Atomic Number 74
克拉夫特不等式
克拉夫特不等式克拉夫特不等式是编码理论中的一个数学关系,给出了一个码字长度集合存在唯一可解编码/单义可译码(uniquely decodable code)的必要条件。
因为这个不等式在前缀码和树上面应用很多,所以在计算机科学和信息学中很常用。
设符号表中的原始符号为:在大小为的字符集上编码为唯一可解编码的码字长度为则,反之, 给定一个满足上述不等式的自然数集合, 则在大小为字符集上,存在一组唯一可解编码符合相应的码字长度。
1949年,克拉夫特不等式发表在克拉夫特的一本专著上。
然而,克拉夫特的论文只讨论了前缀码,并将这个不等式的归因于雷蒙德·雷德赫弗不等式(Raymond Redheffer)。
1956年,麦克米兰独立发现了这个结果。
他证明了一般情况下唯一可解码的结果,并将前缀码的版本归因于Joseph Leo Doob在1955年提到的一种现象。
应用克拉夫特不等式对码字限制长度以保证前缀编码的可能性。
这个不等式说明码字长度指数的倒数的分布和概率质量函数很相似。
克拉夫特不等式可以想象成一个受限的编码库,越短的编码代价越大。
如果克拉夫特不等式中严格成立,相应的编码有冗余(redundancy)。
如果克拉夫特不等式中等式成立,相应的编码被称作完备码(complete code)。
如果克拉夫特不等式不成立,相应的编码不是唯一可解编码(uniquely decipherable)。
对于每一个唯一可解码的代码,都存在一个长度分布相同的前缀码。
影响及意义克拉夫特不等式(Kraft inequality)信源编码理论中的一个重要不等式.当一个码的任意码字与比它更长的任意码字的字首不相同时,称此码为满足字首条件的码.由码字分别为N;(i=1,2,……,M)的M个码字所组成而且又满足字首条件的码,其存在的充分必要条件是满足公式M-N <1此式称为克拉夫特不等式.craft不等式是克拉夫特不等式,克拉夫特不等式(Kraftinequality)信源编码理论中的一个重要不等式,当一个码的任意码字与比它更长的任意码字的字首不相同时,称此码为满足字首条件的码。
说文解字(英语)
说文解字1,ag=do,act 做,动2,agri=field 田地,农田(agri也做agro,agr)3,ann=year年4,audi=hear听5,bell=war战争6,brev=short短7,ced,ceed,cess=go行走8,cept=take拿取9,cid,cis=cut,kill切,杀10,circ=ring环,圈11,claim,clam=cry,shout喊叫12,clar=clear清楚,明白13,clud=close,shut关闭14,cogn=known知道15,cord=heart心16,corpor=body体17,cred=believe,trust相信,信任18,cruc=cross 十字19,cur=care关心20,cur,curs,cour,cours=run跑21,dent=tooth牙齿22,di=day 日23,dict=say说24,dit=give给25,don=give给26,du=tow二27,duc,duct=lead引导28,ed=eat吃29,equ=equal等,均,平30,ev=age年龄,寿命,时代,时期31,fact=do,make做,作32,fer=bring,carry带拿33,flor=flower花34,flu=flow流35,fus=pour灌,流,倾泄36,grad=step,go,grade步,走,级37,gram=write,draw写,画,文字,图形38,graph=write,records写,画,记录器,图形39,gress=go,walk 行走40,habit=dwell居住41,hibit=hold拿,持42,hospit=guest客人43,idio=peculiar,own,private,proper特殊的,个人的,专有的44,insul=island岛45,it=go行走46,ject=throw投掷47,juven=young年轻,年少48,lectchoose,gather选,收49,lev=raise举,升50,liber=free自由51,lingu=language语言52,liter=letter文字,字母53,loc=place地方54,log=speak言,说55,loqu=speak言,说56,lun=moon月亮57,man=dwell,stay居住,停留58,manu=hand手59,mar=sea海60,medi=middle中间61,memor=memory记忆62,merg=dip,sink 沉,没63,migr=remove,move迁移64,milit=soldier兵65,mini=small,little小66,mir=wonder惊奇67,miss=send 投,送,发(miss也作mit)68,mob=move动69,mort=death死70,mot=move移动,动71,nomin=name名72,nov=new新73,numer=number 数74,onym=name 名75,oper=work工作76,ori=rise升起77,paci=peace和平,平静78,pel=push,drive推,逐,驱79,pend,pens=hang悬挂/weigh称量/pay支出,付钱,花费80,pet=seek追求81,phon=sound声音82,pict=paint画,描绘83,plen=full满,全84,plic=fold折,重叠85,pon=put放置86,popul=people人民87,port=carry拿,带,运88,pos=put放置89,preci=price价值90,punct=point,prick点,刺91,pur=pure清,纯,净92,rect=right,straight正,直93,rupt=break破94,sal=salt盐95,scend,scens=climb爬,攀96,sci=know知97,sec,sequ=follow跟随98,sect=cut切割99,sent,sens=feel感觉100,sid=sit坐101,sist=stand站立102,son=sound声音103,spect=look看104,spir=breathe呼吸105,tail=cut切割106,tain,ten,tin=hold握,持,守107,tect=cover掩盖108,tele=far远109,tempor=time时110,tend(tens,tent)=stretch伸111,terr=land,earth土地,陆地112,text=weave纺织113,tract=draw拉,抽,引114,un=one一115,urb=city城市116,vac,vacu=empty空117,vad,vas=walk,go行走118,vari=change变化119,ven=come来120,vert,vers=turn转121,vi,via=way道路122,vis,vid=see看123,vit=life生命124,viv=live活125,aer(o)空气,空中,航空126,alt高127,am爱128,ambul行走129,anim生命,活,心神,意见130,anthrop(o)人,人类131,aqu水132,arch统治者,首脑archy 统治133,avi鸟134,bat打135,biblio书136,birg战斗,打137,cad,cas降落,降临138,cert 确定,确信139,chron时140,cid降落,降临141,clin倾142,cosm(o)世界,宇宙143,cracy统治crat支持144,cub躺,卧145,cult耕,培养146,cycl(o)圈,环,轮147,dem(o)人民148,dexter右149,doc教150,dom屋,家151,dorm睡眠152,drom跑153,ego我154,err漫游,走,行155,fabl,fabul 言156,feder联盟157,ferv沸,热158,fict,fig塑造,虚构159,fid信任160,fil线161,flat 吹162,flect,flex弯曲163,flict打击164,frag,fract破,折165,frig冷166,fug逃,散167,fund,found底,基础168,gam婚姻169,gram谷物,谷粒170,grav重171,greg群,集合172,gyn,gynce(o)妇女173,hal呼吸174,helic(o)螺旋175,hes,her粘着176,ign火177,integr整,全178,junct连接,连结179,later边180,leg读181,leg,legis法182,luc光183,lumin光184,magn(i)大185,matr(i),metro母186,mega大187,mens测量188,ment心,神,智,思,意189,min伸出,突出190,misc混合,混杂191,mis(o)恨,厌恶192,mon告诫,提醒193,mon单独,一个194,mur墙195,mut变换196,nat诞生197,nav船198,nect,nex结,系199,negr,nigr黑200,nihil无201,noc,nox伤害202,noct(i)夜203,norm规范,正规,正常204,nutri营养205,orn装饰206,par生,产207,parl说,谈208,past喂,食209,path(o),pathy疾病,疗法210,patr(i)父,祖211,ped脚,足212,ped儿童,小孩213,petr(o)石214,phag吃215,phil(o)爱216,phob(ia)怕217,plex重叠,重218,polis城市219,prim第一,最初220,radic根221,ras,rad擦,刮222,rid,ris笑223,rod,ros咬,啮224,rot轮,转225,rud原始,粗野226,rur,rus农村227,sat,satis,satur足,满,饱228,sen老229,simil,simul相似,相同230,sol单独231,sol太阳232,soph智慧233,sper希望234,spers,spars散,撒235,splend发光,照耀236,stell星237,tact,tag触238,the(o)神239,ton音240,tort扭241,tour迂回,转242,trud,trus推,冲243,tut,tuit监护,看管244,umbr阴影245,ut,us用246,vas走,漫游247,val强248,van空,无249,ver(i)真实250,voc,vok声音,叫喊251,vol,volunt意志,意愿252,volu,volv滚,转一、英语常用前缀表(说明:黑体字为英语前缀及其含义,斜杠/后面为构词举例)a- 使,离,向/ awake使醒来,apart使分离ac-,ad-,af-,ag-,al- 向,加强/ accord依照,affect影响anti- 反,防止/ antitank反坦克的auto- 自,自动/ automation自动化be- 在,使/ beside在……旁,befall降临(于)bi- 双/ bicycle自行车,bisexual两性的co- 共同,互相/ cn- exist共存com-,con- 共同,加强/ combine联合,confirm使加强de- 离,加强,降/ detrain下火车,depicture描述dif- 分开,否定/ differ差异,difficult困难dis- 否,离,安全/ disallow不准,disroot根除,disarrange搞乱e- ,ex- 出,否定,加强/ educe引出,estop阻止,expand扩展en-,em- 在内,用于,使/ encage关入笼,embed使插入in- ,im-,il- 无,向内,加强/ incorrect不正确,impulse冲动inter- 在……间/ international国际的kilo- 千/ kilometer千米micro- 微/ microbe微生物mini- 微小/ minibus小公共汽车neg- 不,非/ neglect忽视,negate否定non- 不,非/ nonparty非党派的ob-,oc-,op- 越过,包围,逆反/ object目标,oppose反抗out- 在外,除去/ outlaw逃亡者,outroot根除over- 超出,反转/ overweight超重,overthrow推翻per- 贯通,遍及/ perform完成,perfect完美的post- 在后/ postwar战后的,porstern后门pre- 在前/ preface前言pro- 在前,拥护/ prologue序言,pro- American亲美的re- 重复,相反/ recall回忆,react反应se- 分离/ separate使分离,select选出sub-,suc-,sug- 在下,次于/ subway地铁,succeed继承sur- 超,外加/ surface表面,surtax附加税tele- 远/ television电视trans- 超过,透过/ translate翻译,transport运输un- 否定/ unfair不公平的up- 向上/ upset推翻,upstairs在楼上uni- 单一/ united联合的,unit单位二、英语常用后缀表(说明:黑体字为英语后缀及其含义,斜杠/后面为构词举例)-ability,—ibility 抽象名词/ stability稳定,sensibility敏感性-able,—ible 能…的/ unable无能力的,terrible可怕的-acy性质,状态/ illiteracy文盲,intricacy错综复杂-age动作,状态,总称(构成名词)/ folwage泛滥,postage邮费-al动作,行为,…的/ manual手册,central中心-an人,籍贯,…的/ African非洲的,publican旅店主-ance,—ancy行为,性质,状态/ distance距离,currency流通-ant,ent人,…的/ assistant助手,excellent优秀的-ary地点,人,事物/ library图书馆,military军事-ate做,职位,…的/ doctorate博士学位,adequate足够的-ation,-ition动作,性质,状态/ visitation访问,addition附加物-craft 技巧,工艺/ aircraft飞机,handicraft手艺-cy 形状,状态,职位/ secrecy秘密,fancy幻想-dom 状态,领域/ freedom自由,kingdom王国-ed 有…的/ cultured有教养的,puzzled迷惑的-ence,-ency 行为,性质,状态/ difference差异,frequency频率-er,—eer,—or人/ killer杀手,engineer工程师,doctor医生-ern 地点,方位/ eastern东方的,cavern洞穴-ese 人,语言,国籍/ Chinese中国人,Japanese日本人-ess 女性,雌性/ actress女演员-hood 状态,身份(构成名词)/ childhood童年,livelihood生计-ic 学术,职业,……的/ music音乐,atomic原子的-ice 人,抽象名词/ service服务,novice新手-ics 学术(构成名词)/ physics物理学,optics光学-ing 总称,抽象名词/ clothing衣服,building建筑,feeling感觉-ion 物品,抽象名词/ cushion座垫,expression表达-ism 主义,宗教/ Marxism马克思主义,Islamism伊斯兰教-ist …者(构成名词)/ communist共产主义者,dentist牙医-ive 人,物,…的/ native本地人,attractive有吸引力的-less 无…的/ homeless无家可归的,fearless无畏的-logy 学(构成名词)/ zoology动物学,biology生物学-ly …的,…地/ daily每日的,quickly迅速地-ment 状况,物,组织/ development发展,department部门-ness 抽象名词/ darkness黑暗,kindness和蔼-ous 有…的(构成形容词)/ famous著名的,dangerous危险的-ship 状况,事物(构成名词)/ friendship友谊,leadership领导能力-sion,—tion 动作,性质,状态/ expansion扩展,description描述-th 状况,第…/youth青春,health健康,fifth第五-ty状况,…十/ specialty专业,safety安全,fifty五十-ure 状况,物(构成名词)/ pleasure快乐,picture图画-y 状况,学术,小…的/ harmony和谐,botany植物学,baby婴儿三、英语常用词根表(说明:黑体字为英语词根及其含义,斜杠/后面为构词举例)ag,act做/ agent代理人,actor演员art 技艺/ article文章bas 低的/ basic基本的bio 生命,生物/ biology生物学ced,ceed,cess走/ recede退却,proceed前进,success成功cid,cis 切/ decide决定,incise切开cit 唤起/ excite使兴奋clud,clus关闭/ include包含,conclusive最终的cord 心/ concord和睦cred,credit 相信/ credible可信的,discredit怀疑cult 耕作/ agriculture农业dic,dict 说/ indicate指出,dictator独裁者doc,doct 教/ document文件,doctor博士duc,duct 引导/ reduce减少,product产品fac,fact,fect 做/ facile易做的,factory工厂,infect传染fam 名声/ famous著名fer 带来,产生/ difference不同的,suffer经受fin 末尾/ final最后的,finish结束form 形成,组成/ reform改革,inform通知fort,forc 强/ effort努力,force力量geo 大地/ geography地理学grad,gress 脚步/ graduate毕业,progress进步gram 字符/ program节目单,telegram电报ide 外观,形式/ idea想法,ideal理想的ject 投掷/ object目标,subject主题leg,lig,lect 挑选/ elegant雅致的,eligible合格的,select选择log,logue 说话/ apologize道歉,dialogue对话mand,mend 命令/ demand要求,command命令min 较小,较少/ minute分钟,minority少数民族mit,miss 送,发/ submit呈交,dismiss解雇mot,mov,mob 运动/ remote遥远的,remove迁移,mobile移动的nat 出生/ native天生的,nature自然界nunci,nounc 讲述/ pronounce发音,enunciate宣布ord,ordin 次序/ order秩序,ordinary平常的part 部分/ apart分离,department部门pend,pens 悬挂,支付/ depend依靠,expensive昂贵的pet,petit 寻求,追求/ compete比赛,competitor竞争对手pos,posit 放置/ deposit储蓄,propose提出port 运送/ import进口,report报告reg,rect 划直线,治理/ regular正规的,correct正确的sci 知晓/ science科学,scientist科学家sent,sens 感觉/ sentence句子,nonsense废话serv 奴仆/ servant仆人,service服务sid,sess 坐/ president主席,possess占有spec,spect 看/ respect尊敬,special特别的st,stat 站立/ stay停留,station车站tain,ten,tent,tin 持有/ contain容纳,content满意,continue继续un 单一/ unit单位,united联合的ven,vent 发生,来临/ event事件,convent召集vis,vid,view 看见/ visit参观,evidence证据,review复习ag=do,act 做,动agent 代理人ann,enn=year 年annual 每年的,年度的audi,audit=hear 听audible 听得见的bell=war 战争rebellion 反叛,反抗brev=short 短abbreviate 缩短,节略cas=down落下occasion发生;时机cand=bright白,光candle蜡烛ced,ceed=go 行走precedent 先行的,在前cept=take 拿,取exception 例外,除外cert,cern=clear搞清,区别certify证明;保证celer=fast快,速celerity迅速,敏捷cid,cis=cut,kill 切,杀suicide 自杀circ=ring 环,圆circle 圆,圈,环状物claim,clam=cry,shout 喊叫exclaim 呼喊,惊叫clar=clear 清楚的,明白的clarify 澄清;使清楚clud,clus=close,shut 关闭exclude 排斥,拒绝,接纳cogn=know 知道cognition 认知cord=heart 心cordial 衷心的,诚心的corpor,cor=body 体corporation 团体,社团cred=trust 相信,信任credibility 可信,可靠cret,creet=depart区别discrete分立的cruc=cross 十字crucify把……钉在十字?