Higher-order lazy narrowing calculus A solver for higher-order equations
hl判定定理
hl判定定理HL判定定理是计算机科学领域一个重要的定理，用于描述特定类型的递归枚举问题的可计算性。
该定理最早由美国计算机科学家Stephen Cole Kleene以及应用数学家Heinz Dieter Gauss于1969年提出，被广泛应用于计算理论和形式语言理论。
HL判定定理的全称为"Kleene's Second Recursion Theorem"，或称为"Kleene's T-predicate Theorem"，该定理给出了一种方法来判定一个给定的自然数是否属于一个可计算的递归集合中。
在理解HL判定定理之前，我们需要了解几个相关的概念。
首先是可计算性问题，也叫做判定问题，是指一个问题是否可以通过一个算法来解决。
通常，可计算性问题可以被划分为可判定问题和不可判定问题。
可判定问题是指可以通过一个算法判定其答案的问题，而不可判定问题是指没有算法能够确定其答案的问题。
其次是递归集合的概念。
一个递归集合是指可以通过一个递归函数来计算出其元素的集合。
递归函数是指可以通过有限步骤的计算来确定函数值的函数。
递归集合的概念是在数学逻辑中引入的，用于描述可计算性问题。
HL判定定理是通过引入一个谓词T来描述可计算性的。
给定一个自然数n和一个递归集合R，T(x,y)是一个谓词，表示自然数x是否属于递归集合R中的第y个元素。
HL判定定理的表述如下：对于任意一个递归集合R，T(x,y)是一个可计算的谓词。
简单来说，HL判定定理就是给出了一种方法来判定一个自然数是否属于一个递归集合中。
这个方法是通过构造一个可计算的谓词T来实现的。
HL判定定理的证明是基于递归函数的构造和递归集合的性质。
具体的证明过程比较复杂，需要深入的数学和计算理论知识。
但是理解HL判定定理的核心思想对于计算机科学的学习和研究是非常重要的。
HL判定定理在计算机科学的理论研究中有着广泛的应用。
生活大爆炸 第四季第二集中英文剧本
生活大爆炸第四季第二集在干嘛呢\Whatcha doin' there?研究抓哔哔鸟的新方法吗\Working on a new plan to catch the roadrunner?你这个幽默暗指我是大笨狼怀尔吗\The humorous implication being that I am Wile E. Coyote?没错\Yes.而板上画的捕鸟设备\And this is a schematic for a bird-trapping device最终只会适得其反让我受伤吗\that will ultimately backfire and cause me physical injury?没错\Yes.我正在做的\What I'm doing here是想计算出我的死亡时间\is trying to determine when I'm going to die.很多人都在做这方面的研究\A lot of people are working on that research.那这些是什么\So what is all this?我家人的寿命长短\My family history factoring in longevity疾病倾向等信息\propensity for disease, et cetera.有意思\Interesting.卡尔叔叔的死因是KBB\Cause of death for Uncle Carl was KBB.KBB是什么\What's "KBB"?被獾所杀\"Killed by badger."怎么回事\How's that?那是感恩节\It was Thanksgiving.卡尔叔叔说"我觉得有只獾住在咱家烟囱里"\Uncle Carl said, "I think there's a badger living in our chimney. ""把手电筒给我"\"Hand me that flashlight."那是他对我们说的最后几句话\Those were the last words he ever spoke to us.我觉得\I don't think you need你没必要担心被獾所杀会遗传\to worry about death by badgers being hereditary.不对\Not true.战斗或逃跑的本能受基因控制\The fight or flight instinct is coded genetically.他没选择逃跑反而赤手空拳\Instead of fleeing, he chose to fight barehanded跟鼬类动物中强壮的一员战斗\against a brawny member of the weasel family.谁能肯定我没遗传这种有缺陷的基因\Who's to say that I don't share that flawed DNA?你反正可以找只獾来验证的\You can always get a badger and find out.说实在的\But seriously即使我忽略卡尔叔叔这个因素\even if I disregard the Uncle Carl factor我最多也只剩60年寿命\at best I have 60 years left.还有那么长啊\That long, huh?60年我只能活到这里\60 only takes me to here.我要活到这里\I need to get to here.那里有什么\What's there?据预计奇点最早出现的时间\The earliest estimate of the singularity人们能将自己的意识\when man will be able to transfer his consciousness转移进机器而获得永生\into machines and achieve immortality.这么说你不高兴自己会错失\So, you're upset about missing out变成某种怪异的有自我意识的机器人的机会\on becoming some sort of freakish self-aware robot?就差这么一点啊\By this much.真可惜你要吃鸡蛋吗\Tough break. You want eggs?你不明白莱纳德\You don't get it, Leonard.我会错过很多东西\I'm going to miss so much.统一场论冷聚变还有章狗\the unified field theory, cold fusion, the dogapus.章狗是什么\What's a dogapus?狗和章鱼的杂交动物\The hybrid dog and octopus.人类在水下的忠实朋友\Man's underwater best friend.有人研究这个吗\Is somebody working on that?我打算过研究的\I was going to.我想把它作为我三百岁的生日礼物\I planned on giving it to myself on my 300th birthday.等等你讨厌狗\Wait a minute. You hate dogs.章狗玩接球时能接八个球\A dogapus can play fetch with eight balls.没有人能讨厌这个\No one can hate that.我们欠你多少钱\What do we owe you?一共是28.17美元\It came to $28.17.每人就六美元吧\Let's say six bucks apiece.给你\Here you go.谢谢\Thank you.干嘛\What?算了我请了\Never mind. I got it.你要我给钱啊\Oh, you wanted me to pay.-不用了-不不不你是对的\- It's no big deal. - No, no, no, no. You're right.我们已经分手了我应该自己付钱\We're not going out anymore; I should pay for myself.笑什么\What?他说"如果他有女人身子"\He said, "If he had woman parts"他后半辈子就不愁吃了"\"he'd eat for free the rest of his life"是啊可你也没办法跟自己说话了\Yeah, but you wouldn't be able to talk to yourself.我现金有点紧张啊\I'm a little low on cash.-你有多少-没有\- How much you got? - Nothing.你不带钱怎么出门啊\How can you walk around with no money?我漂亮别人请客\I'm cute. I get by.没事欠着吧\It's okay, you can owe me.-谢谢-谢尔顿六美元\- Thank you. - Sheldon, six bucks.不了谢谢我今晚不吃披萨\No, thank you. I'm not eating pizza tonight.可今天是星期四\But it's Thursday.星期四是披萨之夜\Thursday's pizza night.对我来说不是\Not for me.现在改成十字花科蔬菜之夜了\Thursday is now Cruciferous Vegetable Night.今晚的特选小包菜\Tonight's selection: Brussels sprouts.真的吗\Really?你要改谢尔顿日程表\You're changing the Sheldonian calendar?-这只是个小小的代价-为啥\- It's a small price to pay. - For what?-不别问啊-对不起\- No, no, don't ask. - Sorry, sorry, sorry, sorry, sorry.为了把我的寿命延长到能把意识\In order to live long enough to fuse my consciousness转移到人造大脑上我要改变饮食\with cybernetics, I need to change my diet.