Two Cubed Class
2用英语怎么写
1.2用英文怎么写2的英文是two。
词汇分析音标：英[tuː] 美 [tu]释义：n. 两个adj. 两个的num. 二短语Two Whatevers 两个凡是Two Women 烽火母女泪；两个女人；战地两女性；两女Two Cops 特警冤家；两个警察；锄暴特警；两个刑警Two Soldiers 两个士兵；两名士兵；同胞兄弟；幽默英语故事两名士兵Two Lamps 两盏巨灯Perfect Two 新天生一对；天生一对；咸菜贤才大贤永才例句1、They teamed Class One with Class Two.他们将一班和二班编成一队。
我们用两个师包围了这座城市。
3、We talked about two hours, but he hedged over my questions.我们用两个师包围了这座城市。
4、Working together for two months welded them into a group.在一起工作两个月使他们形成了一个团体。
5、He died two months ago.他两个月前去世了。
2.2的英文怎么写2的英文是two。
two英 [tu：] 美 [tu]n. 两个；两个东西；两点钟；一对；adj. 两个的；我同；num. 两个；第二；二；双语例句1. It's a long way to go for two people in their seventies.对于两个七十几岁的人来说，这段路太远了。
他在那儿的时候体重下降了2英石。
3. I undid the bottom two buttons of my yellow and grey shirt.我解开了自己黄灰相间的衬衫上最下面的两个纽扣。
4. It would be difficult to find two men who were more dissimilar.很难找到彼此间差异更大的人了。
2024北京东城区初三一模英语试卷和答案
2024北京东城初三一模英 语2024. 4学校___________ 班级___________ 姓名___________ 教育ID号___________考生须知1. 本试卷共10页，共两部分，五道大题，38道小题，满分60分，考试时间90分钟。
2. 在试卷和答题卡上准确填写学校、班级、姓名和教育ID号。
3. 试题答案一律填涂或书写在答题卡上，在试卷上作答无效。
4. 在答题卡上，选择题用2B铅笔作答，其他试题用黑色字迹签字笔作答。
第一部分本部分共33题，共40分。
从每题列出的四个选项中，选出最符合题目要求的一项。
一、单项填空（每题0.5分，共6分）从下面各题所给的A、B、C、D四个选项中，选择可以填入空白处的最佳选项。
1. My sister loves playing basketball. I want to ask ________ to join our sports club.A. himB. themC. youD. her2. My father is a policeman. He works ________ the police station.A. atB. onC. ofD. with3. Pay attention in class, ________ you will fall behind in your studies.A. andB. orC. butD. so4. Tony is very good at math and ________ solve this math problem quickly.A. canB. mustC. needD. should5. —Ava’s painting is great.—I agree. It’s ________ artwork I’ve ever seen.A. creativeB. more creativeC. most creativeD. the most creative6. —________ did it take you to make this kite?—About 2 hours.A. How longB. How oftenC. How muchD. How soon7. The students of Class Two ________ a science experiment in the lab right now.A. doB. didC. are doingD. have done8. When I was young, my father ________ me to play the piano.A. teachesB. taughtC. will teachD. has taught9. I ________ my room when my father called me for dinner.A. cleanB. will cleanC. was cleaningD. am cleaning10. He ________ to cook for a year. He is now able to prepare delicious meals.A. learnsB. has learnedC. will learnD. is learning11. World Book Day ________ to encourage people to read and write.A. celebratedB. celebratesC. was celebratedD. is celebrated12. —Do you know ________?—At 2:00 p. m. next Friday.A. when the talent show startedB. when did the talent show startC. when the talent show will startD. when will the talent show start二、完形填空（每题1分，共8分）阅读下面的短文，掌握其大意，然后从短文后各题所给的A、B、C、D四个选项中，选择最佳选项。
浙江省杭州市第二中学2024学年高考英语四模试卷(含解析)
浙江省杭州市第二中学2024学年高考英语四模试卷注意事项1．考生要认真填写考场号和座位序号。
2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。
第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。
3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。
第一部分（共20小题，每小题1.5分，满分30分）1．—Did you have difficulty finding Ann'house?—Not really.She___us clear directions and we were able to find it.easily?A．was to give B．had givenC．was giving D．would give2．We went right round to the west coast by sea instead of driving across continent。
A．the；the B．/ ；the C．the；/ D．/ ；/3．American singer Taylor Swift, 21, ________ big at the 2011 Academy of Country Music Awards in the US on April 3rd. A．stood B．gave C．scored D．made4．The Chinese people are hopeful for ________ 2019 will bring for their families and the country.A．how B．whichC．what D．that5．School children must be taught how to deal with dangerous ________.A．states B．conditionsC．situations D．positions6．Many writers are drawn to building a world, _____ readers are somewhat familiar with but also feel distant from our normal lives.A．it B．one C．that D．the one7．I believed him to be honest but his actions showed that he had ________.A．the top dog B．the feet of clayC．his cup of tea D．the apple of his eye8．—Going to watch the Women’s Volleyball Match on Wednesday?—________! Will you go with me?A．Y ou bet B．Y ou got meC．Y ou there D．Y ou know better9．-My computer doesn't work!-Robert is a computer expert. How I wish he______ with me.A．came B．had comeC．is coming D．has come10．Julia has got a pretty _ deal—she was laid off just for being late once!A．rough B．toughC．illegal D．mean11．— Could you turn the TV down a little bit?— ________. Is it disturbing you?A．Take it easy. B．I’m sorry. C．Not a bit D．It depends12．James Smith and his girlfriend went to Chenyi Square to celebrate the New Y ear, never _________.A．returned B．to returnC．returning D．having returned13．He was elected______ president of the company, and _____news came ,in fact, as ______surprise.A．a; the ;X B．X; the ; a C．a; X; the D．the; the; a14．—I say, Harry. What did you say to the laid-off worker just now?—Nothing. I to myself.A．had only talked B．am only talking C．have just talked D．was just talking15．I was expecting a present from her, so I was disappointed I didn’t receive ______.A．it B．one C．that D．the one16．Y ou will have to stay at home all day ______ you finish all your homework.A．if B．unless C．whether D．because17．Wolf Warrior 2, which ________ the “Award for Best Visual Effects” at the Beijing Film Festival, indicates China's film industry has come of age.A．wins B．wonC．has won D．had won18．No matter how carefully you plan your finances, no one can _______ when the unexpected will happen.A．prove B．implyC．demand D．predict19．—Didn’t you go fishing with your friends last Sunday?—No. I ______ to the nursing home as usual.A．went B．go C．have gone D．had gone20．Class Two, our class became the Basketball Champion of our school.A．Beating B．to beat C．Beaten by D．Having beaten第二部分阅读理解（满分40分）阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项。
0625_w11_qp_63剑桥igcse物理真题
Fig. 2.1
Record the temperature θh of this hot water.