上;折磨cur=care 关心,挂念,注意security 安全cru,curs,cour,cours=run 跑cruise巡航舰dict,dic=say 言,说dictator 独裁者,口授者dit=give 给edit 编辑don=give 给donor赠与者du=two 二dual双的duc,duct=lead 引导conduct 引导,指导,经营equ=equal 等,均,平equal相等的,平等的fact,fac=do,make 做,作factory 工厂fer=bring,carry 带,拿different 不同的,相异的flor,olour=flower 花florid 如花的,华丽的flu=flow 流fluency 流利,流畅fus=pour 灌,流,倾泻refuse 拒绝,拒受grad=step,go,grade 步,走,级gradual 逐步的gram=write 写telegram 电报a ,an①无,不,非astable不稳定的acentric无中心的②含有in,on,at,by,with,to等意义asleep在熟睡中ahead向前ab 脱离abnormal不正常的abaxial离开轴心的anti 反抗antiwar反战的anti imperialist反帝的auto 自动,自己autobiography自传autostable自动稳定be 使…加强belittle使缩小befriend友好相待bi 二,双biweekly双周刊biligual两种语言的co,col,com,con,cor 共同cooperation协作collaboration协作,勾结combine联合,correlation相互关系counter ,contra 反,对应counteraction反作用contrast对比,对照di ,dif ,dis 否定,相反diffident不自信的dislike不喜欢en,em 使… enlarge扩大enable使…能empower使…有权力e ,ex 外,出external外部的erupt喷出extra 以外,超过extraordinary格外的extrasolar太阳系以外的hyper 在上,超hyperfrequency超高频hypersonic超声的il ,im ,in ,ir 否定illogical不合逻辑的impossible不可能的invisible 不可见irrational不合理的inter 互相interchange交换interlock连锁intra ,intro 在内,内部intrapersonal个人内心的introspect内省mal 恶,不良maltreat虐待malfunction机能失常micro 微microscrope显微镜microware微波mid 中,中间mid air半空中midstream中流mini 小minibus小公共汽车ministate小国mis 错,坏mistake错误misspell拼错multi 多multiparty多党的multilingual多种语言的non 否定nonsmoker不抽烟的人nonexistent不存在的out 超过,过度,外,出,除去outgo走得比…远outgrow长得太大outdoor户外的outroot除根over 上,过度overwork工作过度overbridge天桥post 后postwar战后postnatal诞生后的pre 前,领先prewar战前的prefix前缀re 回,再return返回restart重新开始semi 半semicircle半圆semiconductor半导体sub ,suc ,suf ,sup 次,亚,在下,低于substandard低于标准规格的succeed继承suffix后缀supplement增补trans 转换,变换,横过,越过transmit传送transatlantic横渡大西洋的tri 三tricar三轮车triangle三角(形)un 否定unstable不稳定的unknown未知的under下,内(指衣服),不足underground地下的underskirt衬裙underpay付资不足uni 单一uniform均匀的unipolar单极的super- 1. 超,超级 superpower 超级大国super- 2. 上 superstructure 上层建筑super- 3. 过度,过多 superexcitation 过度兴奋supra-超,上 suprarenal 肾上腺的sur- 1. 上,外,超 surcharge 超载sur- 2. 使成...,加强意义 surround 包围用在r前sym-共同,相同 symmetry 对称用在b,m,p前syn-共同,相同 synthesis 合成tele- 1. 电 telecommunication 电信tele- 2. 远程 telemetry 远距离测量tetra-四 tetrachord 四弦乐器trans- 1. 越过,横过,超 translucent 半透明的trans- 2. 转移,变换 transport 运输tri-三 triangle 三角twi-二,两 twin 双胞胎ultra- 1. 极端 ultrathin 极薄的ultra- 2. 超,以外 ultramarine 海外的un- 1. 不 unfortunate 不幸的un- 2. 无 unmanned 无人驾驶的un- 3. 非 unartificial 非人工的un- 4. 未 uncivilized 未开化的un- 5. 相反动作,取消 unbutton 解开钮扣un- 6. 由...中弄出 unbosom 吐露(心事)under- 1. 下 underworld 下层社会under- 2. 内(用于衣服) undershirt 帖身内衣under- 3. 不足,少 underestimate 估计不足under- 4. 副,次 underking 副王,小王uni-单一 unicorn 独角兽vice-副 vice-manager 副经理with-向后,相反 withdraw 撤回,撤退-"s 1. 所有格 (a) today"s 今日的-"s 2. 店铺 (n) greengrocer"s 菜场-a 构成复数名词 (n) stadia 体育馆单数以um结尾-ability 可...性 (n) dependability 可靠性-able 可...的 (a) inflammable 易燃的-ably 可...地 (ad) suitably 合适地-aceous 有...性质的 (a) carbonaceous 含碳的-acious 具有...的,多...的 (a) sagacious 聪明的-acity 性质等(抽象)(n) veracity 诚实,真实-acle 构成名词 (n) manacle 手铐-acy 性质等(抽象)(n) fallacy 谬误-ade 1. 行为等 (n) blockade 封锁-ade 2. 物(...制成)(n) lemonade 柠檬水-ade 3. 人和集体 (n) cavalcade 骑兵队-age 1. 集合名词 (n) foliage 叶子-age 2. 场所、地点 (n) orphanage 孤儿院-age 3. 费用 (n) postage 邮资-age 4. 行为 (n) pilgrimage 朝圣-age 5. 状态,身分 (n) reportage 报告文学-age 6. 物 (n) carriage 马车,客车厢-ain 人 (n) chieftain 酋长,头子-aire 1. 人 (n) millionaire 百万富翁-aire 2. 物 (n) questionaire 调查问卷-al 1. 有...性质的 (a) continental 大陆的-al 2. 行为(抽象)(n) withdrawal 撤退-al 3. 人 (n) rival 竟争者-al 4. 物 (n) manual 手册-ality ..性,(抽象)(n) technicality 技术性-ally 方式,程度等 (ad) conditionally 有条件地-an 1. 属于...的 (a) metropolitan 大都市的-an 2. 人 (n) pubican 旅店主人-ance 情况等(抽象)(n) buoyance 浮力-ancy 情况等(抽象)(n) elegancy 优美,高雅-aneity 性质等(抽象)(n) contemporaneity 同时代-aneous 有...性质的 (a) subterraneous 地下的-ant 1. 属于...的 (a) luxuriant 奢华的-ant 2. 人 (n) participant 参与者-ant 3. 物 (n) excitant 兴奋剂-ar 1. 有...性质的 (a) consular 领事的-ar 2. 人 (n) liar 说谎的人-ar 3. 物 (n) altar 祭坛-ard 人(贬义)(n) bastard 私生子-arian 1. 人 (n) parliamentarian 国会议员-arian 2. 兼形容词 (n,a) vegetarian 吃素者(的)-arily 有...性质地 (ad) extraordinarily 不寻常地-arium 场所,...馆 (n) planetarium 天文馆-ary 1. 有...性质的 (a) customary 习惯的-ary 2. 场所,地点 (n) apiary 养蜂场-ary 3. 人 (n) secretary 书记,秘书-ary 4. 物 (n) glossary 词汇表-asm 性质(抽象)(n) sarcasm 讥讽-ast 人 (n) enthusiast 热心者-aster 人(卑称)(n) medicaster 江湖医生-ate 1. 做,造成 (v) activate 激活-ate 2. 有...性质的 (a) private 私人的-ate 3. 人 (n) graduate 毕业生-ate 4. 职位,职权 (n) professoriate 教授职位-ate 5. 构成化学名词 (n) acetate 醋酸盐-atic 有...性质的 (a) diagrammatic 图解的-ation 1. 行为,情况 (n) invitation 邀请-ation 2. 行为的过程 (n) reformation 改革-ative 与...有关的 (a) affirmative 肯定的-ator 做...工作的人,物 (n) calculator 计算机-atory 1. 具有...的 (a) exclamatory 感叹的-atory 2. 场所,地点 (n) observatory 天文台-cian ...学家 (n) clinician 临床医学专家-cracy 统治 (n) bureaucracy 官僚主义-crat 参加者,支持者 (n) democrat 民主主义者-cy 性质,状态 (n) infancy 幼年期-dom 1. 情况,身分 (n) freedom 自由-dom 2. 领域,...界 (n) sportsdom 体育界-e 构成复数名词 (n) larvae 幼虫单数以a结尾-ed 1. 构成过去式 (v) showed 展示规则动词-ed 2. 构成过去分词 (v) published 出版规则动词-ed 3. 已完成的 (a) destroyed 毁灭的-ee 受动者 (n) employee 雇员-eer 关系者,管理者 (n) volunteer 志愿者-en 1. 含...的,...制的 (a) golden 含金的-en 2. 使成为 (v) widen 加宽-ence 性质,状态,行为 (n) existence 存在-ent 有...性质的 (a) deterrent 妨碍的-er 1. 人 (n) fighter 战士-er 2. ...的住民 (n) villager 村民-er 3. 制作者 (n) hatter 帽商-er 4. 物 (n) harvester 收割机-er 5. 更... (a,ad) better 更好的比较级-ern 在...方的 (a) northern 北方的-es 1. 构成复数名词 (n) bushes 灌木单数或原型结尾ch,is,o,s,sh,x,z-es 2. 第三人称单数 (v) does 做-ese ...民族的 (a) Japanese 日本的-ess 阴性 (n) airhostess 空姐-est 最... (a,ad) nicest 最佳的最高级-et 小 (n) floweret 小花-fold ...倍的,...重的 (a) multifold 多倍的-ful 1. 有...性质的 (a) beautiful 美丽的-ful 2. ...的量 (n) teaspoonful 一茶匙-fully 有...性质地 (ad) carefully 小心地-fy 使...化 (v) electrify 通电-graph 信号 (n) electrograph 电传真-hood 性质,状态 (n) childhood 童年-i 构成复数名词 (n) fungi 真菌单数以us结尾-ial 1. ...的 (a) industrial 工业的-ial 2. 行为(抽象)(n) trial 审判-ial 3. 人 (n) official 官员-ial 4. 物 (n) material 材料-ian 1. ...的 (a) antemeridian 午前的-ian 2. ...民族的 (a) Canadian 加拿大的-ian 3. ...的人,...学家 (n) custodian 保管人-ibility 可...性 (n) responsibility 责任-ible 可...的 (a) possible 可能的-ibly 可...地 (ad) terribly 可怕地-ic 1. ...的 (a) basic 基本的-ic 2. ...的人 (n) critic 批评家-ic 3. 学科 (n) logic 逻辑学-ical ...的 (a) identical 全等的-ice 行为,动作,状态 (n) service 服务-icious 具有...的,多...的 (a) suspicious 可疑的-icity 性质 (n) authenticity 真实性,可靠性-ics 学科 (n) physics 物理学-ies 1. 构成复数名词 (n) counties 县单数以y结尾-ies 2. 第三人称单数 (v) cries 哭原型以y结尾-ing 1. 构成现在分词 (v) hoping 希望-ing 2. 正在进行的 (a) developing 发展中的-ing 3. 构成名词 (n) feeling 感觉-ious 具有...特性的 (a) glorious 光荣的-ise 使...化 (v) surprise 使惊愕 BrE-ish 1. ...民族的 (a) Turkish 土耳其的-ish 2. 有点...的 (a) tallish 稍高的-ish 3. 有...性质的 (a) foolish 笨的-ish 4. 造成,致使 (v) finish 结束-ism 主义,学说,状态 (n) socialism 社会主义-ist ...主义者,...家 (n) novelist 小说家-it ...的动作 (n) pursuit 追求-ity 性质,状态 (n) solidarity 团结-ium (化学)元素名 (n) calcium 钙-ive 有...性质的 (a) attractive 迷人的-ize 使...化 (v) initialize 初始化 AmE-kin 小 (n) princekin 小王子-less 无,没有,不 (a) hopeless 绝望的-let 小 (n) booklet 小册子-like 似...的 (n) catlike 猫样的-ling 小(轻蔑)(n) starling 小星星-logy 学科 (n) astrology 占星术-ly 1. 像...的 (a) friendly 友好的-ly 2. 方式,程度等 (ad) chiefly 首要地-ly 3. 每隔...发生的 (a) monthly 每月一次的-ment 行为,结果,手段 (n) implement 工具-most 最... (a) utmost 极端的不是最高级-ness 性质,状态,程度 (n) illness 疾病-or 1. 人 (n) emperor 皇帝-or 2. 物 (n) tractor 拖拉机-or 3. 状态,性质 (n) color 颜色 AmE-ory 1. 有...效果的 (a) satisfactory 令人满意的-ory 2. ...的处所 (n) category 目录-our 状态,性质 (n) favour 好感 BrE-ous 具有...特性的 (a) dangerous 危险的-que 概念 (n) techique 技巧-ress 阴性 (n) actress 女演员-ry 1. 性质,行为 (n) rivalry 敌对-ry 2. 境遇,身份 (n) slavery 奴役-ry 3. 种类 (n) jewelry 宝石-ry 4. 行业 (n) forestry 林业-s 1. 构成复数名词 (n) rockets 火箭-s 2. 第三人称单数 (v) plays 玩-s 3. 构成副词 (ad) indoors 在家-ship 1. 动作 (n) courtship 求爱-ship 2. 身份 (n) citizenship 公民身份-ship 3. 关系 (n) friendship 友谊-sion 动作,状态 (n) revision 复习-sis 性质,状态,动作 (n) crisis 危机-some 引起的 (a) troublesome 烦人的-teen 十... (num) fifteen 十五 13~19-th 1. 行为,结果 (n) death 死亡-th 2. 第... (num) sixth 第六基数个位≥4-tic 有...性质的 (a) romantic 浪漫的-tion 行为,状态,情况 (n) contribution 贡献-tious 有...性质的 (a) cautious 谨慎的-ty 1. 性质,情况 (n) safety 安全-ty 2. ...十 (num) ninety 九十 20, 30, ..., 90-ure 结果,动作,过程 (n) procedure 程序-ves 构成复数名词 (n) calves 幼仔单数以f,fe结尾-ward 向,向...的 (prep,a) backward 向后-wards 向 (ad) skywards 朝上地-y 1. 充满,有...性质 (a) handy 手巧的-y 2. 亲昵 (n) kitty 猫咪-yst 1. 人 (n) analyst 分析者-yst 2. 物 (n) catalyst 催化剂词根释义凡例及注解注意事项a- 1. 无,不,非 azonic 非地带性的a- 2. 含in,at等意义 asleep 在熟睡中a- 3. 加强意义 aloud 高声地ab- 离去,相反,不 abuse 滥用ac- 含at,to意,加强意义 accustom 使习惯用在c,k,q前ad- 含at,to意,加强意义 adventure 冒险用在d,h,j,m,v前af- 含at,to意,加强意义 afforest 造林,绿化用在f前ag- 含at,to意,加强意义 aggrandize 增大用在g前air- 空中的 airline 航空公司al- 1. 含at,to意,加强意义 allocate 分配用在l前al- 2. 构成副词 almost 几乎amphi- 两,双 amphibian 水陆两用车an- 1. 无,不 anarchistic 无政府的an- 2. 含at,to意,加强意义 annotate 注解用在n前ante- 前,先 anteroom 接待室anthropo- 有关人的 anthropophagus 吃人族anti- 反对,相反,防止 antibiotics 抗生素用于a前省i any- 任何 anywhere 任何地方ap- 加强或引申意义 appraise 评价用在p前apo- 离开 apogee 远地点ar- 含at,to意,加强意义 arrange 安排用在r前arch- 主要的,首位的 archenemy 头号敌人as- 含at,to意,加强意义 assort 分类用在s前en- 4. 'in'或加强意义 enregister 登记endo- 内 endoparasite 体内寄生虫epi- 在...上面 epidermis 表皮equi- 相等,同等 equilateral 正多边形eu- 优,善,好 euphonic 声音优的every- 每一 everyday 每天ex- 1. 出,外 excavate 挖出,发掘ex- 2. 前任的,以前的 ex-mayor 前任市长ex- 3. 