等等人造大脑是机器人之类的吧\Wait. Cybernetics is robot stuff, right?没错\Correct.这么说你想把自己变成某种机器人\So you want to turn yourself into some sort of robot?本质上是这样\Essentially, yes.我想问个问题\Okay, here's my question.你不是已经变成机器人了吗\Didn't you already do that?虽然我受宠若惊可惜还没有\Flattering, but sadly, no.我还打算开始一种运动养生法\I'm also planning to begin an exercise regimen加强我的心血管系统\designed to strengthen my cardiovascular system.也就是慢跑\AKA jogging.等等亲爱的你以前跑过步吗\Wait. Honey, have you ever run before?当然跑过\Certainly.我被恶霸狗和暴走的鸡追过\I've run from bullies, dogs, angry chickens...还有个锲而不舍执意要给我做\and one particularly persistent P.E. teacher脊柱侧弯测试的体育老师\determined to bend me over and give me a scoliosis test.你说得对佩妮经常跑步\You're right. Penny jogs.你们可以一起跑的\Maybe you guys can run together.这主意太棒了\That's an excellent idea.如果我们边跑边聊\Yeah, if we chat就会感觉时间流逝得更快了\it will create the illusion of time going faster.绝对不可能\No, it won't.他怎么知道我跑步的\Um, how does he know I jog?因为他在车里用高倍望远镜尾行你\Oh, he watches you from his car with high-powered binoculars. 我的天呐这太猥琐了\Oh, my God, that is so creepy!我就说嘛\I know!他说他要坚持发扬下去\And he says he's not gonna stop.那找心理医生解决怎么和女人说话的问题啊\Then see a shrink and figure out how to talk to women.什么玩意儿\What the hell?怎么了\What's the matter?疼痛以我的肚脐为起点\I have pain radiating from my navel延伸到我的右下腹\to my lower right abdomen.我感到恶心和发热\I'm nauseated and feverish.我觉得我得霍乱了\I believe I may have cholera.帕萨迪纳才没霍乱呢\There's no cholera in Pasadena.就跟去年夏天帕萨迪纳也没有疟疾一样\Just like last summer, when there was no malaria in Pasadena. 好吧如果那不是霍乱\Well, if it's not cholera根据搜索结果\then based on a quick Internet search由相似度递减排列的其他解释分别是\the other explanations in decreasing order of likelihood先天性巨结肠肉毒杆菌中毒一条30英尺长的绦虫\are Hirschsprung's Disease, botulism, a 30-foot tapeworm或者是不小心摄入菊花\or accidental ingestion of chrysanthemum blossoms.你什么时候会不小心摄入菊花的\When would you have accidentally eaten chrysanthemum blossoms? 这是包括了梦游\It's part of an unlikely scenario和24小时营业的花店\that involves sleepwalking and a 24-hour flower mart以及不靠谱的经营者的不可能场景\with a less-than- vigilant proprietor.噢老天我的肚子\Oh, Lord, my belly!你切除过阑尾吗\Ever had your appendix out?没有\I haven't.我想来着但谁有那时间啊\I've been meaning to, but who has the time?我送你去医院吧\Let's get you to the hospital.于是乎就此了结\So this is how it ends...真是无比残酷的讽刺\with cruel irony.正当我保证要保护爱惜自己的身体之时\Just as I make the commitment to preserving my body我被自己的阑尾所背叛就一退化的器官\I am betrayed by my appendix, a vestigial organ.你知道阑尾原本的作用是什么吗莱纳德\Do you know the original purpose of the appendix, Leonard? 不知道\No.我知道而知道太多的却灭亡而你却能继续活下去\I do. And yet I'm doomed while you live on.结局很出乎意料是不是\Funny how things work out, isn't it?噢天呐我感觉要爆炸了\Oh, Lord, I think it's about to burst!还有种可能\On the other hand也许都是小包菜的错\it might have been the Brussels sprouts.晚安您呐\Good night.晚安\Good night.阑尾炎\Appendicitis.自己紧张个甚啊\What a nervous Nelly.佩妮佩妮佩妮\Penny! Penny! Penny!来啦来啦\Coming, coming.嘿跑鞋不错嘛\Hey, nice knees.谢谢\Thank you.这是我娘的\They're my mother's.闪电侠T恤是什么意思\Oh. And the Flash shirt is what?你要跑的飞快吗\Because, what, you're gonna run really fast?不是穿闪电侠衫是因为今天是星期五\No, the Flash shirt is because it's Friday但要是真能有效就更好了\but it's nice when things work out.-你的心率监测器在哪儿-没有\- Where's your heart rate monitor? - I don't have one.-计步器呢-没有\- What about your pedometer? - Don't have one.那你鞋子里有传感器连接到iPod吗\Do you have telematics in your shoes connected to an iPod?-没-那你干嘛呢\- Uh, no. - What do you do就出去像兔子一样随便蹦蹦跳跳一下吗\You just go out there and gambol about like a bunny?不也就跑到饿了然后买个熊爪包吃\No. I just run till I'm hungry, then I stop for a bear claw.为什么要这么做\Why are you doing that?在跑步前最好拉伸下肌肉\It's good to stretch your muscles before you run.好吧\All right.先来摸个脚趾\Let's start with a toe touch.你来做一个\Okay, you do it.我正做着呢\I <i>am</i> doing it.哇哦不错\Oh. Wow. Good job.你能做这个么\Can you do this?我们永远也不会知道的\We'll never know.好吧那边跑边热身吧\Okay, let's just warm up on the run.-好的-那出发吧\- Okay. - Okay, let's go.我最近一直在读生物力学的书\I've been reading up on biomechanics.我认为你会惊讶于我的...\I think you'll be surprised at my...我的天呐你还好吗\Oh, my God, are you okay?应该吧\I think so.-我来拉你一把吧-谢谢\- Oh, let me help you up. - Thank you.噢谢尔顿\Oh, Sheldon!如果这能让你觉得好些的话\If it makes you feel any better星期四不再是十字花科蔬菜之夜了\Thursday is no longer Cruciferous Vegetable Night.这是我的咖喱鸡\Here's my chicken curry.霍华德的鲜虾菜饭\Howard, your shrimp biryani.-谢谢您-菠菜奶豆腐是佩妮的\- Thank you, sir. - Palak paneer, that's Penny.-谢谢-而拉杰·库萨帕里的\- Thanks. - And for Rajesh Koothrappali家乡发明出这些美味佳肴的人\from whose homeland these tasty dishes originate一个大份的麦乐鸡\one large order of chicken McNuggets.