θh = .......................................................... [1]
© UCLES 2011
0625/63/O/N/11
[Turn over
4 2 An IGCSE student is investigating the energy changes that occur when hot water and cold water
are mixed. The student is provided with a supply of hot water and a supply of cold water. The temperature of the cold water θc = 23 °C. (a) The temperature of the hot water is shown in Fig. 2.1.
i = ............................................................... [2]
(c) The student does not have a set square or any other means to check that the pins are vertical. Suggest how he can ensure that his P3 and P4 positions are as accurate as possible. ...................................................................................................................................................
综合智商测试
综合智商测试（一）智商测试－－综合试卷一本次提供的是一份综合智商测试试卷。
从这张试卷中，你将从语言、比较、归纳、推理、判断等方面全面地测查你的智商。
测试时间30分钟！你可以使用纸和笔，不可以使用计算器等工具。
在你做试卷之前，这里有一点说明：由于这张试卷是在使用英语的国家里使用的，因此试卷中有个别题目涉及到一些英语知识。
只要你知道英语的26个字母及1000个左右的词汇，就完全能够做出这些题目。
即使你完全不懂英语，放弃有关语言题目不做，这对你智商的大致测算是没有影响的。
例一：Piece（）Pillsgrips（）swell答案：Pile因为括号内第一个字母是括号前面单词的第四个字母；括号内第二个字母是括号前面单词的第三个字母，括号内第三个字母是括号后面单词的第四个字母；括号内第四个字母是括号后面单词的第三个字母。
需要注意的是，填出的字母要组成一个单词。
如Pile“堆”。
1．从右边的图形中选择一个正确的填入左边的空白处： 1 2 3 4 2．在问号处填上合适的数字：3．在括号内填上合适的字母：GROOM （ROSE）MOUSEPINCH （）ONION4．在括号内填上合适的数字：651 （331）342449（）5235．在方框内填上合适的数字：81224606．在方框内填上合适的字母：B F K Q7．在问号处填上合适的数字：例二：括号里填上的词要即完成前面的单词又作为后一个单词的开头。
Indivi （）ism 答案：dual Individual ：个体 dualism ：两重性8．在问号处填上合适的数字：9．从列出的六个图形中选出合适的填入问号处：12345610．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 611．在括号内填上合适的数字：96（16）2 88（）1112．在方框处填上合适的数字：2 10 43 17 5 3413．在括号内填上合适的数字：98（54）64 81（）3614．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 615．在括号内填上合适的字母：SLOPE（POOR）GROOMPLANE（）SEEMS16．在方框处填上合适的数字：18252116201261517．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 618．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 619．括号里填上的词要和括号外两个单词同义：Joke（）Silence20．在方框处填上合适的字母：C F ID H LE J21．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 622．在方框处填上合适的数字：285681123．在括号内填上合适的字母：BIRD（DRIP）PILLSGRIP （）ELBOW24．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 6 25．按照顺时针方向，自上而下在空格内填上字母，用逗号分开：26．在方框处填上合适的数字：829711413327．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 628．在括号内填上合适的字母：DRUM（LUMP）GULPSLIP（）GODS29．在两个问号处填上合适的字母和数字，用逗号分开：2 E 8 ？B 5 H ？30．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 631．在括号内填上合适的数字：16（93）1514（）1232．在括号内填上合适的字母：SEND（SEED）FEELGAME（）STAY33．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 634．从列出的六个图形中选出合适的填入问号处： 1 2 3 4 5 6综合智商测试（二）智商测试 －－综合试卷二本次提供的是一份综合智商测试试卷。
【原创】校本练习2020-2021学年高二数学选修2-1 3.2.1用向量方法解决平行问题
班级______________姓名________________座号____________1、设平面α的法向量为(1,2,-2),平面β的法向量为(-2,-4,k ),若α∥β,则k 等于( ) A.2B.-4C.4D.-22、若AB ⃗⃗⃗⃗⃗ =λCD ⃗⃗⃗⃗⃗ +μCE ⃗⃗⃗⃗⃗ ,则直线AB 与平面CDE 的位置关系是( ) A.相交B.平行C.在平面内D.平行或在平面内3、若两个不同的平面α与β的法向量分别是a =(1,0,-2),b =(-1,0,2),则平面α与平面β的关系是 ( ) A.平行B.垂直C.相交不垂直D.无法判断4、若直线l 的方向向量为a ,平面α的法向量为u ,则能使l ∥α的是( )A.a =(1,0,0),u =(-2,0,0)B.a =(1,3,5),u =(1,0,1)C.a =(0,2,1),u =(-1,0,1)D.a =(1,-1,3),u =(0,3,1)5、已知直线l 的方向向量a =(2,3,13),平面α的法向量为n =(6,λ,-12),若l ∥α,则λ的值是( ) A.4B.−7118C.253D.−2366、给出下列命题:①若n 1,n 2分别是平面α,β的法向量,则n 1∥n 2⇔α∥β; ②若n 1,n 2分别是平面α,β的法向量,则α∥β⇔n 1·n 2=0; ③若n 是平面α的法向量,且向量a 与平面α共面,则a ·n =0.其中正确命题的个数是( )A.1B.2C.3D.07、在三棱锥P-ABC中,CP,CA,CB两两垂直,AC=CB=1,PC=2,在如图所示的坐标系下,下列向量是平面PAB的法向量的是()) B.(1,√2,1) C.(1,1,1) D.(2,-2,1)A.(1,1,128、已知直线a,b的方向向量分别为m=(4,k,k-1)和n=(k,k+3,3),若a2∥b,则k=.9、已知向量a=(1,3,5),b=(2,4,6),若n与x轴垂直,且a·n=12,n·b=14,则n=.10、已知平面α内的三点A(0,0,1),B(0,1,0),C(1,0,0),平面β的法向量为n=(-1,-1,-1),且β与α不重合,则αβ.(填“⊥”或“∥”)11、如图,在四棱锥P-ABCD中,底面ABCD是边长为1的菱形,∠ABC=π,PP⊥底面ABCD,PA=2,点M为PA的中点,点N为BC的中点.AF 4⊥CD于点F,如图建立空间直角坐标系.求出平面PCD的一个法向量并证明MN∥平面PCD.12、在长方体ABCD-A1B1C1D1中,DA=2,DC=3,DD1=4,M,N,E,F分别是A1D1,A1B1,D1C1,B1C1的中点,求证:平面AMN∥平面EFBD.13、如图,在多面体ABCDEF中,四边形ABCD是正方形,EF∥AB,EF ⊥FB,AB=2EF,∠BFC=90°,BF=FC,H为BC的中点,求证:FH∥平面EDB.1、解析:∵α∥β,∴1-2=2-4=-2k,∴k =4.答案:C2、解析:∵AB ⃗⃗⃗⃗⃗ =λCD ⃗⃗⃗⃗⃗ +μCE ⃗⃗⃗⃗⃗ ,∴AB ⃗⃗⃗⃗⃗ ,CD ⃗⃗⃗⃗⃗ ,CE ⃗⃗⃗⃗⃗ 共面,则AB 与平面CDE 的位置关系是平行或在平面内.答案:D3、解析:∵a=-b ,∴a ∥b ,∴α∥β.答案:A4、解析:∵l ∥α,∴a ⊥u ,即a ·u =0.故选D .答案:D5、解析:∵l ∥α,∴a ⊥n ,即a ·n =0,∴2×6+3λ−16=0,解得λ=−7118.答案:B6、解析:①中,α与β可能重合;②中,α∥β可得到n 1∥n 2.答案:A7、解析:PA ⃗⃗⃗⃗⃗ =(1,0,−2),AB ⃗⃗⃗⃗⃗ =(−1,1,0).设平面PAB 的一个法向量为n =(x ,y ,1),则{x -2=0,-x +y =0,解得{x =2,y =2,∴n =(2,2,1).又(1,1,12)=12n ,∴A 正确.答案:A8、解析:①当k=0时,a 与b 不平行.②当k ≠0时,由4k =k k+3=k -132,解得k=-2.答案:-29、解析:设n =(0,y ,z ),由题意得{3y +5z =12,4y +6z =14,解得{y =-1,z =3.故n =(0,-1,3).答案:(0,-1,3)10、解析:AB ⃗⃗⃗⃗⃗ =(0,1,−1),AC ⃗⃗⃗⃗⃗ =(1,0,−1),则n ·AB ⃗⃗⃗⃗⃗ =−1×0+(−1)×1+(−1)×(−1)=0,n ·AC ⃗⃗⃗⃗⃗ =−1×1+(−1)×0+(−1)×(−1)=0.又α与β不重合,故α∥β.答案:∥11、解:由题设知,在Rt △AFD 中,AF=FD =√22,A (0,0,0),B (1,0,0),F (0,√22,0),D (-√22,√22,0),P(0,0,2),M(0,0,1),N (1-√24,√24,0). MN⃗⃗⃗⃗⃗⃗⃗ =(1-√24,√24,-1),PF ⃗⃗⃗⃗⃗ =(0,√22,-2),PD⃗⃗⃗⃗⃗ =(-√22,√22,-2).设平面PCD 的一个法向量为n =(x ,y ,z ), 则{n ·PF⃗⃗⃗⃗⃗ =0,n ·PD⃗⃗⃗⃗⃗ =0⇒{√22y -2z =0,-√22x +√22y -2z =0,令z =√2,得n =(0,4,√2).因为MN ⃗⃗⃗⃗⃗⃗⃗ ·n =(1-√24,√24,-1)·(0,4,√2)=0,且MN ⊄平面PCD ,所以MN ∥平面PCD.12、证法一:建立如图所示的空间直角坐标系,取MN ,DB 及EF 的中点R ,T ,S ,连接RA ,ST ,则A (2,0,0),M (1,0,4),N (2,32,4),D (0,0,0),B (2,3,0),E (0,32,4),F(1,3,4),R (32,34,4),S (12,94,4),T (1,32,0),∴MN ⃗⃗⃗⃗⃗⃗⃗ =(1,32,0),EF ⃗⃗⃗⃗⃗ =(1,32,0),AR⃗⃗⃗⃗⃗ =(-12,34,4),TS ⃗⃗⃗⃗ =(-12,34,4).∴MN ⃗⃗⃗⃗⃗⃗⃗ =EF ⃗⃗⃗⃗⃗ ,AR⃗⃗⃗⃗⃗ =TS ⃗⃗⃗⃗ , ∴MN ∥EF ,AR ∥TS ,∴MN ∥平面EFBD ,AR ∥平面EFBD.又MN ∩AR=R ,∴平面AMN ∥平面EFBD. 证法二:由证法一可知,A (2,0,0),M (1,0,4),N (2,32,4),D(0,0,0),E (0,32,4),F(1,3,4),则AM ⃗⃗⃗⃗⃗⃗ =(−1,0,4),AN ⃗⃗⃗⃗⃗⃗ =(0,32,4),DE ⃗⃗⃗⃗⃗ =(0,32,4),DF ⃗⃗⃗⃗⃗ =(1,3,4).设平面AMN ,平面EFBD 的法向量分别为n 1=(x 1,y 1,z 1),n 2=(x 2,y 2,z 2),则{n 1·AM⃗⃗⃗⃗⃗⃗ =0,n 1·AN ⃗⃗⃗⃗⃗⃗ =0⇒{-x 1+4z 1=0,32y 1+4z 1=0,令x 1=1,得z 1=14,y1=−23.又{n 2·DE ⃗⃗⃗⃗⃗ =0,n 2·DF ⃗⃗⃗⃗⃗ =0⇒{32y 2+4z 2=0,x 2+3y 2+4z 2=0,令y 2=-1,得z 2=38,x 2=32.∴n 1=(1,-23,14),n 2=(32,-1,38).∴n 2=32n1,得n 1∥n 2.∴平面AMN ∥平面EFBD.13、证明:∵四边形ABCD 为正方形,∴AB ⊥BC.又EF ∥AB ,∴EF ⊥BC.又EF ⊥FB ,FB ∩BC=B ,∴EF ⊥平面BFC ,∴EF ⊥FH.∴AB ⊥FH.又BF=FC ,H 为BC 的中点,∴FH ⊥BC.又AB ∩BC=B ,∴FH ⊥平面ABC.以H 为坐标原点,HB ⃗⃗⃗⃗⃗⃗ 为x 轴正方向,HF ⃗⃗⃗⃗⃗ 为z 轴正方向,建立如图所示的空间直角坐标系.设BH=1,则F (0,0,1),HF ⃗⃗⃗⃗⃗ =(0,0,1).设AC 与BD 的交点为G ,连接GE ,GH ,则E (0,-1,1),G (0,-1,0),∴GE ⃗⃗⃗⃗⃗ =(0,0,1).∴HF ⃗⃗⃗⃗⃗ =GE⃗⃗⃗⃗⃗ ,即HF ∥GE. ∵GE ⊂平面EDB ,FH ⊄平面EDB ,∴FH ∥平面EDB.。
Gradient-based learning applied to document recognition