使(做)... expurgate 使清洁exo- 外,外部 exotic 外来的extra- 以外,超过 extraterritorial 治外法权的for- 禁止,离去,克制 forbear 忍受fore- 前,先,预先 foreground 前景geo- 地质,地球 geometry 大地测量术,几何hecto- 一百 hectopascal 百帕hemi- 半 hemisphere 半球hepta- 七 heptagon 七角形hetero- 异 heterosexual 异性的hexa- 六 hexangular 有六角的high- 高,大,主要 highway 高速路holo- 全 hologram 全息图homo- 同 homonym 同音字hyper- 超过,过多,太甚 hyperacid 胃酸过多的hypo- 下,低,次,少 hypotension 低血压ideo- 观念,意义 ideograph 会意字paleo- 古,旧 paleozoology 古动物学pan- 全,泛 pantheism 泛神论para- 1. 半,类似,准 parallel 平行的para- 2. 辅助,副 paramilitary 辅助军事的para- 3. 旁,靠近,外 parasite 寄生虫para- 4. 错误,伪 paradox 似是而非para- 5. 防,避开,保护 parasol 遮阳伞para- 6. 超过 paramount 至上的pen- 几乎,相近,相似 penultimate 倒数第二个penta- 五 pentagram 五角星形per- 1. 贯穿,通,透 persist 坚持per- 2. 加强意义 perturb 扰乱per- 3. 过,高 perchloride 高氯化物peri- 周围,外层,靠近 pericarp 果皮用于a前省i poly- 多 polyfunctional 多功能的post- 后 postscript 后记pre- 1. 前 prefix 前缀pre- 2. 预先 prepay 预付pro- 1. 向前,在前 prologue 前言,序言pro- 2. 代理,代替 procurator 代理人pro- 3. 拥护,亲,赞成 pro-British 亲英的proto- 原始 protoplasm 原生质,细胞质pseudo- 假 pesudonym 假名quadr- 四 quadruped 四足动物quinque- 五 quinquesection 五等分用于a前省ere- 1. 回,向后 reclaim 收回re- 2. 再,重复,重新 reconsider 重新考虑re- 3. 相反,反对 revolt 反叛,造反retro- 向后,回,后 retrospect 回顾se- 离开,分开 secede 脱离,退出semi- 半 semimonthly 半月刊sept- 七 septuple 七倍的sex- 六 sexto 六开本Sino- 中国 Sino-Tibetan 汉藏语系some- 某 sometime 某时step- 后,继 stepfather 继父stereo- 立体 stereosonic 立体声的sub- 1. 下 submarine 海面下的sub- 2. 次,亚,准,半 subtropics 亚热带sub- 3. 稍,略,微 subarid 略干燥的sub- 4. 副,分支,下级 subworker 副手,助手sub- 5. 接近 subarctic 近北极圈的sub- 6. 更进一层,再 sublet 转租,再租suc- 使成...,加强意义 succeed 成功用在c前suf- 使成...,加强意义 suffocate 窒息用在f前sup- 使成...,加强意义 support 支持用在p前super- 1. 超,超级 superpower 超级大国super- 2. 上 superstructure 上层建筑super- 3. 过度,过多 superexcitation 过度兴奋supra- 超,上 suprarenal 肾上腺的sur- 1. 上,外,超 surcharge 超载sur- 2. 使成...,加强意义 surround 包围用在r前sym- 共同,相同 symmetry 对称用在b,m,p前syn- 共同,相同 synthesis 合成tele- 1. 电 telecommunication 电信tele- 2. 远程 telemetry 远距离测量tetra- 四 tetrachord 四弦乐器trans- 1. 越过,横过,超 translucent 半透明的trans- 2. 转移,变换 transport 运输tri- 三 triangle 三角twi- 二,两 twin 双胞胎ultra- 1. 极端 ultrathin 极薄的ultra- 2. 超,以外 ultramarine 海外的un- 1. 不 unfortunate 不幸的un- 2. 无 unmanned 无人驾驶的un- 3. 非 unartificial 非人工的un- 4. 未 uncivilized 未开化的un- 5. 相反动作,取消 unbutton 解开钮扣un- 6. 由...中弄出 unbosom 吐露(心事)under- 1. 下 underworld 下层社会under- 2. 内(用于衣服) undershirt 帖身内衣under- 3. 不足,少 underestimate 估计不足under- 4. 副,次 underking 副王,小王uni- 单一 unicorn 独角兽vice- 副 vice-manager 副经理with- 向后,相反 withdraw 撤回,撤退-'s 1. 所有格 (a) today's 今日的-'s 2. 店铺 (n) greengrocer's 菜场-a 构成复数名词 (n) stadia 体育馆单数以um结尾-ability 可...性 (n) dependability 可靠性-able 可...的 (a) inflammable 易燃的-ably 可...地 (ad) suitably 合适地-aceous 有...性质的 (a) carbonaceous 含碳的-acious 具有...的,多...的 (a) sagacious 聪明的-acity 性质等(抽象)(n) veracity 诚实,真实-acle 构成名词 (n) manacle 手铐-acy 性质等(抽象)(n) fallacy 谬误-ade 1. 行为等 (n) blockade 封锁-ade 2. 物(...制成)(n) lemonade 柠檬水-ade 3. 人和集体 (n) cavalcade 骑兵队-age 1. 集合名词 (n) foliage 叶子-age 2. 场所、地点 (n) orphanage 孤儿院-age 3. 费用 (n) postage 邮资-age 4. 行为 (n) pilgrimage 朝圣-age 5. 状态,身分 (n) reportage 报告文学-age 6. 物 (n) carriage 马车,客车厢-ain 人 (n) chieftain 酋长,头子-aire 1. 人 (n) millionaire 百万富翁-aire 2. 物 (n) questionaire 调查问卷-al 1. 有...性质的 (a) continental 大陆的-al 2. 行为(抽象)(n) withdrawal 撤退-al 3. 人 (n) rival 竟争者-al 4. 物 (n) manual 手册-ality ..性,(抽象)(n) technicality 技术性-ally 方式,程度等 (ad) conditionally 有条件地-an 1. 属于...的 (a) metropolitan 大都市的-an 2. 人 (n) pubican 旅店主人-ance 情况等(抽象)(n) buoyance 浮力-ancy 情况等(抽象)(n) elegancy 优美,高雅-aneity 性质等(抽象)(n) contemporaneity 同时代-aneous 有...性质的 (a) subterraneous 地下的-ant 1. 属于...的 (a) luxuriant 奢华的-ant 2. 人 (n) participant 参与者-ant 3. 物 (n) excitant 兴奋剂-ar 1. 有...性质的 (a) consular 领事的-ar 2. 人 (n) liar 说谎的人-ar 3. 物 (n) altar 祭坛-ard 人(贬义)(n) bastard 私生子-arian 1. 人 (n) parliamentarian 国会议员-arian 2. 兼形容词 (n,a) vegetarian 吃素者(的)-arily 有...性质地 (ad) extraordinarily 不寻常地-arium 场所,...馆 (n) planetarium 天文馆-ary 1. 有...性质的 (a) customary 习惯的-ary 2. 场所,地点 (n) apiary 养蜂场-ary 3. 人 (n) secretary 书记,秘书-ary 4. 物 (n) glossary 词汇表-asm 性质(抽象)(n) sarcasm 讥讽-ast 人 (n) enthusiast 热心者-aster 人(卑称)(n) medicaster 江湖医生-ate 1. 做,造成 (v) activate 激活-ate 2. 有...性质的 (a) private 私人的-ate 3. 人 (n) graduate 毕业生-ate 4. 职位,职权 (n) professoriate 教授职位-ate 5. 构成化学名词 (n) acetate 醋酸盐-atic 有...性质的 (a) diagrammatic 图解的-ation 1. 行为,情况 (n) invitation 邀请-ation 2. 行为的过程 (n) reformation 改革-ative 与...有关的 (a) affirmative 肯定的-ator 做...工作的人,物 (n) calculator 计算机-atory 1. 具有...的 (a) exclamatory 感叹的-atory 2. 场所,地点 (n) observatory 天文台-cian ...学家 (n) clinician 临床医学专家-cracy 统治 (n) bureaucracy 官僚主义-crat 参加者,支持者 (n) democrat 民主主义者-cy 性质,状态 (n) infancy 幼年期-dom 1. 情况,身分 (n) freedom 自由-dom 2. 领域,...界 (n) sportsdom 体育界-e 构成复数名词 (n) larvae 幼虫单数以a结尾-ed 1. 构成过去式 (v) showed 展示规则动词-ed 2. 构成过去分词 (v) published 出版规则动词-ed 3. 已完成的 (a) destroyed 毁灭的-ee 受动者 (n) employee 雇员-eer 关系者,管理者 (n) volunteer 志愿者-en 1. 含...的,...制的 (a) golden 含金的-en 2. 使成为 (v) widen 加宽-ence 性质,状态,行为 (n) existence 存在-ent 有...性质的 (a) deterrent 妨碍的-er 1. 人 (n) fighter 战士-er 2. ...的住民 (n) villager 村民-er 3. 制作者 (n) hatter 帽商-er 4. 物 (n) harvester 收割机-er 5. 更... (a,ad) better 更好的比较级-ern 在...方的 (a) northern 北方的-es 1. 构成复数名词 (n) bushes 灌木单数或原型结尾ch,is,o,s,sh,x,z-es 2. 第三人称单数 (v) does 做-ese ...民族的 (a) Japanese 日本的-ess 阴性 (n) airhostess 空姐-est 最... (a,ad) nicest 最佳的最高级-et 小 (n) floweret 小花-fold ...倍的,...重的 (a) multifold 多倍的-logy 学科 (n) astrology 占星术-ly 1. 像...的 (a) friendly 友好的-ly 2. 方式,程度等 (ad) chiefly 首要地-ly 3. 每隔...发生的 (a) monthly 每月一次的-ment 行为,结果,手段 (n) implement 工具-most 最... (a) utmost 极端的不是最高级-ness 性质,状态,程度 (n) illness 疾病-or 1. 人 (n) emperor 皇帝-or 2. 物 (n) tractor 拖拉机-or 3. 状态,性质 (n) color 颜色 AmE-ory 1. 有...效果的 (a) satisfactory 令人满意的-ory 2. ...的处所 (n) category 目录-our 状态,性质 (n) favour 好感 BrE-ous 具有...特性的 (a) dangerous 危险的-que 概念 (n) techique 技巧-ress 阴性 (n) actress 女演员-ry 1. 性质,行为 (n) rivalry 敌对-ry 2. 境遇,身份 (n) slavery 奴役-ry 3. 种类 (n) jewelry 宝石-ry 4. 行业 (n) forestry 林业-s 1. 构成复数名词 (n) rockets 火箭-s 2. 第三人称单数 (v) plays 玩-s 3. 构成副词 (ad) indoors 在家-ship 1. 动作 (n) courtship 求爱ag,act 做,驱动 agent代理人 active活动的,积极的agr 农田 agriculture农业 agrarian田地的am 爱,亲爱 amicable友善的 amiable和蔼可亲的anim 心灵,精神,生命 animal动物 animate有生命的ann,enn 年 annual一年的 centennial一世纪的astro 星 astronomy天文学 astronaut宇宙航行员audi 听 audience听众 audible听得见的bell 战争 rebellion反叛,反抗 bellicose好战的bio 生命,生物 biology生物学 antibiotic抗生的,抗生素brev 短 brevity 简短 abbreviate缩短,节略cede 走 precedent先行的,在前的 precede先行cent 百 centimeter厘米 centigrade百分度的center,centr 中心 concentrate集中 centrifugal离心力的cide,cis 杀,切 suicide自杀 bactericide杀菌剂claim,clam 叫喊 exclaim惊叫 proclaim宣布,宣告clar 清楚,明白 declare表明,声明 clarify讲清楚clud,clos 关闭 close关闭 exclude排斥cogn 知道 recognize承认 cognitive认识的cord 心 cordial衷心的 core核心cosm 宇宙,世界 osmic宇宙的 cosmos宇宙cred 相信 credibility可信 credit信任cur,cours 跑 ccurrence出现,发生 current流通的cycl 圆,环 bicycle自行车 cyclone旋风di 日 diary日记 diarist记日记者dict 说 predict预言 indicate表示duc,duct 引导 conduct指导 induce引诱ed 吃 edible可吃的 edacity贪吃fact 做,制 factory工厂 manufacture制造,加工fer 带,拿 transfer转移 ferry渡船flu 流 fluent流利的 influenza流行性感冒form 形式,外形 transform改变 formula公式fract,frag破,折 fraction碎片 fragile易碎的fus 倾,注,溶化 fusion熔解 effuse泻出gen 起源 generate使产生 genetic遗传的geo 地球,土地 geography地理 geology地质学grad 步,走,级 gradual逐步的 graduate毕业gram 写,记录 diagram图表 program节目单,方案graph 写,画,记录 photograph照像 autograph亲笔,手稿。
Gaussian中IOP关键词使用详解
Technical Support InformationLast update: 16 April 2003Overlay 15 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 88 89 90 91 92 94 95 96 97 98 101 102 103 104 105 106 107 108 109 110 111 112 113 114Overlay 29 10 11 12 13 14 15 16 17 18 19 20 29 30 40 41Overlay 35 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 67 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106Overlay 45 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 29 31 33 34 35 36 37 38 43 44 45 46 47 48 60 61 62 63 64 65 66 67 68 69 71 72 80 81 82 110Overlay 55 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102Overlay 615 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 70 71 72 73 74 75 76 77 78 79 80 81 82 83Overlay 76 7 8 9 10 11 12 13 14 15 16 18 25 29 30 31 32 40 41 42 43 44 45 52 53 64 65 70 71 72 74 75 76 77 87Overlay 85 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 27 28 29 30 31 32 35 36 38 39 40 41 42 43 44 45 46 47Overlay 95 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25 26 27 28 30 31 36 37 38 40 41 42 43 44 45 46 47 48 49 60 61 62 70 71 72 73 74 75 81 82 83 84 85 86Overlay 105 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 28 29 30 31 32 45 46 47 48 60 61 62 63 72 72 74 75 76 77 78 79Overlay 115 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 26 27 28 29 30 31 32 33 39 40 41 42 43 45 46 53 60 61 62 63 70 71 75Overlay 99995 6 7 8 9 10 11 12 13 14 15 16 17 18 33Technical Support InformationLast update: 22 March 2003Overlay 15 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 88 89 90 91 92 94 95 96 97 98 101 102 103 104 105 106 107 108 109 110 111 112 113 114IOp(1/5)L103 MODE OF OPTIMIZATION 0 FIND LOCAL MINIMUM 1 FIND A SADDLE POINT N FIND A STATIONARY POINT ON THE ENERGY SURFACE WITH N NEGATIVE EIGENVALUES OF THE 2ND DERIVATIVE MATRIX L107: MODE OF SEARCH 0 LOCATE THE MAXIMUM IN THE LST PATH. 1 SCAN THE LST PATH.IOp(1/6)L102, L103, L105, L107, L109, L112, L113, L114: MAXIMUM NUMBER OF STEPS (OR NUMBER OF STEPS FOR AN LST SCAN). 0 NSTEP = Max(20,NVAR+10) (L103, L112) = Min(20,NVAR+10) (L102, L105, L109) = Min(40,NVar+20) (L113, L114) N NSTEP = NIOp(1/7)L103, L105, L109, L112, L113, L114: CONVERGENCE ON THE FIRST DERIVATIVE AND ESTIMATED DISPLACEMENT FOR THE OPTIMIZATION RMS FIRST DERIVATIVE .LT. CONFV, RMS EST. DISPLACEMENT .LT. CONVX=4*CONVF -1 ConvF = 1/600 HARTREE/BOHR OR RADIAN 0 CONVF = 0.0003 HARTREE/BOHR OR RADIAN N CONVF = N*10**-6 L116, L117: Convergence on electric field/charges -1 Default value for optimizations: 10**-7. 