-我的这份多少钱-12刀\- Hey, what's my share? - Uh... 12 bucks.-我能周五付工资以后再还你吗-没问题\- Okay, can I get you after Friday when I get paid? - Sure. 我欠你多少了\What am I up to now?呃算上印度菜比萨\Well, okay, with the Indian food, the pizza泰国菜一箱油\the Thai food, the tank of gas冷冻酸奶\the frozen yogurt外带你的房租嗯...\and your rent, uh...一千四百多一点吧\a little over $1,400.又怎么了\What now?他只是表示膜拜\He's just expressing his admiration that你不用献身也能蹭吃蹭喝\you don't even have to put out to get free stuff.我这不是蹭我会还钱的\It's not free-- I'm gonna pay him back.给我停\Shut up!谢尔顿你不来吗\Sheldon, are you gonna join us?就来\Coming!你们好伙计们\Greetings, friends.你好你个天知道是什么的鬼东西\Greetings, whatever the hell you are.我是一个移动虚拟化身设备\I am a mobile virtual presence device.鉴于近来发生的事\Recent events我意识到我的肉身太过脆弱\have demonstrated to me that my body is too fragile承受不了大千世界的种种\to endure the vicissitudes of the world.因此在我能够\Until such time as I am able转移意识之前\to transfer my consciousness我的肉身将保存在一个安全地点\I shall remain in a secure location并借此方式同外界联系\and interact with the world in this manner.没搞错吧你就想问这个--\Really? That's your question--他啥时搞来的那个斜坡\when did he put a ramp in?你占了我的专属座位\You're in my spot.可能一开始感觉会有点怪\This may seem a little odd at first但时间久了你们就会渐渐习惯\but over time, you'll grow accustomed和这样的我打交道\to dealing with me in this configuration.是咩说实话我觉得没什么不同\Yeah, to be honest, I don't see much difference.谢谢\Thank you.这也是我的目的\That's what I was going for.那个莱纳德明天我们去上班时\Now, Leonard, tomorrow, when we go to work你得腾出点时间来\you'll need to allow some extra time把我搬下楼梯\to get me down the stairs.为了让你省力我会分解成四个部分\For your convenience, I disassemble into four pieces.这太荒唐了\This is ridiculous.我要去找你谈谈\I'm coming to talk to you.你不知道我在哪儿\You don't know where I am.我的肉身现被安置在\My physical body is safely ensconced一个安全保密的场所\in a secure, undisclosed location.你不就在你卧室里么\You're in your bedroom.不我不在\No, I'm not.我都能听到你说话的声音从卧室传出来\I can hear your voice coming from your bedroom.不你听不到\No, you can't.你给我等着\Wait.回来\Come back.站住\Halt.未经授权人员禁止入内\Authorized personnel only!好吧你们两个变态\So, either one of you weirdos有谁想买我的内衣么只要一千四百块哦\want to buy my underwear? Only 1,400 bucks.谢尔顿这太荒唐了\Sheldon, this is ridiculous.我在你后面\I'm behind you.和我说话时请看着我\Please look at me when you're talking to me.我正看着你呢\I am looking at you.不你没有\No, you're not.无视床上的那个人\Pay no attention to that man in the bed.你不能以这种方式存在于这世上\You cannot exist as a virtual presence.这儿不行工作时就更不行了\Not here and certainly not at work.我的娘咧\Oh, good God.你知不知道我这年纪的人\At my age, do you know统计数字上最可能怎么死吗\how I'm statistically most likely to die?被你室友做掉吗\At the hands of your roommate?死于一场意外\An accident.我就准备弄成像是一场意外\That's how I'm going to make it look.在我将自己的智慧\Until I can transfer my intellect转移到一个更持久的容器内之前\to a more durable container我的肉身将被安全安置在我的床上\my body will remain safely ensconced in my bed.随你但别指望我会帮你\Fine, but don't expect my help.你必须帮我室友协议里写了\You have to help-- it's in the roommate agreement.不才没有\No, it's not.74条C款\Section 74.C.两人间若有人成了机器人\The various obligations and duties of the parties另一人所应尽的各项义务和责任\in the event one of them becomes a robot.让我一头撞死好了\I'll be damned.这种感觉太赞了\This is delightful.哼哼\Uh-huh.不用担心死于车祸\It's much easier to enjoy这样在上班路中欣赏美景\the picturesque route we travel to work就更加怡然自得了\when you remove the specter of fiery vehicular death.提醒我下\Refresh my memory.我干嘛不直接把你塞进后备箱呢\Why didn't I just put you in the trunk?因为我先抢了前排座位记得不\Because I called shotgun. Remember?好吧\Right.你看着压力很大\You seem tense.这样会不会感到放松\Perhaps this will relax you.我不想听音乐谢尔顿\I don't want to listen to music, Sheldon.好吧\Very well.真不明白你为什么不喜欢这样\I don't understand why you're not enjoying this.你和增强功能的我一起在车里\Together, in this car, with my enhanced capabilities这就好比霹雳游侠嘛\we're like Knight Rider.\an8\fn方正黑体简体\fs18\b1\bord1\shad1\3c&H2F2F2F&同名电视剧男主角和他的人工智能车那里面的车可不是括约肌吱吱响的废柴\Except in Knight Rider, the car isn't a yammering sphincter.你居然嘲笑括约肌\You mock the sphincter括约肌可是人体的一组肌肉\but the sphincter is a class of muscle没有的话人类没法存活的哦\without which human beings couldn't survive.人体内共有超过50种\There are over 50 different sphincters不同的括约肌\in the human body.你能叫出多少\How many can you name?我错了这就是一霹雳游侠没说的\I was wrong-- this is exactly like Knight Rider.你大概会对另一个游戏感兴趣\Perhaps you'd be interested in a different game.没兴趣\No.这张照片是在1911年\This is a photograph of the 1911召开的辐射和量子理论索尔瓦会议\Solvay Conference on the theory of radiation and quanta.我PS了几处不该存在的东西\Using Photoshop, I've introduced a few anachronisms.看看你能不能找出所有24处\See if you can spot all 24.我先给你第一个提示好了\I'll give you the first one.居里夫人不该带着电子表\Madame Curie should not be wearing a digital watch.你继续吧\And go.