Gradient-Based Learning Appliedto Document RecognitionYANN LECUN,MEMBER,IEEE,L´EON BOTTOU,YOSHUA BENGIO,AND PATRICK HAFFNER Invited PaperMultilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient-based learning technique.Given an appropriate network architecture,gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns,such as handwritten characters,with minimal preprocessing.This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task.Convolutional neural networks,which are specifically designed to deal with the variability of two dimensional(2-D)shapes,are shown to outperform all other techniques.Real-life document recognition systems are composed of multiple modules includingfield extraction,segmentation,recognition, and language modeling.A new learning paradigm,called graph transformer networks(GTN’s),allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure.Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training,and theflexibility of graph transformer networks.A graph transformer network for reading a bank check is also described.It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal checks.It is deployed commercially and reads several million checks per day. Keywords—Convolutional neural networks,document recog-nition,finite state transducers,gradient-based learning,graphtransformer networks,machine learning,neural networks,optical character recognition(OCR).N OMENCLATUREGT Graph transformer.GTN Graph transformer network.HMM Hidden Markov model.HOS Heuristic oversegmentation.K-NN K-nearest neighbor.Manuscript received November1,1997;revised April17,1998.Y.LeCun,L.Bottou,and P.Haffner are with the Speech and Image Processing Services Research Laboratory,AT&T Labs-Research,Red Bank,NJ07701USA.Y.Bengio is with the D´e partement d’Informatique et de Recherche Op´e rationelle,Universit´e de Montr´e al,Montr´e al,Qu´e bec H3C3J7Canada. Publisher Item Identifier S0018-9219(98)07863-3.NN Neural network.OCR Optical character recognition.PCA Principal component analysis.RBF Radial basis function.RS-SVM Reduced-set support vector method. SDNN Space displacement neural network.SVM Support vector method.TDNN Time delay neural network.V-SVM Virtual support vector method.I.I NTRODUCTIONOver the last several years,machine learning techniques, particularly when applied to NN’s,have played an increas-ingly important role in the design of pattern recognition systems.In fact,it could be argued that the availability of learning techniques has been a crucial factor in the recent success of pattern recognition applications such as continuous speech recognition and handwriting recognition. The main message of this paper is that better pattern recognition systems can be built by relying more on auto-matic learning and less on hand-designed heuristics.This is made possible by recent progress in machine learning and computer ing character recognition as a case study,we show that hand-crafted feature extraction can be advantageously replaced by carefully designed learning machines that operate directly on pixel ing document understanding as a case study,we show that the traditional way of building recognition systems by manually integrating individually designed modules can be replaced by a unified and well-principled design paradigm,called GTN’s,which allows training all the modules to optimize a global performance criterion.Since the early days of pattern recognition it has been known that the variability and richness of natural data, be it speech,glyphs,or other types of patterns,make it almost impossible to build an accurate recognition system entirely by hand.Consequently,most pattern recognition systems are built using a combination of automatic learning techniques and hand-crafted algorithms.The usual method0018–9219/98$10.00©1998IEEE2278PROCEEDINGS OF THE IEEE,VOL.86,NO.11,NOVEMBER1998Fig.1.Traditional pattern recognition is performed with two modules:afixed feature extractor and a trainable classifier.of recognizing individual patterns consists in dividing the system into two main modules shown in Fig.1.Thefirst module,called the feature extractor,transforms the input patterns so that they can be represented by low-dimensional vectors or short strings of symbols that:1)can be easily matched or compared and2)are relatively invariant with respect to transformations and distortions of the input pat-terns that do not change their nature.The feature extractor contains most of the prior knowledge and is rather specific to the task.It is also the focus of most of the design effort, because it is often entirely hand crafted.The classifier, on the other hand,is often general purpose and trainable. One of the main problems with this approach is that the recognition accuracy is largely determined by the ability of the designer to come up with an appropriate set of features. This turns out to be a daunting task which,unfortunately, must be redone for each new problem.A large amount of the pattern recognition literature is devoted to describing and comparing the relative merits of different feature sets for particular tasks.Historically,the need for appropriate feature extractors was due to the fact that the learning techniques used by the classifiers were limited to low-dimensional spaces with easily separable classes[1].A combination of three factors has changed this vision over the last decade.First, the availability of low-cost machines with fast arithmetic units allows for reliance on more brute-force“numerical”methods than on algorithmic refinements.Second,the avail-ability of large databases for problems with a large market and wide interest,such as handwriting recognition,has enabled designers to rely more on real data and less on hand-crafted feature extraction to build recognition systems. The third and very important factor is the availability of powerful machine learning techniques that can handle high-dimensional inputs and can generate intricate decision functions when fed with these large data sets.It can be argued that the recent progress in the accuracy of speech and handwriting recognition systems can be attributed in large part to an increased reliance on learning techniques and large training data sets.As evidence of this fact,a large proportion of modern commercial OCR systems use some form of multilayer NN trained with back propagation.In this study,we consider the tasks of handwritten character recognition(Sections I and II)and compare the performance of several learning techniques on a benchmark data set for handwritten digit recognition(Section III). While more automatic learning is beneficial,no learning technique can succeed without a minimal amount of prior knowledge about the task.In the case of multilayer NN’s, a good way to incorporate knowledge is to tailor its archi-tecture to the task.Convolutional NN’s[2],introduced in Section II,are an example of specialized NN architectures which incorporate knowledge about the invariances of two-dimensional(2-D)shapes by using local connection patterns and by imposing constraints on the weights.A comparison of several methods for isolated handwritten digit recogni-tion is presented in Section III.To go from the recognition of individual characters to the recognition of words and sentences in documents,the idea of combining multiple modules trained to reduce the overall error is introduced in Section IV.Recognizing variable-length objects such as handwritten words using multimodule systems is best done if the modules manipulate directed graphs.This leads to the concept of trainable GTN,also introduced in Section IV. Section V describes the now classical method of HOS for recognizing words or other character strings.Discriminative and nondiscriminative gradient-based techniques for train-ing a recognizer at the word level without requiring manual