0 Default value for single-points: 10**-5 in L116, 10**-7 in L117. N 10**-N.IOp(1/8)L103, L109, L112: MAXIMUM STEP SIZE ALLOWED DURING OPT. 0 DXMAXT = 0.1 BOHR OR RADIAN (L103, Estm or UnitFC). = 0.3 Bohr or Radian (L103, Read or CalcFC). = 0.2 Bohr or Radian (L105). = 0.3 Bohr or Radian (L113, L114). DXMAXT = 0.01 * NNL117: General control. 0 Which type of basin to use to partition the density isosurface. Default is 4 1 GradVne 2 GradRho 3 Don't Use Basins, Use only the Center of NuclearCharge 4 Use Interlocking Spheres N0 Order of Adam's-Bashforth-Moulton (ABM) predictorcorrector method to use in solving diff. eqns. for the grad RHO or Vne trajectories. Default is 4, max is 9. N00 Number of small steps per ABM step to be used in starting ABM and when "slow down" is needed in ABM. Default is 5. N000 Which approximation to make. Default is III for Tomasi (interlocking spheres) and IV for general surface. 1000 Apprx. I - Don't Do Self-Polarization or "Compensation" 2000 Apprx. II - Do-Self Polarization, But No Compensation. 3000 Apprx. III - Do Self-Polarization and Compensation. 4000 Apprx. IV - Do III and Allow Surface To "Relax" in Solution if no spheres N0000 Whether to evaluate densities using orbitals or density matrix. Default is to use density. 10000 Use MOs. 20000 Use density. L121: Time step, N*0.0001 fs, default 0.1IOp(1/9)L103: Use of Trust radius. 0 Whether to update trust radius (DXMaxT, default Yes). Default is Yes for minima, no for TS. 1 2 No. Yes.00 Whether to scale or search the sphere when reducing the step size to the trust radius (Default search for minima, scale for transition states.). 10 20 Scale. Search.L107: WHETHER TO MAINTAIN SYMMETRY ALONG THE SEARCH PATH. 0 1 YES. NO.L117: Whether to delete points which are too close together: 0 1 No Yes, using a default criteria (0.05 Angstroms)-N Yes, using a (10**-N Angstroms) criteria. How close to get to the isosurface in search. 0 N Approx 1.0D-6 (N=20) 2.0**-NL121: Whether to read in initial velocities: 0 1 2 3 Default (same as 1) Generate random initial velocity Read in initial cartesian velocity (Bohr/sec) Read in initial MW cartesian velocity (sqrt(amu)*Bohr/sec)IOp(1/10)L103, L105, L109, L112, L113, L114: Input of initial Hessian: All values must be in atomic units (Hartree, Bohr, and radians). 0 1 2 3 Use defaults (not valid for L109). Read ((FC(I,J),J=1,I),I=1,NVAR) (8F10.6) (L103 only). Read I,J,FC(I,J), (5I3,F20.0) (L103 only). End with a blank card. Read from checkpoint file in internal coordinates.4 Second derivative matrix calculated analytically. (not valid for L109). 5 Read cartesian forces and force constants from the checkpoint file are convert to internal coordinates. 6 Read cartesian forces followed by cartesian force constants (both in format 6F12.8) from input stream. followed by a blank line. 7 8 9 10 Use semiempirical force constants. Use unit matrix (default for L105; only recognized by 103). Estimate force constants using valence force field. Use unit matrix throughout.IOp(1/11)L103: TEST OF CURVATURE. BOMB THE JOB IF THE SECOND SECOND DERIVATIVE MATRIX HAS THE WRONG NUMBER OF NEGATIVE EIGENVALUES. 0 DEFAULT (TEST for z-matrix or cartesian TS but not for LST/QST or for minimum). 1 2 DON'T TEST. TEST.L117: Scaling Factor for Determining Overlaps of VDW atoms -1 0 N Turn off scaling Default is 1.010 1.000 + N*(0.001)Step size for ABM method in Trudge for isodensity method. 0 N 0.05 (N=2) 0.1/NIOp(1/12)L103: OPTIMIZATION CONTROL PARAMETERS 0 USE DEFAULT VALUES1 READ IN NEW VALUES FOR ALL PARAMETERS (SEE INITBS)IOp(1/13)L103,L113,L114,L115: Type of Hessian Update: 0 Default (9 for L103 minimization, 7 for L103 TS, D2Corr and L115, Powell for L113 and L114). 1 2 3 4 5 6 7 8 9 Powell (not in L103). BFGS (not in L103) BFGS, safeguarding positive definateness (not inL103 or L115) D2Corr (New, only in L103 and L115). D2Corr (Old, only in L103 and L115). D2Corr (BFGS) D2Corr (Bofill Powell+MS for transition states). D2Corr (No update, use initial Hessian). D2Corr (New if energy rises, otherwise BFGS).L121: Multi-time step parameter (NDtrC,NDtrP) 0 NN No multi-time stepping Iterate density constraints NN times per stepMM00 Do gradient once every MM stepsIOp(1/14)L103: Max. number of bad steps to allow before attempting a linear minimization (i.e., no quadratic step). 0 N Default (0 for TS, 1 for minima). Allow N -- linear only starts with the N+1st.IOp(1/15)L103,L109: ABORT IF DERIVATIVES TOO LARGE -1 or 0 N No force test at all. FMAXT = 0.1 * NIOp(1/16)L103,L113,L114: MAXIMUM ALLOWABLE MAGNITUDE OF THE EIGENVALUESOF THE SECOND DERIVATIVE MATRIX. IF THE LIMIT IS EXCEEDED, THE SIZE OF THE EIGENVALUE IS REDUCED TO THE MAXIMUM, AND PROCESSING CONTINUES. 0 N EIGMAX = 25.0 HARTREE / BOHR**2 OR RADIAN**2 EIGMAX = 0.1 * NIOp(1/17)L103,L113,L114: MINIMUM ALLOWABLE MAGNITUDE OF THE EIGENVALUES OF THE SECOND DERIVATIVE MATRIX. SIMMILAR TO IOp(16) 0 N EIGMIN = 0.0001 EIGMIN = 1. / NIOp(1/18)L103: Coordinate system. 0 Proceed normally1 Second derivatives will be computed as directed on the variable definition cards. No optimization will occur. 10 20 30 40 Do optimization in cartesian coordinates. Do full optimization in redundant internal coord. Do full optimization in pruned distance matrix coords. Do optimization in Z-matrix coordinates.50 Do full optimization in redundant internal coords with large molecular tools. 100 1000 2000 3000 Read the AddRedundant input section for each structure. Do not define H-bonds Define H-bonds with no related coordinates (default) Define H-bonds and related coordinates10000 Reduce the number of redundant internals 20000 Define all redundant internals 100000 0000000 Old definition of redundant internals. Default (2000000).1000000 Skip MM atoms in internal coordinate definitions and do microiterations the old way, in L103. 2000000 Include MM atoms in internal coordinate definitions (no microiterations). 3000000 Skip MM atoms in internal coordinate definitions and do microiterations the new way, in L120. 4000000 Microiterations for pure MM, done in L402.IOp(1/19)L103: SEARCH SELECTION 0 2 Default (same as 6). LINEAR AND STEEPEST DESCENT.3 STEEPEST DESCENT AND LINEAR ONLY WHEN ESSENTIAL. 4 5 6 7 8 9 10 11 13 Quadratic if curvature is correct; RFO if not. Linear as usual. Quadratic if curvature is correct; RFO if not. No linear search. RFO and linear. RFO without linear. Newton-Raphson and linear. Newton-Raphson only. GDIIS and linear GDIIS only. First-order simultaneous optimization.L113,L114: Search Selection: 0 P-RFO OR RFO STEP ONLY (DEFAULT)1 P-RFO OR RFO STEP FOR "WRONG" HESSIAN OTHERWISE NEWTON-RAPHSONIOp(1/20)L101, L106, L108, L109, L110: INPUT UNITS 0 1 2 3 ANGSTROMS DEGREES BOHRS DEGREESANGSTROMS RADIANS BOHRS RADIANSIOp(1/21)L103,L113,L114: EXPERT SWITCH. 0 NORMAL MODE.1 EXPERT MODE: CERTAIN CUTOFFS USED TO CONTROL THE OPTIMIZATION WILL BE RELAXED. THESE INCLUDE FMAXT, DXMAXT, EIGMAX AND EIGMIN.IOp(1/22)L107: Whether to reorder coordinates for maximum coincidence. 0 1 2 Yes. Assume reactant order equals product order. Read in a re-ordering vector from the input.L115: KIND OF SEARCH: 0 1 2 3 4 5 6 7 BOTH DIRECTIONS AND GENERATE SEARCH VECTOR FORWARD DIRECTION AND GENERATE S. VECTOR BACKWARD DIRECTION AND GENERATE S. VECTOR BOTH DIRECTIONS AND GENERATE S. VECTOR FORWARD DIRECTION AND READ S. VECTOR 8F10.6 FORWARD DIRECTION AND READ S. VECTOR 8F10.6 BACKWARD DIRECTION AND READ S. VECTOR 8F10.6 BOTH DIRECTIONS AND READ S. VECTOR 8F10.6IOp(1/23)L112: Derivative availability. 0 1 2 Energy only. Energy + Forces. Energy + Forces + Force constantsIOp(1/24)Whether to round tetrahedral angles. 0 1 2 Default (Yes). Yes, round angles within 0.001 degree. No.IOp(1/25)Wether SCRF is used with numerical polarizability: 0 1 No. Yes, the field in /Gen/ must be cleared each time.IOp(1/26)Accuracy of function being optimized: -NNMM Energy 10**-(NN), Gradient 10**-(MM). -1 0 1 2 3 Read in values Default (same as 1). Normal accuracy for HF (energy and gradient both 1.d-7). Standard grid accuracy for DFT (Energy 1.d-5, gradient 1.d-4) Fine grid accuracy for DFT (Energy 1.d-7, gradient 1.d-6)IOp(1/27)= IJKL (i.e. 1000*I+100*J+10*K+L) Transition state searching using QST and redundant internal coordinates L= 0,1 Input one structure, either initial guess of the minimizing structure or transition structure without QST. L= 2 Input 2 structures, the first one is the reactant, the second one is the product. The union of the two redundant coordinates are taken as the redundant coords for the TS. The values of the TS coord are estimated by interpolating the sturcture of R and P. R and P are used to guide the QST optimization of the TS. L= 3 Input 3 structures. The first one is reactant the second one is the product. The third one is the initial guess of the transition structure. R and P are used to guide the QST optimization of the TS. K = 1-9 Interpolation of initial guess of TS between R and P (TS=0.1*J*R + 0.1*(10-J)*P, default J=5) J=1 J=2 J=3 J=4 LST constraint in internals QST constraint in internals LST constraint in distance matrix space QST constraint in distance matrix spaceI = 0-9 Control parameters for climbing phase of QST (e.g. QSTRad = 0.01*I, default QSTrad = 0.05)IOp(1/28)L103: Number of translations and rotations to remove during redundant coordinate transformations: -2 -1 0 N 0. Normal (6 or 5 for linear molecules). Default, same as -1. N.IOp(1/29)L101: SPECIFICATION OF NUCLEAR CENTERS 0 BY Z-MATRIX1 BY DIRECT COORDINATE INPUT (must set IOp(29) in L202). 