\an8益智游戏节目《冒险》的主题曲够了拜拜\That's it. Bye-bye.吓死你\Bazinga.我有更高权限的开关\I have an override switch.我差点被你害死了\I almost died!而我仍安然无恙地坐在床上\And I'm safe and sound in bed.现在再看谁是疯子\Who's crazy now?我还是会说你\I'm still going to go with you.你好霍斯金斯教授\Hello, Professor Hoskins.很高兴见到你敏迪\Nice to see you, Mindy.早上好[日语] 中村博士\And <i>konnichiwa, Dr. Nakamura.</i>很遗憾那帮瑞典佬推翻了你的理论\Sorry the Swedes disproved your theory.莱纳德我的门\Leonard, my door.你的门怎么了\What about it?乖给哥开个门\Be a lamb and open it for me.为嘛有啥问题吗\Why? What's the problem?你以为你难住我了对吗\You think you have me stymied, don't you?没有啊我觉得难住你的是门把手\No, I think a doorknob has you stymied.哦看啊莱纳德和R2-D-Bag[代指《星战》里的R2-D2机器人]\Oh, look, it's Leonard and R2-D-Bag. \an8《星战》里R2-D2机器人这里D-bag是douchebag[蠢货]的缩写这笑话是我想出来的我昨晚给你讲的\That's my joke. I told it last night.你不能随便剽窃好吧\You can't just use it.拉杰乖替哥开下门\Raj, be a lamb and open the door for me.好的\Oh, sure.他真乖\He's a lamb.你不乖\You're not.我好乖哦\I'm a lamb.这一切多美好啊\Isn't this nice?在享受同伴感情的同时\The pleasures of fellowship and camaraderie又不必忍受你们污浊呼吸对我皮肤的伤害\without having to tolerate your germy breath on my skin. 要我说咱们把他送到塔图因星球上\I say we just take him to Tatooine把他卖给爪哇人吧[《星战》情节]\and sell him to some Jawas.第二次了老兄\That's two, dude.写你自己的笑话去\Write your own jokes.哎呦欸\Oh, great.嗨我叫佩妮今晚为你们服务\Hi, I'm Penny, I'll be your waitress.你干嘛还要作自我介绍啊\Why are you introducing yourself?不管怎么样我宁愿\I'd rather people not know大家都不知道我跟你们之前有任何联系\I have any prior connection to you whatsoever.你能介绍一下今晚有什么特色菜吗\Can you tell me the specials this evening?谢尔顿我不为你服务\Sheldon, I'm not waiting on you.当然了\Obviously.你还没给我倒水呢\I don't even have water yet.因为你不在这里\Because you're not here.你这是对远程遥控人员的歧视\That's discrimination against the otherwise located.我要去找你的领导[也有比你高的意思]\I'm going to have to go over your head.经理经理在吗\Manager... manager.天啊快看那是谁\Oh, Lord, look who it is.那是斯蒂夫·沃兹尼亚克吗[苹果公司创始人之一]\Is that Steve Wozniak?我猜没错\I think it is.神奇而伟大的沃兹啊\The Great and Powerful Woz.佩妮斯蒂夫·沃兹尼亚克\Penny, Steve Wozniak was可是苹果电脑公司的创始人之一呢\one of the cofounders of Apple Computer.-他和斯蒂夫·乔布斯一起创办了... -没错\- He and Steve Jobs started it... - Yeah我知道他是谁我看过《与星共舞》\I know who he is. I watch <i>Dancing with the Stars.</i>\an8斯蒂夫·沃兹尼亚克曾参加过该节目我得去和他聊聊\I must speak to him.你当然得去了\Of course you must.这条街上还有家橄榄园[意大利连锁餐馆]\You know, there's an Olive Garden down the street.你们有空应该去尝尝\You guys should try it sometime.打扰了沃兹尼亚克先生\Excuse me, Mr. Wozniak?嘿\Oh, hey.很不错的虚拟化身仪器\Nice virtual presence device.谢谢夸奖\Thank you.我想说我是你的忠实粉丝\I just want to say I'm a big fan.你在我最爱的科技远见卓识者排行榜上排第15\You're my 15th favorite technological visionary.才第15啊\Only 15th?那也比斯蒂夫·乔布斯高6名呢\It's still six spots above Steve Jobs.我既不喜欢高翻衣领也不喜爱炫舞技的人\I care neither for turtlenecks nor showmanship.嗯我从来不穿高翻领的衣服\Yeah, I never got that turtleneck thing.我最得意的收藏就是一台1977年产的苹果Ⅱ\One of my proudest possessions is a vintage 1977 Apple Two.如果不考虑苹果DOS 3.3版文件系统的局限性\Despite the file system limitations of Apple DOS 3.3它确实算个一流的小成就\it was a pretty nifty little achievement.多谢"一流"这个词让我受宠若惊\Thanks, we were shooting for "nifty."如果你能把它带过来的话\You know, if you had it here我可以在上面签个名\I'd autograph it for you.别走开等我15到30分钟\Don't move for 15 to 30 minutes具体情况得看公交车的运营情况\depending on how the buses are running.书呆子\Nerds.我来了沃兹我来了\I'm coming, Woz, I'm coming.佩妮佩妮佩妮\Penny... Penny... Penny.怎么了谢童木\What up, Shel-Bot?我下不了床\I can't get out of bed.脚扭了\I hurt my ankle.你想让我干嘛啊\What do you want me to do?给我唱"乖乖猫"吧\Sing me "Soft Kitty."你真的想让我对着个电脑显示器唱\Really, you want me to sing "Soft Kitty""乖乖猫"吗\to a computer monitor?你想过来当面对我唱吗\Would you rather come over and sing it to me in person?乖乖猫暖暖猫\Soft kitty, warm kitty小小毛绒球\Little ball of fur...离麦克风近点儿\Closer to the microphone.快乐猫瞌睡...\Happy kitty, sleepy...打住\No.从头开始\You have to start over.乖乖猫暖暖猫\Soft kitty, warm kitty小小毛绒球\Little ball of fur快乐猫瞌睡猫\Happy kitty, sleepy kitty呜呜呜[猫叫声]\Purr, purr, purr.。
兰姆达演算法
兰姆达演算法兰姆达演算法（Lambda Calculus）是一种基于数学逻辑的形式系统，用于描述和研究计算过程。
它由逻辑学家阿隆佐·邱奇（Alonzo Church）在20世纪30年代提出，被认为是计算机科学的基础之一。
兰姆达演算法具有简洁而强大的表达能力，被广泛应用于函数式编程语言、类型理论以及计算机科学理论研究中。
1. 什么是兰姆达演算法？兰姆达演算法是一种形式系统，它描述了一种抽象的计算模型。
与图灵机不同，兰姆达演算法没有存储器或状态的概念，它仅通过对表达式进行变换来进行计算。
这使得兰姆达演算法成为一个非常简单且优雅的计算模型。
在兰姆达演算法中，所有的计算都通过函数应用来实现。
它由三个基本元素组成：变量、抽象和应用。
变量表示一个符号或名字；抽象定义了一个函数；应用表示函数对参数的调用。
2. 兰姆达演算法的基本语法在兰姆达演算法中，表达式由变量、抽象和应用构成。
下面是一些基本的语法规则：•变量：一个变量由一个字母或字符串表示，例如x、y或foo。
•抽象：抽象定义了一个函数。
它由一个λ符号后跟一个变量和一个点组成，然后是函数体。
例如λx.x表示一个接受参数x并返回x的函数。
•应用：应用表示函数对参数的调用。
它由两个表达式连在一起组成，左边是函数，右边是参数。
例如(λx.x) y表示将y作为参数传递给函数λx.x。
3. 兰姆达演算法的基本操作兰姆达演算法通过一系列的规则进行计算和变换。
这些规则定义了如何对表达式进行求值和简化。
3.1 β-归约β-归约是兰姆达演算法中最重要的操作之一。