segmentation and labeling are presented in Section VI. Section VII presents the promising space-displacement NN approach that eliminates the need for segmentation heuris-tics by scanning a recognizer at all possible locations on the input.In Section VIII,it is shown that trainable GTN’s can be formulated as multiple generalized transductions based on a general graph composition algorithm.The connections between GTN’s and HMM’s,commonly used in speech recognition,is also treated.Section IX describes a globally trained GTN system for recognizing handwriting entered in a pen computer.This problem is known as “online”handwriting recognition since the machine must produce immediate feedback as the user writes.The core of the system is a convolutional NN.The results clearly demonstrate the advantages of training a recognizer at the word level,rather than training it on presegmented, hand-labeled,isolated characters.Section X describes a complete GTN-based system for reading handwritten and machine-printed bank checks.The core of the system is the convolutional NN called LeNet-5,which is described in Section II.This system is in commercial use in the NCR Corporation line of check recognition systems for the banking industry.It is reading millions of checks per month in several banks across the United States.A.Learning from DataThere are several approaches to automatic machine learn-ing,but one of the most successful approaches,popularized in recent years by the NN community,can be called“nu-merical”or gradient-based learning.The learning machine computes afunction th input pattern,andtheoutputthatminimizesand the error rate on the trainingset decreases with the number of training samplesapproximatelyasis the number of trainingsamples,is a number between0.5and1.0,andincreases,decreases.Therefore,when increasing thecapacitythat achieves the lowest generalizationerror Mostlearning algorithms attempt tominimize as well assome estimate of the gap.A formal version of this is calledstructural risk minimization[6],[7],and it is based on defin-ing a sequence of learning machines of increasing capacity,corresponding to a sequence of subsets of the parameterspace such that each subset is a superset of the previoussubset.In practical terms,structural risk minimization isimplemented byminimizingisaconstant.that belong to high-capacity subsets ofthe parameter space.Minimizingis a real-valuedvector,with respect towhichis iteratively adjusted asfollows:is updated on the basis of a singlesampleof several layers of processing,i.e.,the back-propagation algorithm.The third event was the demonstration that the back-propagation procedure applied to multilayer NN’s with sigmoidal units can solve complicated learning tasks. The basic idea of back propagation is that gradients can be computed efficiently by propagation from the output to the input.This idea was described in the control theory literature of the early1960’s[16],but its application to ma-chine learning was not generally realized then.Interestingly, the early derivations of back propagation in the context of NN learning did not use gradients but“virtual targets”for units in intermediate layers[17],[18],or minimal disturbance arguments[19].The Lagrange formalism used in the control theory literature provides perhaps the best rigorous method for deriving back propagation[20]and for deriving generalizations of back propagation to recurrent networks[21]and networks of heterogeneous modules[22].A simple derivation for generic multilayer systems is given in Section I-E.The fact that local minima do not seem to be a problem for multilayer NN’s is somewhat of a theoretical mystery. It is conjectured that if the network is oversized for the task(as is usually the case in practice),the presence of “extra dimensions”in parameter space reduces the risk of unattainable regions.Back propagation is by far the most widely used neural-network learning algorithm,and probably the most widely used learning algorithm of any form.D.Learning in Real Handwriting Recognition Systems Isolated handwritten character recognition has been ex-tensively studied in the literature(see[23]and[24]for reviews),and it was one of the early successful applications of NN’s[25].Comparative experiments on recognition of individual handwritten digits are reported in Section III. They show that NN’s trained with gradient-based learning perform better than all other methods tested here on the same data.The best NN’s,called convolutional networks, are designed to learn to extract relevant features directly from pixel images(see Section II).One of the most difficult problems in handwriting recog-nition,however,is not only to recognize individual charac-ters,but also to separate out characters from their neighbors within the word or sentence,a process known as seg-mentation.The technique for doing this that has become the“standard”is called HOS.It consists of generating a large number of potential cuts between characters using heuristic image processing techniques,and subsequently selecting the best combination of cuts based on scores given for each candidate character by the recognizer.In such a model,the accuracy of the system depends upon the quality of the cuts generated by the heuristics,and on the ability of the recognizer to distinguish correctly segmented characters from pieces of characters,multiple characters, or otherwise incorrectly segmented characters.Training a recognizer to perform this task poses a major challenge because of the difficulty in creating a labeled database of incorrectly segmented characters.The simplest solution consists of running the images of character strings through the segmenter and then manually labeling all the character hypotheses.Unfortunately,not only is this an extremely tedious and costly task,it is also difficult to do the labeling consistently.For example,should the right half of a cut-up four be labeled as a one or as a noncharacter?Should the right half of a cut-up eight be labeled as a three?Thefirst solution,described in Section V,consists of training the system at the level of whole strings of char-acters rather than at the character level.The notion of gradient-based learning can be used for this purpose.The system is trained to minimize an overall loss function which measures the probability of an erroneous answer.Section V explores various ways to ensure that the loss function is differentiable and therefore lends itself to the use of gradient-based learning methods.Section V introduces the use of directed acyclic graphs whose arcs carry numerical information as a way to represent the alternative hypotheses and introduces the idea of GTN.The second solution,described in Section VII,is to eliminate segmentation altogether.The idea is to sweep the recognizer over every possible location on the input image,and to rely on the“character spotting”property of the recognizer,i.e.,its ability to correctly recognize a well-centered character in its