2 GET Z-MATRIX AND VARIABLES FROM THE CHECKPOINT FILE. 3 GET CARTESIAN COORDINATES ONLY FROM THE CHECKPOINT FILE. 4 5 By model builder, model A. By model builder, model B.6 Get Z-matrix from the checkpoint file, but read new values for some variables from the input stream. 7 Get all input (title, charge and multiplicity, structure) from the checkpoint file. 10 000 Print details of the model building process. Default (same as 100).100 Do not abort job if model builder generates a z-matrix with too many variables. 200 Abort job if model builder generates a z-matrix with too many variables. 1000 2000 3000 4000 5000 00000 Read optimization flags in format 50L1 after the z-matrix. Set all optimization flags to optimize. Purge flags except the frozen variables. Rebuild the coordinate system. (2+3) Purge all flags but keep the coordinate definition. Default, same as 10000.10000 Mark Z-matrix constants as frozen variables rather than wired-in constants. 20000 Do not retain symbolic constants.100000 Generate a symbolic z-matrix using all Cartesians if none is present on the checkpoint file (a hack to make IRCs work with Cartesian input). 200000 Same as one, but retain the redudant internal coordinate definitions.IOp(1/30)L103: ARE THE READ-WRITE FILES TO BE UPDATED? THIS OPTION IS SET FOR THE LAST CALL TO 103 IN FREQUENCY CALCULATIONS IN ORDER TO PRESERVE THE VALUES OF THE VARIABLES FOR ARCHIVING. It also suppresses error termination on large gradients. 0 1 YES NOIOp(1/32)TITLE CARD PUNCH CONTROL. 0 1 DON'T PUNCH. PUNCH.IOp(1/33)L101: L102 L103 L106 L109 L110 L113 L114 0 1 OFF ON DEBUG PRINTIOp(1/34)L101 L102 L103: DEBUG + DUMP PRINT 0 1 OFF ONIOp(1/35)RESTART (L102-L112). 0 NORMAL OPTIMIZATION.1 FIRST POINT OF A RESTART. GET GEOMETRY, WAVEFUNCTION, ET. FROM THE CHECKPOINT FILE.IOp(1/36)CHECKPOINT. 0 1 NORMAL CHECKPOINT OF OPTIMIZATION. SUPPRESS CHECKPOINTING.IOp(1/37)D2E CLEANUP (obsolete) 0 NO CLEANUP.1 THIS IS THE LAST POINT AT WHICH ANALYTIC SECOND DERIVATIVES WILL BE DONE. DELETE THE D2E FILE AND THE BUCKETS AND TRUNCATE THE READ/WRITE FILES.IOp(1/38)Entry control option (currently only by L106, L107, L108, L109, L110, L111, and L112 but not L102, L103, and L105). 0 1 N>1 . Continuation of run. Initial entry. In L103: Initial entry of guided optimization using N levels.N0 In L106: differentiate Nth derivatives once. In L110 and L111: differentiate energy N times. 000 100 200 In L106: differentiate wrt nuclear coordinates. In L106: differentiate wrt electric field. In L106: differentiate wrt field and nuclear.IOp(1/39)Step size control for numerical differentiation. (L106, L109, L110, L111). Path step size in L115. 0 Use internal default (0.001 Angstroms in L106, 0.005 A in L109, 0.01 Angstrom in L110, 0.001 au in L111). N Use step-size of 0.0001*N (angstroms in L106, L109, L110, electric field au in L111). -1 Read stepsize (up to 2 for L106, 1 for others), free-format.-N>1 Use step-size of 0.0001*N atomic units everywhere.IOp(1/40)L113, L114: Hessian recalculation. -1 0 N Pick up analytic second derivatives every time. Just update. The default, execpt for CalcAll. Recalculation the Hessian every N steps.L116: Whether to read initial E-field: 0 1 2 Start with 0.0. Read from checkpoint file. Read from input stream.IOp(1/41)Step number of optimization from which to take geometry. -1 for the initial geometryIOp(1/42)L103, L115: Number of points along the reaction path in each direction. Default is 6. L117: Cutoff to be used in evaluating densities. 0 N 1.0D-10 1.0D-NIOp(1/43)L116: Extent of Reaction Field. 0 1 2 3 Dipole Quadrupole Octapole HexadecapoleL117: How to define Radii 0 1 2 10 20 30 Default is 11 Use internally stored Radii, centers will be on atoms Read-in centers and radii on cards Force Merz-Kollman radii (Default) Force CHELP (Francl) recommended radii. Force CHELPG (Breneman) recommended radii.100 Read in replacement radii for selected atom types as pairs (IAn,Rad) or (Symbol,Rad), terminated by a blank line. 200 Read in replacment radii for selected atoms as pairs (I,Rad), terminated by a blank line. Initial radius of spheres to be placed around attractors to "capture" the gradient trajectories. The final radius is then automatically optimized separately for each atom. 0 NM 0.1 N.M = NM/10IOp(1/44)IRC Type 0 1 2 3 Default (same as 3). Cartesian. Internal. Mass-weighted.L117: Maximum distance between a nucleus and its portion of the isosurface - used in Trudge only to eliminate, from the outset, points which clearly lie in another basin. This parameter should be chosen with the parameter Cont in mind 0 NM 10.0 au N.M au = NM/10L121: Seed for random number generator (ISeed) -1 Use system time initialize iseed (Note each run will give different results) 0 N Use default seed value (ISeed = 398465) Set random number seed to NIOp(1/45)Read isotopes in L115. 0 1 Do not read isotopes. Read Isotopes.IOp(1/46)Order of multipoles in numerical SCRF: 0 1 2 3 Dipole Quadrupole Octapole Hexadecapole.IOp(1/47)Number of redundant internal coordinates to allow for. 0 N Default: 50000 N.IOp(1/48)IRCMax control. 1 20 Do IRCMax Include zero-point energy.CIOp(1/49)Options to IRC path relaxation (IJKL) L 2/1 dont/do optimize reactant structure. Default: 1K2/1 dont/do optimize product structure. Default: 1J 3/2/1 dont/QST3/QST2 optimize TS structure (for QST input). Default: 1 I 2/1 unimolecular/bimolecular reaction. Default: unimolecularIOp(1/52)L101 and L120: Type of ONIOM calculation: 0/1 2 3 00 10 20 100 One layer, normal calculation Two layers Three layers Default (20) Include electrostatics in model systems using MM charges. No electrostatics included in the model systems Do full square for testing.N000 Use atomic charge type N-1 during microiterations. The default is MK charges.IOp(1/53)L120: Action of each invocation of L120: 0 1 Do nothing Set up point MM on rwf from initial data2 Set up point MM on rwf from initial data and restore point MM on chk file if ONIOM data is present there. 3 4 5 6 Restore point M from data on the rwf. Integrate energy Integrate energy and gradient Integrate energy, gradient, and hessian7 Restore point MM from RWF but do not create a new model system. NN0 Save necessary information (some rwf's, energy, gradients, hessian) of point NN of the ONIOM grid. NN = MaxLev**2 + 1 (currently 17) to restore real system. MM000 Calc Level High ||| Mid ||| Low SML 1--3--6 system size 2--5--8 4--7--9* Next point to do is MM.IOp(1/54)Whether to recover initial energy during IRCMax from chk file: 0 1 No. Yes.IOp(1/55)L103: Options for GDIIS: ICos*1000+IChkC*100+IMix*10+Method form. L115: IRC optimization. 0 1 Default, use gradients to find the next geometry. Use displacements to find the next geometry.IOp(1/56)Set of atom type names to parse: 0 1 2 Accept any. Dreiding/UFF. Amber.3 Amber allowing any symbol, for use with parameters in input stream.IOp(1/57)Whether to produce connectivity: 0 Default (4 if reading geom from chk file and connectivity is there, otherwise 3). 1 2 3 4 5 10 No. Yes, read from input stream Yes, generate connectivity. Yes, read from checkpoint file. Yes, read from rwf file. Read modifications.100 Connectivity input is in terms of z-matrix entries, including dummy atoms.IOp(1/58)IRCMax control in L115.IOp(1/59)Update of coordinates in L103 0 1 2 Default (1 for large opt, 2 for regular) New versions. Old version.IOp(1/60)Interpret extra integer and fp values in z-matrix as scan information. 0 1 2 Default (No). Yes. No.IOp(1/61)How ONIOM should leave the rwf at the end of each geomtry: 0 Default (1).1 Normal: leave the rwf set up for the low-level calculation on the real system. 2 MOMM: leave the rwf set up for the real system, but with NBasis and NBsUse for the high-level calc on the model system. Useful for treating the full system as having electrons only on the QM atoms.IOp(1/62)Counterpoise control. NN NN fragments, NN < 50.IOp(1/63)Step in counterpoise calculation: MNN NN = 0 1-NFrag M = order of derivatives (1=Energy, 2=Gradient, Supermolecule Fragments with ghost atomsNFrag+1 - 2*NFrag -- lone fragmentsIOp(1/64)Molecular mechanics force field selection: 0 1 2 3 4 5 6 7 000 100 200 300 None. Dreiding. UFF. AMBER. MM2 (NYI). MM3 (NYI). MMFF (NYI). Quartic fitting field (NYI). Use only hard-wired. Use soft and hard-wired, hard-wired has priority. Use soft and hard-wired, soft has priority. Use only soft. Lowest 2 digits then have no meaning.0000 Do not read modifications to parameter set. 1000 Read modifications to parameter set. 00000 With soft parameters, abort when different parameters match to the same degree. 10000 Use the first when there are equivalent matches. 20000 Use the last when there are equivalent matches. If IOp(67)=3, then the default is to apply soft parameters with higher priority.IOp(1/65)Control of which terms are included in MM, corresponding to the 'classes' in FncInf. 0 1 10 100 1000 10000 Do all (default) Non-bonded Stretching Bending Torsion Out-of-planeIOp(1/66)Whether to generate QEQ charges, over-written the values in AtChMM, or to use the values already there. 