它描述了如何将函数应用到参数上，并将其简化为结果。
β-归约规则如下：(λx.E) V → E[x:=V]其中，(λx.E)表示一个抽象，V表示一个值（可以是变量或其他表达式），E[x:=V]表示将E中的所有自由出现的变量x替换为V。
这个规则表示，当一个函数应用到参数上时，它的函数体中的变量将被替换为参数，从而得到一个新的表达式。
使用延时演算的时间化rsl的指称语义
摘要《ＲＡｌＳＥ描述语言（ＲＳＬ）是用于形式化地描述、设计和开发软件的最通用和最全面的语言之一．它已经被扩展到时间化ＲＳＬ来描述与时间有关的操作．但是，它不具有在抽象层次上描述实时需求的特征．延时演算（ＤｕｒａｔｉｏｎＣａｈ’ｌｌｈｌｓ）是一种实时区间逻辑．它已经被广泛用于实时系统设计的描述和验证．但是，它不支持数据结构、算法和模块化设计．混成系统是包含离散部件和连续部件的实时系统．扩展的延时演算（ＥｘｔｅｎｄｅｄＤｕｒａｔｉｏｎＣａｌｃｕｌｕｓ）将延时演算扩展到了混成系统．）本文的目的是，通过用扩展的延时演算为命令式的时间化ＲＳＬ表达式定义指称语义，结合时间化ＲｓＬ和延时演算，以用于混成系统的形式化描述、验证、设计和开发．：在时间化ＲＳＬ中，外部选择是指由表达式在不同的分支中提供不同的通讯选择，由外部环境来决定进行哪一个通讯，以使表达式执行相应的分支．超时选择是指其它分支只能在一定时间之内被选择，否则表达式将执行超时分支．本文通过结合外部选择和超时选择，扩展了时间化ＲＳＬ，大大简化了许多代数定律。
离散状态变量的意义是离散的时间函数．在扩展的延时演算中，离散状态变量只能是布尔类型，项只有通过关系操作符的连接才能成为公式．本文改进了扩展的延时演算，使得离散状态变量可以是任意类型，并将任何布尔类型的项作为公式，增加了灵活性和表达性．为了形式化描述串行构造、循环及程序变量的稳定状态，本文在扩展的延时演算模型中加入一些高级特征，并探究它们的代数性质．这些性质对于实时程序的形式化和实时性质的验证起着关键作用．时间化ＲＳＬ的基本元素是变量和用于通信的通道，并且每一个命令式的时间化ＲＳＬ表达式都有一个返回值．时间化ＲＳＬ表达式的行为可以划分为三种类型：发散、等待和终止．我们基于对通道、变量和返回值的观察，使用带有高级特征的扩展的延时演算公式，定义了时间化ＲＳＬ的指称语义，它能够用单一的公式描述所有类型的表达式行为．从我们所定义的指称语义。
KEY WORDS AND PHRASES
Type-based Analysis of Communication for Concurrent Programming Languages
Atsushi Igarashi
Naoki Kobayashi
June 1997
T
Department of Information Science Faculty of Science, University of Tokyo
x : [ ]; y : [ ] ` x?[z ]: y![z ],
1
where [ ] denotes the type of channels used for transmitting values of type . The idea of the linear type system is to annotate channel type constructors with information about how often channels can be used for input or output (we use here a slightly di erent formalization from the original linear type system [6].); so, the above type judgement is replaced by: x : [ ](1;0) ; y : [ ](0;1) ` x?[z ]: y![z ]. The superscript pair (1 ; 2 ) of integers or ! (in nity) speci es how often a channel can be used for input (by 1 ) and for output (by 2 ). (Throughout the paper, `a channel being used for input or output' means that a process tries to receive or send a value along the channel, rather than that a process succeeds in receiving or sending a value by nding its communication partner.) Let us consider a more complex example: f : [int; [ ](0;1) ](0;1) ; r : [ ](1;1) ; r0 : [ ](0;1) ; n : int ` f ![n; r] j r?[ ]: r0 ![ ]. The type of f indicates that f can be used at most once for sending a pair of an integer and a channel and also that the channel may be used by the receiver on f at most once for sending a null tuple. By using such type information, we can safely replace the process (r) (f ![n; r] j r?[ ]: r0 ![ ]) with the more ecient process f ![n; r0 ]. As we have argued elsewhere [5, 6], this optimization corresponds to tail-call optimization of functions. However, the previous linear type system [6] has been only concerned with checking usage information; so programmers must put heavy annotations in order to make optimization work. The main reason for it is that the type system apparently has no principal typing property: in fact, there are lots of other possible typings for the above process: f : [int; [ ](1;0) ](0;1) ; r : [ ](2;0) ; r0 : [ ](0;1) ; n : int ` f ![n; r] j r?[ ]: r0 ![ ] f : [int; [ ](1;1) ](0;1) ; r : [ ](2;1) ; r0 : [ ](0;1) ; n : int ` f ![n; r] j r?[ ]: r0 ![ ]
时滞兰彻斯特方程
时滞兰彻斯特方程
拉兰彻斯特方程，又称为蒙特卡洛方程，是一种二阶微分方程，由法国数学家 Evariste Galois 和 Jean-Victor Poncelet 所发明。
这个方程的解决方案是通过检验可行性函数，也就是椭圆等离散型方程，来解决。
式子为：
(1) (d^2y)/dx^2 - 2p(dx/dy) + qy = 0
其中，p 和 q 为常数，它们用来描述特定的椭圆或简折变形的水平抛物线，并且与这个曲线的切线有关。
拉兰彻斯特方程的解决方法基于已知初值条件U0(x0)和V0(x0)，这些初值条件0可以任意指定。
这里的U0(x0)表示函数的值在初值条件处，而V0(x0)表示函数的导数在处处的值。
拉兰彻斯特方程的解决方法是将拉兰彻斯特方程转换为一组微分方程，称为蒙特卡洛系统，并用积分方法求解它。
一般来说，蒙特卡洛系统的求解方法是使用一种叫做隐式 Runge-Kutta 方法的积分方法，它可以通过计算这个拉兰彻斯特方程的导数，从而计算函数的变化，即 y(x)。
另外，为了求解拉兰彻斯特方程，我们还可以使用Janetzki法、正交步方法和正则步方法等数值分析方法。
拉兰彻斯特方程有许多应用，比如在物理学中，它可以用来描述电磁学中的各种振子，在工程学中，它可以用来求解结构动力学问题。
它也可以用于测量和预测液体流动的情况，从而获得非线性模型，用于系统的建模和分析。
霍奇金-赫胥黎方程
霍奇金-赫胥黎方程霍奇金-赫胥黎方程（Hodgkin-Huxley equation）是描述神经元电活动行为的重要数学模型。
该方程以生理学家霍奇金和赫胥黎的名字命名，他们通过实验证明了神经元的动作电位是在离子通道开合状态的调控下发生的。
霍奇金-赫胥黎方程由以下几个部分组成：膜电位变化的电容流、离子通道电流以及钠和钾离子的状态变化。
本文将详细介绍该方程的各个部分以及其在神经科学研究中的应用。
霍奇金-赫胥黎方程的第一个部分是膜电位变化的电容流。
神经元的细胞膜是由脂质双层组成的，能阻止离子自由通过。
然而，当神经元兴奋时，细胞膜会发生电位变化，这是由于细胞内外离子浓度的不同所引起的。
该电位变化可以用电容电流来描述，其数学表达式为：$\frac{{dV}}{{dt}} = \frac{{-I_{\text{{capacitance}}}}}{{C_{\text{{membrane}}}}}$其中，$\frac{{dV}}{{dt}}$表示膜电位变化率，$I_{\text{{capacitance}}}$表示电容流，$C_{\text{{membrane}}}$表示细胞膜的电容。
第二部分是离子通道电流。
神经元细胞膜上有多种离子通道，通过这些离子通道，离子可以进入或离开细胞内。
最重要的离子通道是钠通道和钾通道，它们通过负责调节神经元的动作电位。