inputfield,even in the presence of other characters besides it,while rejecting images containing no centered characters[26],[27].The sequence of recognizer outputs obtained by sweeping the recognizer over the input is then fed to a GTN that takes linguistic constraints into account andfinally extracts the most likely interpretation.This GTN is somewhat similar to HMM’s,which makes the approach reminiscent of the classical speech recognition[28],[29].While this technique would be quite expensive in the general case,the use of convolutional NN’s makes it particularly attractive because it allows significant savings in computational cost.E.Globally Trainable SystemsAs stated earlier,most practical pattern recognition sys-tems are composed of multiple modules.For example,a document recognition system is composed of afield loca-tor(which extracts regions of interest),afield segmenter (which cuts the input image into images of candidate characters),a recognizer(which classifies and scores each candidate character),and a contextual postprocessor,gen-erally based on a stochastic grammar(which selects the best grammatically correct answer from the hypotheses generated by the recognizer).In most cases,the information carried from module to module is best represented as graphs with numerical information attached to the arcs. For example,the output of the recognizer module can be represented as an acyclic graph where each arc contains the label and the score of a candidate character,and where each path represents an alternative interpretation of the input string.Typically,each module is manually optimized,or sometimes trained,outside of its context.For example,the character recognizer would be trained on labeled images of presegmented characters.Then the complete system isLECUN et al.:GRADIENT-BASED LEARNING APPLIED TO DOCUMENT RECOGNITION2281assembled,and a subset of the parameters of the modules is manually adjusted to maximize the overall performance. This last step is extremely tedious,time consuming,and almost certainly suboptimal.A better alternative would be to somehow train the entire system so as to minimize a global error measure such as the probability of character misclassifications at the document level.Ideally,we would want tofind a good minimum of this global loss function with respect to all theparameters in the system.If the loss functionusing gradient-based learning.However,at first glance,it appears that the sheer size and complexity of the system would make this intractable.To ensure that the global loss functionwithrespect towith respect toFig.2.Architecture of LeNet-5,a convolutional NN,here used for digits recognition.Each plane is a feature map,i.e.,a set of units whose weights are constrained to be identical.or other2-D or one-dimensional(1-D)signals,must be approximately size normalized and centered in the input field.Unfortunately,no such preprocessing can be perfect: handwriting is often normalized at the word level,which can cause size,slant,and position variations for individual characters.This,combined with variability in writing style, will cause variations in the position of distinctive features in input objects.In principle,a fully connected network of sufficient size could learn to produce outputs that are invari-ant with respect to such variations.However,learning such a task would probably result in multiple units with similar weight patterns positioned at various locations in the input so as to detect distinctive features wherever they appear on the input.Learning these weight configurations requires a very large number of training instances to cover the space of possible variations.In convolutional networks,as described below,shift invariance is automatically obtained by forcing the replication of weight configurations across space. Secondly,a deficiency of fully connected architectures is that the topology of the input is entirely ignored.The input variables can be presented in any(fixed)order without af-fecting the outcome of the training.On the contrary,images (or time-frequency representations of speech)have a strong 2-D local structure:variables(or pixels)that are spatially or temporally nearby are highly correlated.Local correlations are the reasons for the well-known advantages of extracting and combining local features before recognizing spatial or temporal objects,because configurations of neighboring variables can be classified into a small number of categories (e.g.,edges,corners,etc.).Convolutional networks force the extraction of local features by restricting the receptive fields of hidden units to be local.A.Convolutional NetworksConvolutional networks combine three architectural ideas to ensure some degree of shift,scale,and distortion in-variance:1)local receptivefields;2)shared weights(or weight replication);and3)spatial or temporal subsampling.A typical convolutional network for recognizing characters, dubbed LeNet-5,is shown in Fig.2.The input plane receives images of characters that are approximately size normalized and centered.Each unit in a layer receives inputs from a set of units located in a small neighborhood in the previous layer.The idea of connecting units to local receptivefields on the input goes back to the perceptron in the early1960’s,and it was almost simultaneous with Hubel and Wiesel’s discovery of locally sensitive,orientation-selective neurons in the cat’s visual system[30].Local connections have been used many times in neural models of visual learning[2],[18],[31]–[34].With local receptive fields neurons can extract elementary visual features such as oriented edges,endpoints,corners(or similar features in other signals such as speech spectrograms).These features are then combined by the subsequent layers in order to detect higher order features.As stated earlier,distortions or shifts of the input can cause the position of salient features to vary.In addition,elementary feature detectors that are useful on one part of the image are likely to be useful across the entire image.This knowledge can be applied by forcing a set of units,whose receptivefields are located at different places on the image,to have identical weight vectors[15], [32],[34].Units in a layer are organized in planes within which all the units share the same set of weights.The set of outputs of the units in such a plane is called a feature map. Units in a feature map are all constrained to perform the same operation on different parts of the image.A complete convolutional layer is composed of several feature maps (with different weight vectors),so that multiple features can be extracted at each location.A concrete example of this is thefirst layer of LeNet-5shown in Fig.2.Units in thefirst hidden layer of LeNet-5are organized in six planes,each of which is a feature map.A unit in a feature map has25inputs connected to a5case of LeNet-5,at each input location six different types of features are extracted by six units in identical locations