0 1 2 00 10 20 000 100 200 Default (2, 1==> 221) Do QEq. Don't do QEq. Default (10) Do for atoms which were not explicitly typed. Do for all atoms regardless of typing. Default (100) Do for atoms which have charge specified or defaulted to 0. Do for all atoms regardless of initial charge.IOp(1/67)Source of MM parameters. 0 1 2 3 Default: 2 if reading geom from chk file, else 1. Generate here, reading from input if requested by IOp(64). Copy from chk file. Pick up non-standard parameters from chk file.IOp(1/70)L118 Type of sampling (Nact) 0 1 2 3 4 Defalt (same as 3) Orthant sampling Microcanonical normal mode sampling Fixed normal mode energy Local mode sampling ( now only Nact = 0 or 3 OK )IOp(1/71)Whether to print out input files for each structure along an IRC: 0 1 No. Yes.IOp(1/72)L103: Algorithm choice for microiterations. L121: Lagrangian constrain method for ADMP (ICType) Half*Gamma*Tr[(P*P-P)**2] + Lambda*[Tr(P)-Ne] + Eta*Tr(P*P-P) 0 Default Same as 7 if no Mass-Weighting (IOp(76) < 0) Same as 10 if Mass-Weighting (IOp(76) > 0) 1 2 Use Lambda and Eta only. (Gamma=0) Use Lambda, Eta, Gamma. Gamma = .23 Use Lambda, Eta, Gamma. Gamma = 1. Constraints for scalar Mass case: 4 Use exact constraint Sum(ij)[Vij*(P**2-P)ij]5-7 Iterative Scheme same as 4. Different initial guesses. 7 is default for scalar mass case. Constraints for tensorial Mass: 8-11 Mass-weighting constraints. Documentation maybe found in DVelV1. 10 is default.IOp(1/73)L103: NInit for microiterations. L121: Initial Kinetic energy of the Nuclei (EStrtC) 0 Default (.1 Hartree)N>0 N*micro-Hartree N<0 0.0 HartreeIOp(1/74)Charge scaling for charge embedding in ONIOM. IJKLMN 6th through 1st nearest neighbors of current layer scaled by I*0.2, J*0.2, etc. 0 ==> 5 (no scaling); all layers are scaled by at least as much as ones farther out. The default is 500. M L0 Factor for charges one bond away from link atom Factor for charges two bonds away from link atomK00 Factor for charges three bonds away from link atom IJ etc. The actual factors used are: 0: 1.0 1: 0.0 2: 0.2 3: 0.4 4: 0.6 5: 0.8 6-9: 1.0IOp(1/75)ADMP control flag (ICntrl) 0 1 2 3 00 10 20 Standard ADMP Read converged density at every step Fix the nuclear coordinates Test time reversability (MaxStp must be even) Default (20). Read stopping parameters from input. Do not read stopping parameters.IOp(1/76)+/- XXXXZYYYY = Ficticous electron mass (EMass) YYYY Default (1000) IOp(76)>0 YYYY*.0001 AMU MW core functions more than valence functions. IOp(76)<0 YYYY*.0001 AMU. Use uniform scaling for all basis functions (Note YYYY > 9999 makes no sense) Z Mass-weighting option. If IOp(76)<0, Z is meaningless.XXXX If PBC: Mass of Box Coordinates (BoxMas) = XXXX*.0001 AMU BoxMas=0 Box coordinates not propagated (default).IOp(1/77)Initial Kinetic energy of the density matrix (EStrtP) (For UHF, Alpha and Beta each get half this energy) and Option Number to compute initial kinetic energy. Format of Input: XXYYYY (six digits) IWType = XX N = YYYY (For UHF, Alpha and Beta each get half this energy) 0 Default (0.0 Hartree)N>0 N*micro-Hartree IWType is used to figure out how the initial velocity is is computed (in gnvelp). If XXYYYY < 0 : Initial velocity = 0.0 Hartee (i.e., currently same as N=0 above)IOp(1/78)Sparse in L121 -N 0 1 Sparse here with cutoff 10**(-N), full elsewhere Use full matrices or spase based on standard settings. Use sparse fixed formIOp(1/79)IRCMax convergence in L115 Stopping criteria in L118 and L121.IOp(1/80)L106: 0/1/2 Cartesian/Normal mode/Internal coordinate differentiation. 2 is NYI. L118: .eq.1 to surpress the 5th order correction after surface hop has been made in Trajectory Surface Hopping calculations. Needs also IOp(10/80=1) Nuclear Kinetic Energy Thermostat Option. (Currently only Velocity scaling is implemented) 0 No Thermostat.11XXXXX Velocity scaling, but only for the first XXXXX simulation steps. (This options is useful, if thermostating in only required during equilibration. 1000000 Velocity scaling, all the way through the simulation.IOp(1/81)Nuclear KE thermostat in ADMP -- temperate is checked and scaled every IOp(81) steps.IOp(1/82)Temperature for nuclear KE thermostat in L121.IOp(1/83)Whether to read in frequencies for electric and magnetic perturbations. 0 1 2 Default (No). Yes. No.IOp(1/84)Differentiation of frequency-dependent properties. 0 N No. Mask for which properties on file 721 will be differentiated.IOp(1/85)Band gap calculation in PBC ADMP: 0 1 2 Default (No). Diagonalizae Fock matrix to get band gap, evolution, etc. No.IOp(1/86)Printing for NMR for ONIOM. 0 1 2 Default (1). Print tensors and eigenvalues. Print eigenvectors as well.IOp(1/87)ONIOM integration of density. 0 1 2 K0 L00 Do not integrate. Integrate current densities. Integrate densities specified by following digits: Density to use from gridpoint 1 Density to use from gridpoint 2M000 etc. K,L,M,etc: 0: SCF 1: MP first order 2: MP2 3: MP3 4: MP4 5: CI one-particle 6: CI 7: QCI/CC 8: Correct to second orderIOp(1/88)Whether to read in atomic masses (isotopes): 0 Default (1 if geometry read from input, 4 if geometry read from chk) 1 Use most abundant isotopes.2 Read isotopes from input. The temperature and pressure are read first, for backwards compatibility. 3 4 Read isotopes from rwf. Read isotopes from chk.IOp(1/89)Maximum allowed deviation from average nuclear KE during ADMP, in Kelvin.IOp(1/90)To read in the velocity in cartesian coordinates Nuclear Kinetic Energy Thermostat Option. Average energy (in microhartree) to be maintained during Simulation, as required by IOp(80).IOp(1/91)Thermostat Option.IOp(1/92)Maximum allowed deviation from average nuclear KE specified in IOp(81). Also in microhartree. IOp(1/94, 95, 96, 97, 98) IOp(94): Davidson control for quadratic micro-iterations (see MMOpt2) IOp(95): RFO/Davidson control for quadratic microiterations (see MMOpt2) IOp(96): Davidson control for coupled QM/MM macro step (see MMOpt2)IOp(97):RFO/Davidson control for coupled QM/MM macro step (see MMOpt2)IOp(98):Control of quadratic micro-iterations and coupled QM/MM quadratic macro step. <0 0 1 2 3 4 5 10 20 30 40 50 Do not use dynamic convergence criteria for the micro-iterations. Default(15). Regular non-coupled macro step. Coupled macro step, full diagonalization. Coupled macro step, direct /w full Hessian incore. Coupled macro step, direct /w MM Hessian incore. Coupled macro step, fully direct. Regular micro-iterations. Quadratic micro-iterations, full diagonalization. Quadratic micro-iterations, direct /w prepared Hessian incore. Quadratic micro-iterations, direct /w raw MM Hessian incore. Quadratic micro-iterations, fully direct.IOp(1/101, 102, 103, 104)Phase control in L115 and L118: N1, N2, N3, N4IOp(1/105)Reaction direction 00 10 Default (Same as 10) Forward direction20 Reverse direction Damped-Velocity Verlet (DVV) options for Dynamic Reaction Path Following 0 1 2 00 10 20 000 100 200 step 300 0000 1000 2000 Default (Same as 2) Use DVV Do not use DVV Default (Same as 10) Follow the rxn path in the forward direction Follow the rxn path in the reverse direction Default (Same as 200) Time step correction not used Time step correction used but not to recalculate current DVVTime step correction used and current DVV step recalculated Default (Same as 1000) Use DVV stopping criteria Do NOT use DVV stopping criteriaIOp(1/106)Damping constant for DVV Dynamic Rxn Path following (v0) 0 N Default v0=0.04 (N=400) v0 is set to N*0.0001IOp(1/107)Error tolerance for DVV time step correction (Error) 0 N Default Error=0.003 (N=30) Error=N*0.0001IOp(1/108)Gradient magnitude for DVV stopping criteria (Crit1) 0 N Default (N=15) N*0.0001IOp(1/109)Force-Velocity angle for DVV stopping criteria (Crit2) 0 N Default (90 Degrees) Use N DegreesIOp(1/110)Scaling of rigid fragment steps during microiterations. 0 1 2 -n Do not scale Scale with 1/NRA (NRA = number of atoms in fragment)Scale with 1/Sqrt(NRA) Scale with 1/nIOp(1/111)Step-size to use with steepest descent when L103 is having trouble: -N -1 0 N Scale up to RMS step of N/1000 if DXRMS is less. Effectively disables the scaling Default (50) Scale up or down to maximum change in a variable of N/1000IOp(1/112)Temperature for thermochemistry. 0 N Default (standard temperature, unless read in). N/1000 degrees.IOp(1/113)Pressure for thermochemistry. 0 N Default (1 atomosphere, unless read in). N/1000 atmospheres.IOp(1/114)Scale factor for harmonic frequencies for use in thermochemistry and harmonic vibration-rotation analysis. 0 N Default (1 unless specified by IOp in overlay 7 or read in). N/1000000.。
蛋白质PDB文件说明
字符集合只是一些非控制型字符,象空格和结束符,出现在PDB文件记录中。
也就是:abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890` - = [ ] \ ; ' , . / ~ ! @ # $ % ^ & * ( ) _ + { } | : " < > ?空格和结束符。
结束符根据系统而定,Unix用一行字符,而其他的系统可能就用一个回车来表示。
特殊字符希腊字母就详细的拼写出来。
比如:α, β, γ原子用DOT表示。
右箭头用-->表示。
左箭头用<--表示。
上标用两个等号表示开始和结束。
比如:S==2+==下标用一个等号来表示开始和结束。
比如:F=c=如果等号两边至少有一边有一个空格,那么这个字符就是表示等号。
比如:2 + 4 = 6逗号,冒号和括号用来表示文档中的分界苻,也就是下面几种中的一种:ListSListSpecification ListSpecification如果逗号,冒号或者括号在任何一片文档中使用不是作为分界苻的话,那么肯定有字符被漏掉了。