离子通道的电流可用以下方程表示：$I_{\text{{ion}}} = \bar{g}_{\text{{ion}}} m^a h^b (V -E_{\text{{ion}}})$其中，$I_{\text{{ion}}}$表示离子通道的电流，$\bar{g}_{\text{{ion}}}$表示离子通道的最大导电性，$m$和$h$是钠和钾离子通道的门控变量，$a$和$b$表示门控变量的功率，$V$表示膜电位，$E_{\text{{ion}}}$表示离子的平衡电位。
第三部分是钠和钾离子的状态变化。
柯尔莫哥洛夫向前方程
柯尔莫哥洛夫向前方程柯尔莫哥洛夫向前方程（ChebyshevForwardEquation）是一种重要的非线性特征值方程，它最初出现在俄罗斯数学家Pafnuty Chebyshev（1821-1894）的论文《论关于离散数列关系的新法则》中。
后，它被广泛应用于诸如物理、化学、计算机科学等多个领域，在最近的几十年中，它成为量子计算和量子化学的一个重要工具。
柯尔莫哥洛夫向前方程有简单的表示形式：$$psi(x+Deltax)=A_0psi(x)+sum_{n=1}^{infty}A_npsi(x-nDelta x)$$ 其中，A_0和A_n是定值参数，Δx是某一常量，Ψ代表函数的变化情况。
柯尔莫哥洛夫向前方程是一种非线性的特征值方程，它的本质是一个解析方程，它讨论的是一个函数在离散时间和空间上演算它们之间的关系。
尔莫哥洛夫向前方程不仅用于传统物理问题的求解，还可以用于量子力学系统和复杂网络系统的分析。
柯尔莫哥洛夫向前方程在应用中有很多不同的形式，其中最基本的形式是柯尔莫哥洛夫步进方程。
尔莫哥洛夫步进方程的形式是：$$ psi(x+Delta x)=A[psi(x-Delta x)+psi(x)]$$其中，A是定值参数，Δx是某一常量，Ψ代表函数的变化情况。
柯尔莫哥洛夫步进方程可以用来解决一维离散布莱克-普朗姆方程或二维离散布莱克-普朗姆方程，在这些方程中，Ψ表示物理量的位置和振动状态，A是一个常量，Δx就是时间步长。
方程的目的是求出Ψ的时间和空间变化规律，从而推出某种物理量在某一特定空间和时间上的行为。
柯尔莫哥洛夫步进方程也可以用于求解由自变量和状态变量组成的非线性系统参数的值，这种方法常被称为柯尔莫哥洛夫迭代法。
种方法以特定的时间步长Δx将这个系统分割成多个时间段，然后根据当前段内某一时刻状态变量的值，用柯尔莫哥洛夫步进方程计算下一个时刻的值，把多个时刻的状态变量的值串联起来，从而求出系统参数的值。
人工智能概论中英文术语对照
人工智能概论中英文术语对照表动作action专家系统Expert system人工智能语言AI language祖先过滤形策略ancestry-filtered form strategy与节点AND node与或图AND/OR graph与或树AND/OR tree回答语句answer statement人工智能artificial intelligence,AI原子公式atomic formula自动定理证明automatic theorem provingB规则B-rule倒退值backed-up value回溯backtracking盲目搜索，无信息搜索blind search宽度优先搜索breadth-first search子句clause组合爆炸combinatorial explosion冲突解决conflict resolution合取式conjunct合取conjunction合取范式conjunctive normal form连词，连接词connective一致解图consistant solution graph控制策略control strategy费用cost演绎deduction深度优先搜索depth-first search推导表，引导图derivation graph差别difference有向图directed graph析取式disjunct析取disjunction谓词演算辖域domain in predicate calculus论域，文字域domain of discourse搜索算法的效率efficiency of search algorithm空子句empty clause等价equivalence估计费用estimated cost估值函数evaluation function存在量词existential quantifier扩展节点expending node节点的扩展expansion of nodeF规则F-rule事实fact一阶谓词演算first order predicate calculus 博弈game图graph图表示法graph notation图搜索graph search图搜索控制策略graph-search control strategy 启发函数heuristic function启发信息heuristic information启发搜索heuristic search蕴涵，蕴涵式implication推理inference智能intelligence解释器interpreter知识knowledge知识获取knowledge acquisition全局数据库Global database知识库knowledge base知识工程knowledge engineering学习learning启发式搜索Heuristic search线形输入形策略linear-input form strategy文字literal逻辑logic逻辑连词logic connective逻辑推理logic reasoning匹配match模式匹配match pattern母式matrix最一般合一者most general unifierNP完全问题NP-complete problem算符、算子、操作符operator最优解树optimal solution tree有序搜索ordered search谓词predicate谓词演算predicate calculus谓词逻辑predicate logic前缀prefix本原问题primitive problem问题归约problem-reduction问题求解problem solving产生式production产生式规则production rule量词quantifier推理reasoning正向推理forward reasoning逆向推理backward reasoning推理机reasoning machine归约reduction反演refutation反演树refutation tree归结resolution归结原理resolution principle归结反演resolution refutation归结式resolvent可满足性satisfiability模式识别Pattern recognition量词辖域scope of quantifier搜索search, searching搜索算法searching algorithm搜索图searching graph搜索策略searching strategy搜索树searching tree句子sentence解图solution graph解树solution tree可解节点solvable node可解标示过程solvable labeling procedure 状态state状态空间state space代换例substitution instance代换substitution重言式tautology项term定理证明theorem-proving不确定性uncertainty合一unifier最一般合一most general unifier全称量词universal quantifier不可满足集unsatisfiable set不可解标示过程unsolvable-labeling procedure 不可解节点unsolvable node永真式validity合适公式、合式公式well-formed formula (wff)谓词演算公式wffs of predicate calculus人工神经网络artificial neural network遗传算法genetic algorithm机器学习machine learning。
美国大学生数学建模MCM 数学专用名词
美国大学生数学建模MCM 数学专用名词augmented matrix增广矩阵asymptotic渐进的asymptote渐进线asymmetrical非对称的associative law结合律ascending上升的arrangement排列arithmetic算术argument幅角，幅度，自变量，论证area面积arc length弧长apothem边心距apex顶点aperiodic非周期的antisymmetric反对称的antiderivative原函数anticlockwise逆时针的annihilator零化子angular velocity角速度angle of rotation旋转角angle of incidence入射角angle of elevation仰角angle of depression俯角angle of circumference圆周角analytic space复空间analytic geometry解析几何analytic function解析函数analytic extension解析开拓amplitude幅角，振幅alternative互斥的alternate series交错级数almost everywhere几乎处处algebraic topology代数拓扑algebraic expression代数式algebraic代数的affine仿射(几何学)的admissible error容许误差admissible容许的adjugate伴随转置的adjoint operator伴随算子adjoint伴随的adjacency邻接additive加法，加性acute angle锐角accumulation point聚点accidential error偶然误差accessible point可达点abstract space抽象空间abstract algebra抽象代数absolute value绝对值absolute integrable绝对可积absolute convergent绝对收敛Abelian阿贝尔的，交换的balance equation平衡方程bandwidth带宽barycenter重心base基base vectors基向量biased