in the six feature maps.A sequential implementation of a feature map would scan the input image with a single unit that has a local receptive field and store the states of this unit at corresponding locations in the feature map.This operation is equivalent to a convolution,followed by an additive bias and squashing function,hence the name convolutional network.The kernel of the convolution is theOnce a feature has been detected,its exact location becomes less important.Only its approximate position relative to other features is relevant.For example,once we know that the input image contains the endpoint of a roughly horizontal segment in the upper left area,a corner in the upper right area,and the endpoint of a roughly vertical segment in the lower portion of the image,we can tell the input image is a seven.Not only is the precise position of each of those features irrelevant for identifying the pattern,it is potentially harmful because the positions are likely to vary for different instances of the character.A simple way to reduce the precision with which the position of distinctive features are encoded in a feature map is to reduce the spatial resolution of the feature map.This can be achieved with a so-called subsampling layer,which performs a local averaging and a subsampling,thereby reducing the resolution of the feature map and reducing the sensitivity of the output to shifts and distortions.The second hidden layer of LeNet-5is a subsampling layer.This layer comprises six feature maps,one for each feature map in the previous layer.The receptive field of each unit is a 232p i x e l i m a g e .T h i s i s s i g n i fic a n tt h e l a r g e s t c h a r a c t e r i n t h e d a t a b a s e (a t28fie l d ).T h e r e a s o n i s t h a t i t it h a t p o t e n t i a l d i s t i n c t i v e f e a t u r e s s u c h o r c o r n e r c a n a p p e a r i n t h e c e n t e r o f t h o f t h e h i g h e s t l e v e l f e a t u r e d e t e c t o r s .o f c e n t e r s o f t h e r e c e p t i v e fie l d s o f t h e l a y e r (C 3,s e e b e l o w )f o r m a 2032i n p u t .T h e v a l u e s o f t h e i n p u t p i x e l s o t h a t t h e b a c k g r o u n d l e v e l (w h i t e )c o ro fa n d t h e f o r e g r o u n d (b l ac k )c o r r e s p T h i s m a k e s t h e m e a n i n p u t r o u g h l y z e r o r o u g h l y o n e ,w h i c h a c c e l e r a t e s l e a r n i n g I n t h e f o l l o w i n g ,c o n v o l u t i o n a l l a y e r s u b s a m p l i n g l a y e r s a r e l a b e l ed S x ,a n d l a ye r s a r e l a b e l e d F x ,w h e r e x i s t h e l a y L a y e r C 1i s a c o n v o l u t i o n a l l a y e r w i t h E a c h u n i t i n e a c hf e a t u r e m a p i s c o n n e c t28w h i c h p r e v e n t s c o n n e c t i o n f r o m t h e i n p t h e b o u n d a r y .C 1c o n t a i n s 156t r a i n a b l 122304c o n n e c t i o n s .L a y e r S 2i s a s u b s a m p l i n g l a y e r w i t h s i s i z e 142n e i g h b o r h o o d i n t h e c o r r e s p o n d i n g f T h e f o u r i n p u t s t o a u n i t i n S 2a r e a d d e d ,2284P R O C E E D I N G S O F T H E I E E E ,V O L .86,N O .11,N O VTable 1Each Column Indicates Which Feature Map in S2Are Combined by the Units in a Particular Feature Map ofC3a trainable coefficient,and then added to a trainable bias.The result is passed through a sigmoidal function.The25neighborhoods at identical locations in a subset of S2’s feature maps.Table 1shows the set of S2feature maps combined by each C3feature map.Why not connect every S2feature map to every C3feature map?The reason is twofold.First,a noncomplete connection scheme keeps the number of connections within reasonable bounds.More importantly,it forces a break of symmetry in the network.Different feature maps are forced to extract dif-ferent (hopefully complementary)features because they get different sets of inputs.The rationale behind the connection scheme in Table 1is the following.The first six C3feature maps take inputs from every contiguous subsets of three feature maps in S2.The next six take input from every contiguous subset of four.The next three take input from some discontinuous subsets of four.Finally,the last one takes input from all S2feature yer C3has 1516trainable parameters and 156000connections.Layer S4is a subsampling layer with 16feature maps of size52neighborhood in the corresponding feature map in C3,in a similar way as C1and yer S4has 32trainable parameters and 2000connections.Layer C5is a convolutional layer with 120feature maps.Each unit is connected to a55,the size of C5’s feature maps is11.This process of dynamically increasing thesize of a convolutional network is described in Section yer C5has 48120trainable connections.Layer F6contains 84units (the reason for this number comes from the design of the output layer,explained below)and is fully connected to C5.It has 10164trainable parameters.As in classical NN’s,units in layers up to F6compute a dot product between their input vector and their weight vector,to which a bias is added.This weighted sum,denotedforunit (6)wheredeterminesits slope at the origin.Thefunctionis chosen to be1.7159.The rationale for this choice of a squashing function is given in Appendix A.Finally,the output layer is composed of Euclidean RBF units,one for each class,with 84inputs each.The outputs of each RBFunit(7)In other words,each output RBF unit computes the Eu-clidean distance between its input vector and its parameter vector.The further away the input is from the parameter vector,the larger the RBF output.The output of a particular RBF can be interpreted as a penalty term measuring the fit between the input pattern and a model of the class associated with the RBF.In probabilistic terms,the RBF output can be interpreted as the unnormalized negative log-likelihood of a Gaussian distribution in the space of configurations of layer F6.Given an input pattern,the loss function should be designed so as to get the configuration of F6as close as possible to the parameter vector of the RBF that corresponds to the pattern’s desired class.The parameter vectors of these units were chosen by hand and kept fixed (at least initially).The components of thoseparameters vectors were set to1.While they could have been chosen at random with equal probabilities for1,or even chosen to form an error correctingcode as suggested by [47],they were instead designed to represent a stylized image of the corresponding character class drawn on a7。
冀教版-英语-八上-教案 第7课