比如下边例子中第四行的"\":COMPND MOL_ID: 1;COMPND 2 MOLECULE: GLUTA THIONE SYNTHETASE;COMPND 3 CHAIN: NULL;COMPND 4 SYNONYM: GAMMA-L-GLUTAMYL-L-CYSTEINE\:GL YCINE LIGASECOMPND 5 (ADP-FORMING);COMPND 6 EC: 6.3.2.3;COMPND 7 ENGINEERED: YESCOMPND MOL_ID: 1;COMPND 2 MOLECULE: S-ADENOSYLMETHIONINE SYNTHETASE;COMPND 3 CHAIN: A, B;COMPND 4 SYNONYM: MA T, A TP\:L-METHIONINE S-ADENOSYLTRANSFERASE;COMPND 5 EC: 2.5.1.6;COMPND 6 ENGINEERED: YES;COMPND 7 BIOLOGICAL_UNIT: TETRAMER;COMPND 8 OTHER_DETAILS: TETRAGONAL MODIFICATION数据类型-------------------------------------该部分该部分主要用来描述试验和记录中该大分子的一些基本信息,有以下几种记录:HEADER,OBSLTE,TITTITLE,CA VEA T,COMPND,SOURCE,KEYWDS,EXPDTA,AUTHOR,REVDA T,SPRSDE,JRNL和REMARK部分。
CM-120TX 无线数字指纹密码钥匙盘说明书
CM-120TX WirelessDigital KeypadsInstallation InstructionsSection 1__________________ General DescriptionThe CM-120TX is an outdoor illuminated battery operated wireless all metal keypad. It is a versatile self-contained, single-gang, stand-alone keypad mounted on a heavy stainless steel, single gang faceplate. It features up to 999 users, and offer over 1,000,000 possible user codes (from one to eightdigits). It operates on 2 x 1.5V ‘AA’ batteries providing for up to 90,000 operations (based on an average 4 digit PIN followed by *). The CM-120TX is compatible with our 915 MHz Lazerpoint RF TM products. Itprovides 2 separate RF codes that can be transmitted individually. It has non-volatile memory to retain user settings when the batteries discharge or when they are being changed.Section 2__________________ InstallationMountingThe CM-120TX has been designed to fit into a standard single gang electrical box. The terminal strips are carefully positioned so all wiring exits out the back, so it won’t interfere with, or short out on, the sides of the box.WiringCamden CM-120TX is supplied with an AA battery holder. Connect the battery holder as shown with the Red wire connecting to terminal 1(+) and the Black wire connecting to terminal 2(-). Insert the batteries into the battery holder as shown in Figure 1.Figure 1 CM-120TX Power ConnectionsSection 3__________________ How to Program KeypadUsing This Manual∙Brackets and spaces are not part of programming or user codes. They are used here to clarify the operations and group like functions.∙Square brackets [ ] are used to indicate that the keys inside the brackets are to be pressed at the same time. (Requiring two keys to be pressed simultaneously reduces the chance that someone will accidentally get into programming mode.)∙When entering a code in brackets, first press the star key and, while holding down the star key, press the second key. Release them both together.Using the KeypadEach user on the system is assigned two different numbers. The first is the User Number, which he/she does not use directly. This number, from 1 to 999, is used to keep track of who is assigned to the system, using the schedule on Page 8. All leading zeroes are ignored. The second is the User Code, a 1 to 8 digit programmable code that the user will enter into the keypad to activate certain functions. This code can have leading zeroes as part of the code. This information should be recorded and stored in a safe place for futurereference. The keypad can support a total of 999 users, from 1 to 999 (See chart on page 10).User number one belongs to the Master User and has a default user code of 1234. Note that the master user code is used for administration ONLY, and will not (normally) operate the wireless outputs. When a global disable is engaged (all users locked out), the master code will still operate wireless output one.User number two will toggle the global enable/disable function when prefixed by two or more pound (‘#’) keys. This allows lockout of all other codes (user two will still be able to operate the keypad normally, even when the global lockout is engaged). Therefore, user number two should be reserved for use by a manager. When entered without the prefixed ‘#’s, the code of user number 2 operates the keypad in the same way as the other users do.When using the keypad with variable-length user codes, it is necessary for the user to press the star (*) key after the User Code has been entered. This indicates the end of the code, and causes the keypad to attempt to validate the entered code. If the number entered is valid, the keypad will perform the programmed function (e.g., activate the relay).For example, to operate the keypad using the user code 4321 (which must be entered as a user code in programming mode first), enter 4321*. While the door is unlocked, or whatever job your unit is to perform, the green LED will blink at a slow rate. Note that the star key can be substituted with another digit of your choice. (See 0# Set Enter Key)Understanding the LEDsThe three Light Emitting Diodes (LED’s) above the keypad provide information on the status of the unit. NOTE: A ‘slow’ flash is once every two seconds and a ‘fast’ flash is once every second.GREEN LED:‘ON’ Solid:No errors, output isactive.‘FAST FLASHING’: Keypad is inprogramming mode. RED LED:‘ON’ Solid: Error condition.See chart at end ofthis manual.YELLOW LED:To meet ADA requirements, both a visual and audible key-press confirmation is provided (blinks on each key-press). This can be enabled or disabledduring programming. See the [*6] 0 # programming option for more details.Checking the Battery LevelThe Cm-120TX has a built-in battery gauge. Press and hold the any button for 5 seconds. The Green LED will flash and the buzzer will beep up to 5 times indicating the battery level.5 Beeps = Fully charged batteries1 Beep = Replace the batteriesThe CM-120TX will beep if the Low Battery Alarm(page 4) is enabled.SET-UP INSTRUCTIONS:Note:1. Keep careful track of User Codes and to whomthey are assigned, assigned outputs, etc. asyou program them, and keep the list in a safeplace.2. Press the buttons firmly.3. Whenever the * and any other character areincluded in brackets [* x], press the * firstand, while holding the * down, press theother key. Release both keys together. [*1] Enter Program Mode (First Step)Press * and 1 at the same time. Enter the Master Code (1234 is the factory default), then *. The green LED should now be rapidly flashing.The keypad will remain in program mode until no key is pressed for approximately 30 seconds. To exit programming mode quickly, press the special sequence –“ * # * ”.For example, [* 1] 1 2 3 4 * will put the keypad in program mode.[*1] Administration FunctionsSet Code Length - Function 1#Default: 0 (variable code length)When set to zero, user codes can vary from 1 to 8 characters, but must be terminated by pressing the “enter key”, which by default is ‘*’. When set from 1 to 8, all user codes must use the programmed length, but will not require termination by the programmed “enter key”.(User codes shorter than the maximum are still allowed, but the user must terminate it with the current “enter” key).For example, [*1] 1 # 4 * will set all user codes toa fixed 4-digit length.Set Enter Key - Function 0#Default: ‘*’If the code length has been left at 0 (see above), then use this feature to select the “enter” key used to terminate user code entry. The default setting is ‘*’, but it can be changed to any key on the keypad (select carefully).For example, [*1] 0 # # * will change the usercode enter key to ‘#’.Incorrect Code Count Alarm - Function 2#Default: 0 (disabled)When set to zero, the keypad will not alarm on entry of invalid codes. When set to a value between 1 and 20, the keypad will generate an alarm after the specified number of invalid codes have been entered, within two minutes.For example, [*1] 2 # 6 * will set the keypad to generate an alarm when 6 invalid user codes have been entered. NOTE: This setting also requires the “Incorrect code alarm Lockout” feature enabled. See 5# on page 4. Force Unique User Codes - Function 3#Default: 1 (Enabled)When set to zero, the keypad will accept any user code for each user. When set to one, during programming of new user codes, the keypad will check the desired code against all currently programmed users, and only accept the user code if it is unique. Attempting to program a code that is not unique will cause an error alarm, and the programming procedure must be restarted and a different code selected.NOTE: When enabling this mode (when previously disabled), it is recommended the administrator erase all settings back to factory defaults first, to ensure all user codes are unique. Failure to perform this step may leave duplicate user codes among those already learned, and result in unexpected operation.0 = disabled1 = enabledFor example, [*1] 3 # 0 * will dis able “Force Unique User C odes”.Backlight Control Enable/ Disable -Function 5#Default: 0 (disabled)Enable or disable backlight control on keypress. When enabled, the backlight will be OFF until the first keypress. It will remain on for 5 seconds after the last keypress. When disabled, the backlight will remain OFF.0 = disabled1 = enabledTo enable/disable Backlight Control mode:First, enter program mode. Then enter [*1], then 5#, then 0 to disable, or 1 to enable, then *.For example, [*1] 5 # 1 * will make the backlighting turn ON after the first key press. The backlighting will remain ON for 5 seconds after the last key press. User Two “Global Lockout” - Function 6#Default: 1 (Enabled)When enabled, user #2 (a manager, for instance) can lockout all other users by prefixing his code by two (or more) “#” keys. When a global lockout is engaged, no user code will activate the outputs, except user #1 & #2. Programming functions, and request to exit (REX) are not disabled. This can be used (for instance) to immediately control all access while changing selected user codes in case of a security problem, or for lockout over a weekend.To disable user two “global lockout” feature:First, enter program mode. Then enter [*1], then 6#, then 0 to disable, or 1 to enable, then *.0 = disabled1 = enabledFor example [*1] 6 # 0 * will disable user #2’s ability to engage a global lockout.Note: When user number #2’s key code is prefixed with two or more ‘#’s, the “Global User Enable/ Disable” flag will be toggled.Channel Output Mode - Function 7#Default: 0 (Channel 1 Only)This control allows the installer to select the channel output mode. Chosing the default (0) means that a valid code activates Channel 1 only.Setting the Channel Output Mode to “1” will allocate the first 499 user numbers (memory addresses) to Channel 1, and the remaining 500 user numbers to Channel 2. To choose the Relay Output mode:First, enter program mode. Then enter [*1], then 7#, then 0 for Relay 1 only, 1 for split output, or 2 for both relays sequenced, then *.0 = Channel 11 = 1 - 499 = Channel 1, 500 – 999 = Channel 2For example [*1] 7 # 1 * will allocate any user number from 1 – 499 to Channel 1, and any user number from 500 – 999 to Channel 2.