ｌ ’ Ｓ ｔ ｏ ｕ ｇ ｈ ｎ ｅ ｓ ｓ ｉ ｎ ｗ ｅ ｌ ｄ ｅ ｄ ｊ ｏ ｉ ｎ ｔ Ｈ Ａ Ｚ ｗ ｅ ｒ ｅ ｇ ｉ ｖ ｅ ｎ ．Ｔ ｈｅ ｓ ｕ ｇ ｇ ｅ ｓ ｔ ｉ ｏ ｎ ｓ ｉ ｎ ｃ ｌ ｕ ｄ ｅ ｔ ｈ ａ ｔ ｔ ｈ ｅ ｒ ｅ ｉ ｓ ａ ｍ ｏ ｄ ｅ ｒ ａ ｔ ｅ ａ ｍｏ ｕ ｎ ｔ ｏ ｆ ｍａ ｒ ｔ ｅ ｎ ｓ ｉ ｔ ｅ ｉ ｎ ｗ ｅ ｌ ｄ ｅ ｄ ｊ ｏ ｉ ｎ ｔ Ｈ Ａ Ｚ ；ｉ ｆ ａ ｄ ｄ ｉ ｎ ｇ ａ ｓ ｍ ｌ ａ ｌ ａ ｍ ｏ ｕ ｎ ｔ ｏ ｆ ｅ ｌ ｅ ｍ ｅ ｎ ｔ Ｔ ｉ ｉ ｎ ｔ ｈ ｅ ｓ ｔ ｅ ｅ ｌ ，ｉ ｔ ｃ ａ ｎ ｒ ｅ —