Lesson 7: Don’t Be Late for ClassTeaching content:1. Mastery words: geography,sometime ,painter,timetable2. Grasp the patterns:（1）I hope to see them sometime. （2）It’s one of my favourites.（3）I don’t need to be good at it. （4）What time is it ,please? It ‘s 2:13.（5）Class will start in two minutes!3. Learn about “Present Perfect Tense”Teaching goals:Knowledge goal：1.Remember the mastery words.2. Understand the meaning of the dialogue.3. Learn the usage of some phrases.Ability goal：1.Learn how to talk about Preferences . 2.The usage of“Present Perfect Tense”. Emotional goal：Be confident in learning English and dare to express in English.Key points:1. How to talk about Preferences2. The usage of useful patterns.Important points1.What class did you have?2. I hope to see them sometime.3.I don’t need to be good at it.4.What time is it ,please? It ‘s 2:13.5.Class will start in two minutes!Difficult points:Simple Present Perfect TenseTeaching aids:audiotape and slide projectorType: dialogueTeaching procedures:1. Opening classGreet the students in English and make sure they can response correctly.2. New lessonStep 1. PresentationLearning aims: 1. Master the new words.2. Learning the dialogue.Step 2. LearnLearn the following words by yourselves within 3 minutes, and then read and write them. geography,sometime ,painter,timetableStep 3. CheckAsk some students to write the words on the blackboard, read them and tell the other students the meanings of them. Get the students finish slides6-8.Step 4. Lead in1.Ask the following questions:1. How many subjects do you study ? What are they?2. What subject are you good at?2.Show the subject of lesson1Step 5. listenAsk the students to listen to the text twice, then complete Let’s Do It! No.2. Then check the answers as a class.Step 6. Read and answerStudents read the text ,then answer the following questions1. What is Brian’s favourite subject ?2. How many pictures has Brian painted this week?3.What does Jenny think of Brian’s painting?4. What is jenny at art this year?Step 7.Read and discussAsk the students to sit together in small groups, then discuss the language points in the text. Language points1. I hope to see them sometime. .(1)hope to do sth. ，表示希望干某事，相当于句型：wish to do sth.e.g. I hope to see my friends as soon as possible.(2)I hope so或I hope not. 用于简略回答e.g. –can your friend come tomorrow?- I hope so或I hope not.(3) hope +句子e.g. I hope I will have fish for super.2. I don’t need to be good at it.don’t need to do sth.=needn’t do sth.3.What time is it ? 表示“几点了”之意。
1997年专业英语四级真题试卷(题后含答案及解析)
1997年专业英语四级真题试卷(题后含答案及解析)题型有：1. DICTATION 2. LISTENING COMPREHENSION 3. CLOZE 4. GRAMMAR & VOCABULARY 5. READING COMPREHENSION 6. WRITINGPART I DICTATION (15 MIN)Directions: Listen to the following passage. Altogether the passage will be read to you four times. During the first reading, which will be read at normal speed, listen and try to understand the meaning. For the second and third readings, the passage will be read sentence by sentence, or phrase by phrase, with intervals of 15 seconds. The last reading will be read at normal speed again and during this time you should check your work. You will then be given 2 minute 1．正确答案：Legal Age for Marriage Throughout the United States, the legal age for marriage shows some difference. The most common age without parents’ consent is 18 for both females and males. However, persons who are under age in their home state can get married in another state, and then return to the home state legally married. Each state issues its own marriage license. Both residents and non-residents are qualified for such a license. The fees and ceremonies vary greatly from state to state. Most states, for instance, have a blood test requirement, but a few do not. Most states permit either a civil or religious ceremony, but a few require the ceremony to be religious. In most states a waiting period is required before the license is issued. This period is from one to five days depending on the state. A three-day-wait is the most common. In some states there is no required waiting period.PART II LISTENING COMPREHENSION (20 MIN)Directions: In Sections A, B and C you will hear everything ONCE ONLY. Listen carefully and then answer the questions that follow. Mark the correct answer to each question on your answer sheet.SECTION C NEWS BROADCASTDirections: In this section, you will hear several news items. Listen to them carefully and then answer the questions that follow.听力原文：The authorities in Hong Kong have released the second group of Vietnamese boat people from detention after Vietnam refused to accept them. The group of sixteen have been detained in 1991 when they entered Hong Kong. The release last month of more than 100 boat people in Hong Kong caused protest from local residents opposing any move to allow the boat people to stay permanently. There are still some 24,000 Vietnamese boat people in detention camps in Hong Kong.2．What are the attitudes of the local residents?A．They protested against detaining boat people.B．They protested against letting them stay forever.C．They urged Vietnam to accept the boat people.D．They urged Britain to accept the boat people.正确答案：B听力原文：NATO troops are to join their former Cold War enemies in training exercises in Poland this week. The drills which will begin on the 17th are the first major joint exercises of the Western and Eastern armies under NATO’s partnership. Some 900 soldiers from 13 countries will take part. NATO says it will be a good way to share peace-keeping experiences and develop a common understanding of operational procedures.3．NATO troops will join in______.A．Cold War.B．training exercises.C．Western armies.D．Eastern armies.正确答案：B4．Soldiers from _________ countries will participate.A．17B．30C．13D．43正确答案：C听力原文： A twenty-year action plan for cutting the rate of world population growth is expected to win wide approval today in Cairo. Delegates at the UN-sponsored conference on population complete the final talks on the plan Monday. The document is non-binding but it will serve as a guideline for countries and states that fund health care and family planning programs. The world population of 5.7 billion currently is growing at more than 90 million a year.5．Who sponsored the conference on population?A．Cairo.B．The United Nations.C．The World Bank.D．The World Health Organization.正确答案：B6．The current rate of annual increase in the world population is about______.A．9 million.B．5.7 millionC．90 million.D．20 million.正确答案：C7．Which of the following concerning the document is NOT true?A．The document will cover the next two decades.B．The document will win support from the delegates.C．The document will serve as a guideline.D．The document will be completed after the conference.正确答案：D听力原文：In the Philippines a ferry carrying at least 400 people has sunk after an apparent collision with a cargo ship. There was no immediate report of casualties. The accident occurred at about 11:30 a. m. , local time, at the mouth of Manila Bay shortly after the ferry left the Manila port. A Philippines coast guard’s spokesman said the ferry had been hit by a 12,000 ton Singapore registered cargo vessel. Further details were not immediately available.8．The news item reported a(n)______.A．air crash.B．traffic accident.C．lorry crash.D．ferry accident.正确答案：D9．It was reported to have occurred______.A．inside Manila’s port.B．in Singapore.C．near the Manila Bay.D．in Malaysia.正确答案：C10．There were _________ people on board.A．30B．