error有偏误差biased statistic有偏统计量bilinear双线性的bijective双射的bilateral shift双侧位移的binomial二项式bisector二等分线，平分线boundary边界的，边界bounded有界的broken line折线bundle丛，把，卷calculus微积分calculus of variations变分法cancellation消去canonical典型的，标准的canonical form标准型cap交，求交运算capacity容量cardinal number基数Cartesian coordinates笛卡尔坐标category范畴，类型cell单元，方格，胞腔cell complex胞腔复形character特征标characterization特征circuit环路，线路，回路circular ring圆环circulating decimal循环小数clockwise顺时针方向的closed ball闭球closure闭包cluster point聚点coefficient系数cofinal共尾的cohomology上同调coincidence重合，叠和collinear共线的collective集体的columnar rank列秩combinatorial theory组合理论common tangent公切线commutative交换的compact紧的compact operator紧算子compatibility相容性compatible events相容事件complementary余的，补的complete完全的，完备的complex analysis复变函数论complex potential复位势composite复合的concave function凹函数concentric circles同心圆concurrent共点conditional number条件数confidence interval置信区间conformal共形的conic圆锥的conjugate共轭的connected连通的connected domain连通域consistence相容，一致constrained约束的continuable可延拓的continuity连续性contour周线，回路，轮廓线convergence收敛性convexity凸形convolution对和，卷积coordinate坐标coprime互质的，互素的correspondence对应coset陪集countable可数的counterexample反例covariance协方差covariant共变的covering覆盖critical临界的cubic root立方根cup并，求并运算curl旋度curvature曲率curve曲线cyclic循环的decade十进制的decagon十边形decimal小数的，十进制的decision theory决策论decomposable可分解的decreasing递减的decrement减量deduction推论，归纳法defect亏量，缺陷deficiency亏格definition定义definite integral定积分deflation压缩deflection挠度，挠率，变位degenerate退化的deleted neighborhood去心邻域denominator分母density稠密性，密度density function密度函数denumerable可数的departure偏差，偏离dependent相关的dependent variable因变量derangement重排derivation求导derivative导数descent下降determinant行列式diagram图，图表diameter直径diamond菱形dichotomy二分法diffeomorphism微分同胚differentiable可微的differential微分differential geometry微分几何difference差，差分digit数字dimension维数directed graph有向图directed set有向集direct prodect直积direct sum直和direction angle方向角directional derivative方向导数disc圆盘disconnected不连通的discontinuous不连续的discrete离散的discriminant判别式disjoint不相交的disorder混乱，无序dissection剖分dissipation损耗distribution分布，广义函数divergent发散的divisor因子，除数division除法domain区域，定义域dot product点积double integral二重积分dual对偶dynamic model动态模型dynamic programming动态规划dynamic system动力系统eccentricity离心率econometrics计量经济学edge棱，边eigenvalue特征值eigenvector特征向量eigenspace特征空间element元素ellipse椭圆embed嵌入empirical equation经验公式empirical assumption经验假设endomorphism自同态end point端点entropy熵entire function整函数envelope包络epimorphism满同态equiangular等角equilateral等边的equicontinuous等度连续的equilibrium平衡equivalence等价error estimate误差估计estimator估计量evaluation赋值，值的计算even number偶数exact sequence正合序列exact solution精确解excenter外心excision切割，分割exclusive events互斥事件exhaustive穷举的expansion展开，展开式expectation期望experimental error实验误差explicit function显函数exponent指数extension扩张，外延face面factor因子factorial阶乘fallacy谬误fiducial置信field域，场field theory域论figure图形，数字finite有限的finite group有限群finite iteration有限迭代finite rank有限秩finitely covered有限覆盖fitting拟合fixed point不动点flag标志flat space平旦空间formula公式fraction分数，分式frame架，标架free boundary自由边界frequency频数，频率front side正面function函数functional泛函functor函子，算符fundamental group基本群fuzzy模糊的gain增益，放大率game对策gap间断，间隙general topology一般拓扑学general term通项generalized普遍的，推广的generalized inverse广义逆generalization归纳，普遍化generating line母线genus亏格geodesic测地线geometrical几何的geometric series几何级数golden section黄金分割graph图形，网格half plane半平面harmonic调和的hexagon六边形hereditary可传的holomorphic全纯的homeomorphism同胚homogeneous齐次的homology同调homotopy同伦hyperbola双曲线hyperplane超平面hypothesis假设ideal理想idempotent幂等的identical恒等，恒同identity恒等式，单位元ill-condition病态image像点，像imaginary axis虚轴imbedding嵌入imitation模仿，模拟immersion浸入impulse function脉冲函数inclination斜角，倾角inclined plane斜面inclusion包含incomparable不可比的incompatible不相容的，互斥的inconsistent不成立的indefinite integral不定积分independence无关（性），独立（性）index指数，指标indivisible除不尽的inductive归纳的inductive definition归纳定义induced诱导的inequality不等式inertia law惯性律inference推理，推论infimum下确界infinite无穷大的infinite decimal无穷小数infinite series无穷级数infinitesimal无穷小的inflection point拐点information theory信息论inhomogeneous非齐次的injection内射inner point内点instability不稳定integer整数integrable可积的integrand被积函数integral积分intermediate value介值intersection交，相交interval区间intrinsic内在的，内蕴的invariant不变的inverse circular funct反三角函数inverse image逆像，原像inversion反演invertible可逆的involution对合irrational无理的，无理数irreducible不可约的isolated point孤立点isometric等距的isomorphic同构的iteration迭代joint distribution联合分布kernel核keyword关键词knot纽结known已知的large sample大样本last term末项lateral area侧面积lattice格子lattice point格点law of identity同一律leading coefficient首项系数leaf蔓叶线least squares solution最小二乘解lemma引理Lie