400C．110D．120正确答案：B听力原文：John met me at the door and said his dormitory wasn’t full, but in fact it was.11．What does the speaker mean?A．John was unhappy with his dormitory.B．John’s dormitory wasn’t full.C．John didn’t meet me at the door.D．There wasn’t any vacant room.正确答案：D听力原文：We just can’t get over the fact that Jane failed while Mary succeeded.12．What does the statement imply?A．We are sorry that we both failed.B．Mary is envious of Jane’s success.C．We are amazed by the fact.D．Jane is envious of Mary’s success.正确答案：C听力原文：At the moment there was no course I enjoyed more than composition.13．The speaker thinks thatA．writing is his favourite course.B．he prefers other courses to composition.C．one particular course is better than writing.D．he doesn’t like any course, least of writing.正确答案：A听力原文：If I had known the exercises should be handed in today, I’d have finished them yesterday.14．What does the speaker imply?A．He didn’t finish the exercises yesterday.B．The exercises were handed in yesterday.C．He knew the exercises should be handed in today.D．He doesn’t need to hand in the exercises today.正确答案：A听力原文：I woke up at 8:30, knowing that the appointment was at 9:45, butdespite all my plans, I still got there at 10:00.15．The speaker was_________ minutes late.A．50B．15C．30D．10正确答案：B听力原文：If only I had paid more attention to my spelling in the examination.16．What does the statement mean?A．The speaker didn’t attend the exam.B．The speaker didn’t do the spelling.C．The speaker was good at spelling.D．The speaker ignored his spelling.正确答案：D听力原文：Come in, John. Please excuse the mess. We only moved in here a month ago and we’re in the middle of house decoration.17．According to the statement, the house is______.A．badly built.B．noisy inside.C．very dirty.D．in disorder.正确答案：D听力原文：David decided to take the overnight express train to Rome. Usually he would have gone by plane. But now he wanted to have some time on his own before he got back home.18．David decided to take the express train because______.A．he was in a hurry to get home.B．he did not enjoy flying at all.C．he needed time to be on his own.D．he had booked a seat on the train.正确答案：C听力原文：My students went camping last weekend. They had a wonderful time and they stayed warm and dry in spite of the weather.19．The weather last weekend was______.A．warm and dry.B．cold and wet.C．cool and crisp.D．sunny and lovely.正确答案：B听力原文：A: Why did you get up at 6:40 ? I thought your meeting wasn’t until 10:30.B: I wanted to visit the park before I left. It’s the first time I’ve seen it.20．Between getting up and her meeting, the woman had about______.A．6 hours.B．40 minutes.C．4 hours.D．30 minutes.正确答案：C听力原文：A: London is a gorgeous city. From here you can see the Palace Skies.B: Wait until we can get to Paris and Madrid. And don’t forget about Rome.21．The conversation probably took place in______.A．Rome.B．Paris.C．London.D．Madrid.正确答案：C听力原文：A. Do you have any idea what the passage is about?B: I’m as much in the dark as you are.22．What does the woman mean?A．She hasn’t read the passage.B．She doesn’t understand it either.C．She cannot read it in darkness.D．She suggests that the man read it.正确答案：B听力原文：A: I’d like to apply for the position you have advertised in China Daily.B: A good command of English and computing is a must as far as the position is concerned.23．What does the woman mean?A．The job is advertised in English.B．The advertisement is in an English paper.C．She offers the man English and computer skills.D．English and computer skills are essential for the job.正确答案：D听力原文：A: I see that Vincent is smiling again.B: Yes, he decided to speak to his boss’s mother about his problem at work rather than to go directly to his boss.24．Vincent solved his problem by______.A．going directly to the boss.B．talking to his parents.C．asking his mother to speak to his boss.D．telling his boss’ mother about it.正确答案：D听力原文：A: We got the computer repaired last week.B: Oh, so it could be fixed.25．What had the woman assumed?A．They had received a broken computer.B．She knew how to repair the computer.C．The computer couldn’t be fixed.D．They’d have to buy another one.正确答案：C听力原文：A: There was a storm warning on the radio this morning. Did you happen to be listening?B: No, but what a shame! I guess we’ll have to change our sailing plans. Would you rather play golf or go cycling?26．The couple had previously planned to______.A．go boating.B．play golf.C．go cycling.D．play tennis.正确答案：APART III CLOZE (15 MIN)Directions: There are 20 blanks in the following passage. Decide which of the choices given below would best complete the passage if inserted in the corresponding blanks.Unlike most sports, which evolved over time from street games, basketball was designed by one man to suit a particular purpose. The man was Dr. James Naismith, and his purpose was to invent a vigorous game that could be played indoors in the winter.In 1891, Naismith was an instructor at a training school, which trained physical education instructors for the YMCAs. That year the school was trying 【B1】______ up with a physical activity that the men could enjoy 【B2】______ the football and baseball seasons. None of the standard indoor activities 【B3】______ their interest for long. Naismith was asked to solve the problem by the school. He first tried to 【B4】______ some of the popular outdoor sports, but they were all too rough. The men were getting bruised from tackling each other and 【B5】______ hit with equipment. So, Naismith decided to invent a game that would incorporate the most common elements of outdoor team sports without having the real physical contact. Most popular sports used a ball. So he chose a soccer ball because it was soft and large enough that it【B6】______ no equipment, such as a bat or a racket to hit it. Next he decided 【B7】______ an elevated goal, so that scoring would depend on skill and accuracy rather than on 【B8】______ only. His goals were two peach baskets, 【B9】______ to ten-foot-high balconies at each end of the gym. The basic 【B10】______ of the game was to throw the ball into the basket. Naismith wrote rules for the game, 【B11】______ of which, though with some small changes, are still 【B12】______ effect.Basketball was an immediate success. The students【B13】______ it to their friends, and the new sport quickly 【B14】______ on. Today, basketball is one of the most popular games 【B15】______ the world.27．【B1】A．to have comeB．comingC．comeD．to come正确答案：B解析：语法知识。
dp杂题
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DP 杂题选讲
Badania naukowe
设 f(i, j) 为 A[1..i] 与 B[1..j] 的 LCS，g(i, j) 为 A[i..n] 与 B[j..m] 的 LCS。
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Claris
DP 杂题选讲
Nim z utrudnieniem
A 和 B 两个人玩游戏，一共有 m 颗石子，A 把它们分成了 n 堆，每堆石子数分别为 a1 , a2 , ..., an 。每轮可以选择一堆石子， 取掉任意颗石子，但不能不取。谁先不能操作，谁就输了。 在游戏开始前，B 可以扔掉若干堆石子，但是必须保证扔掉 的堆数是 d 的倍数，且不能扔掉所有石子。A 先手，请问 B 有 多少种扔的方式，使得 B 能够获胜。 1 ≤ n ≤ 500000, 1 ≤ d ≤ 10, 1 ≤ ai ≤ 106 , m ≤ 107 。 Memory Limit: 64MB Source：POI 2016
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Claris