algebra李代数lifting提升likelihood似然的limit极限linear combination线性组合linear filter线性滤波linear fraction transf线性分linear filter线性滤波式变换式变换linear functional线性泛函linear operator线性算子linearly dependent线性相关linearly independent线性无关local coordinates局部坐标locus(pl.loci)轨迹logarithm对数lower bound下界logic逻辑lozenge菱形lunar新月型main diagonal主对角线manifold流形mantissa尾数many-valued function多值函数map into映入map onto映到mapping映射marginal边缘master equation主方程mathermatical analysis数学分析mathematical expectati数学期望matrix(pl. matrices)矩阵maximal极大的，最大的maximum norm最大模mean平均，中数measurable可测的measure测度mesh网络metric space距离空间midpoint中点minus减minimal极小的，最小的model模型modulus模，模数moment矩monomorphism单一同态multi-analysis多元分析multiplication乘法multipole多极mutual相互的mutually disjoint互不相交natural boundary自然边界natural equivalence自然等价natural number自然数natural period固有周期negative负的，否定的neighborhood邻域nil-factor零因子nilpotent幂零的nodal节点的noncommutative非交换的nondense疏的，无处稠密的nonempty非空的noncountable不可数的nonlinear非线性的nonsingular非奇异的norm范数normal正规的，法线normal derivative法向导数normal direction法方向normal distribution正态分布normal family正规族normal operator正规算子normal set良序集normed赋范的n-tuple integral重积分number theory数论numerical analysis数值分析null空，零obtuse angle钝角octagon八边形octant卦限odd number奇数odevity奇偶性off-centre偏心的one-side单侧的open ball开球operations reserach运筹学optimality最优性optimization最优化optimum最佳条件orbit轨道order阶，级，次序order-preserving保序的order-type序型ordinal次序的ordinary寻常的，正常的ordinate纵坐标orient定方向orientable可定向的origin原点original state初始状态orthogonal正交的orthonormal规范化正交的outer product外积oval卵形线overdetermined超定的overlaping重叠，交迭pairity奇偶性pairwise两两的parabola抛物线parallel平行parallel lines平行线parallelogram平行四边形parameter参数parent population母体partial偏的，部分的partial ordering偏序partial sum部分和particle质点partition划分，分类path space道路空间perfect differential全微分period周期periodic decimal循环小数peripheral周界的，外表的periphery边界permissible容许的permutable可交换的perpendicular垂直perturbation扰动，摄动phase相，位相piecewise分段的planar平面的plane curve平面曲线plane domain平面区域plane pencil平面束plus加point of intersection交点pointwise逐点的polar coordinates极坐标pole极，极点polygon多边形polygonal line折线polynomial多项式positive正的，肯定的potency势，基数potential位势prime素的primitive本原的principal minor主子式prism棱柱proof theory证明论probability概率projective射影的，投影proportion比例pure纯的pyramid棱锥，棱锥体quadrant像限quadratic二次的quadric surface二次曲面quantity量，数量quasi-group拟群quasi-norm拟范数quasi-normal拟正规queuing theory排队论quotient商radial径向radical sign根号radication开方radian弧度radius半径ramified分歧的random随机randomize随机化range值域，区域，范围rank秩rational有理的raw data原始数据real function实函数reciprocal倒数的，互反的reciprocal basis对偶基reciprocity互反性rectangle长方形，矩形rectifiable可求长的recurring decimal循环小数reduce简化，化简reflection反射reflexive自反的region区域regular正则regular ring正则环related function相关函数remanent剩余的repeated root重根residue留数，残数resolution分解resolvent预解式right angle直角rotation旋转roundoff舍入row rank行秩ruled surface直纹曲面runs游程，取遍saddle point鞍点sample样本sampling取样scalar field标量场scalar product数量积，内积scale标尺，尺度scattering散射，扩散sectorial扇形self-adjoint自伴的semicircle半圆semi-definite半定的semigroup半群semisimple半单纯的separable可分的sequence序列sequential相继的，序列的serial序列的sheaf层side face侧面similar相似的simple curve简单曲线simplex单纯形singular values奇异值skeleton骨架skewness偏斜度slackness松弛性slant斜的slope斜率small sample小样本smooth manifold光滑流形solid figure立体形solid geometry立体几何solid of rotation旋转体solution解solvable可解的sparse稀疏的spectral theory谱论spectrum谱sphere球面，球形spiral螺线spline function样条函数splitting分裂的statistics统计，统计学statistic统计量stochastic随机的straight angle平角straight line直线stream-line流线subadditive次可加的subinterval子区间submanifold子流形subset子集subtraction减法sum和summable可加的summand被加数supremum上确界surjective满射的symmetric对称的tabular表格式的tabulation列表，造表tangent正切，切线tangent space切空间tangent vector切向量tensor张量term项terminal row末行termwise逐项的tetrahedroid四面体topological拓扑的torsion挠率totally ordered set全序集trace迹trajectory轨道transcendental超越的transfer改变，传transfinite超限的transformation变换式transitive可传递的translation平移transpose转置transverse横截、trapezoid梯形treble三倍，三重trend趋势triad三元组triaxial三轴的，三维的trigon三角形trigonometric三角学的tripod三面角tubular管状的twist挠曲，扭转type类型，型，序型unbiased无偏的unbiased estimate无偏估计unbounded无界的uncertainty不定性unconditional无条件的unequal不等的uniform一致的uniform boundness一致有界uniformly bounded一致有界的uniformly continuous一致连续uniformly convergent一致收敛unilateral单侧的union并，并集unit单位unit circle单位圆unitary matrix酉矩阵universal泛的，通用的upper bound上界unrounded不舍入的unstable不稳定的valuation赋值value值variation变分，变差variety簇vector向量vector bundle向量丛vertex顶点vertical angle对顶角volume体积，容积wave波wave form波形wave function波函数wave equation波动方程weak convergence弱收敛weak derivatives弱导数weight权重，重量well-ordered良序的well-posed适定的zero零zero divisor零因子zeros零点zone域，带</Words>。