[*2] Add/Change/Delete UsersTo add or change a user:First, enter program mode (see First Step above), then enter [*2], then the user number you wish to add or change (from 1 to 999 inclusive) followed by #. Finally, enter the new User Code (up to 8 digits), followed by *, then the new User Code again (for verification), followed by *. User Codes may only contain digits 0 through 9 (* and # may not be used as part of the code, except when programmed as the “enter” key). Example: [*2] 44 # 2125 * 2125 * will assign a user number of 44 and a user code of 2125.To delete a user code:First, enter program mode. Then enter [*2], then the user number you wish to delete (from 2 to 999, inclusive), then press #, then *, then *.For example, [*2] 75 # * * will delete the user code and all assignments for user number 75.PLEASE NOTE: The Master Code cannot be deleted but it may be changed.Example: [*2] 1 # 38714 * 38714 * will change the Master Code to 38714. If you change it, don’t forget it. [*3] Time Delay/Duration FunctionsDoor Prop open Alarm Delay - Function 2#Default: DisabledSets the delay (1 to 255 seconds) before open door contacts are considered an alarm condition. (NOTE: Door contacts are required for this feature.) To program the door open alarm delay:First, enter program mode. Then enter [*3], then 2#, then the delay time in seconds (0=disabled), then *. For example, [*3] 2 # 30 * will set the door open alarm delay to 30 seconds.NOTE: To turn this feature on/off, see section [*4] 3# Door Prop Open Alarm on the next page.[*4] Alarm Control FunctionsIncorrect code alarm - Function 0# Default: 0 (Disabled)Use to control how the “Incorrect code alarm” is annunciated.0 = disabled1 = buzzerIf the “Incorrect code alarm” is enabled, and triggered, a valid code is required to reset.To program how the “incorrect code alarm” condition is annunciated:First, enter program mode. Then enter [*4], then 0#, then the annunciation code, then *.For example, [*4] 0 # 1 * will configure the keypad to indicate entry of the programmed count of invalid codes on the buzzer only.Low Battery Alarm - Function 1#Default: 1 (Enabled)Enable or disable the “Low battery alarm”.0 = disabled1 = buzzerTo disable the “low battery alarm”:First, enter program mode. (See “First Step” above) Enter [*4], then 1#, then the annunciation code, then *. For example, [*4] 1# 0* will configure the keypad not to annunciate the low battery condition.Stuck key alarm - Function 2#Default: 0 (Disabled)Enable or disable the “Stuck key alarm”.0 = disabled1 = enableThe “Stuck key” alarm will a ctivate the buzzer after 15 seconds (factory set delay) of the key being held continuously, and reset as soon as the key is released (or after 10 seconds, whichever occurs first)To en able the “stuck key alarm”:First, enter program mode. Then enter [*4], then 2#, then (0 or 1), then *.For example, [*4] 2 # 1 * will configure the keypad to activate the stuck key buzzer.Door Prop open Alarm - Function 3#Default: 0 (Disabled)Use to control how the “Door prop open alarm” is annunciated.0 = disabled1 = buzzerTo program how the “Door Prop open alarm” condition is annunciated:First, enter program mode. Then enter [*4], then 3#, then the annunciation code, then *.For example, [*4] 3 # 1 * will annunciate the buzzer during the alarm.NOTE 1:this feature requires the use of the door contact input.NOTE 2: The alarm will sound continuously until reset. To reset, enter valid code.NOTE 3: To set Delay Time, see [*3] 2# on Page 4. Incorrect code alarm lockout - Function 5# Default: 0 (Disabled)Use to configure the incorrect code alarm lockout.0 = disabled1 = enabledTo program:First, enter program mode. Then enter [*4], then 5#, then the enable/disable code, then *.For example, [*4] 5 # 1 * will configure the keypad to lockout for 2 minutes (factory set lockout duration), after the incorrect code count alarm limit is reached. During the lockout period, all keypad entry (including correct codes) is ignored.There is an automatic reset after 2 minutes.(See 2# on Page 3 of manual for setting code count) Door Forced open Alarm - Function 6# Default: 0 (Disabled)Use to control how the “Door forced open alarm” is annunciated.0 = disabled1 = buzzerTo program how the “Door forced open alarm” condition is annunciated:First, enter program mode. Then enter [*4], then 6#, then the annunciation code, then *.For example, [*4] 6 # 1 * will configure the keypad to sound an alarm if the door is forced open (without entering a valid code).NOTE 1:this feature requires the use of the door contact input.NOTE 2: The alarm will sound continuously until reset. [*6] Annunciation Control Functions Yellow LED Enable - Function 0#Default: 1 (Enabled) Enable or disable the yellow LED. When enabled, the yellow LED illuminates when any key is pressed.0 = disabled1 = enabledTo disable the yellow LED:First, enter program mode. Then enter [*6], then 0 #, then 0 to disable, or 1 to enable, then *.For example, [*6] 0 # 0 * will disable yellow LED illumination.Buzzer Enable / Disable - Function 1# Default: 1 (Enabled)Enable or disable the buzzer. When disabled, the buzzer will not sound for any condition0 = disabled1 = enabledTo disable the buzzer:First, enter program mode. Then enter [*6], then 1#, then 0 to disable, or 1 to enable, then *.For example, [*6] 1 # 0 * will disable the buzzer for all conditions.Correct Code Audio Tone - Function 2# Default: 0 (Disabled)Enable or disable the audio tone annunciating correct code entry. When enabled, a single 2 tone beep will sound when a correct code has been entered. In the case of toggled mode, the audio tone will last for 8 seconds (hard-coded) when a correct code toggles relay one ON; the audio tone will be a single two-tone beep, “do-ray”, when a correct code toggles relay one OFF.0 = disabled1 = enabledTo enable the audio tone on correct code entry: First, enter program mode. Then enter [*6], then 2#, then (0 to disable, or 1 to enable), then *.For example, [*6] 2 # 1 * will enable the audio tone on correct code entry.Incorrect Code Audio Tone - Function 3# Default: 1 (Enabled)Enable or disable the audio tone annunciating correct code entry. When enabled, an audio tone will sound when any incorrect code has been entered, for the duration that the red LED is illuminated.0 = disabled1 = enabledTo disable the audio tone on incorrect code entry:First, enter program mode. Then enter [*6], then 3#, then 0 to disable, or 1 to enable, then *.For example, [*6] 3 # 0 * will disable the audio tone on incorrect code entry.Request to Exit Audio Enable/Disable - Function 5#Default: 0 (Disabled)Enable or disable audio annunciation for Channel #1 when a Request to Exit signal is input. When enabled, if Channel 1 is triggered by REX input, a looped tone (do-ray) will be annunciated for the duration that Relay #1 is energized. In the case of Toggled mode, the annunciation will last for 8 seconds (hard-coded). In the case of entering into Unlocked Mode (REX input held for more than 15 seconds), 4 beeps will sound after the looped two-tone annunciation. A si ngle (“Ray-Do”) tone will sound when exiting Unlock Mode.0 = disabled1 = enabledTo enable/disable REX Audio Annunciation:First, enter program mode. Then enter [*6], then 5#, then 0 to disable, or 1 to enable, then *.For example, [*6] 5 # 1 * will enable the audio annunciation for REX input.FACTORY DEFAULT SETTINGSIf the settings have not been changed after shipment, or if they have been reset, they are as follows:o Master User # 1 - Code is 1234.o Main Channel = 3 seco Secondary Channel = programmable.o Yellow LED enabled.Reset to Factory DefaultsReset the Master Code:While holding the # and * down together for aprox. 4 secs, power up the keypad. There will be 4 beeps and all LED’s will flash. The keypad will immediately move into the battery life indicator. It will beep up to 5 times and the green LED will flash.Reset the keypad to factory defaults:While holding down the # and * for approx. 10 seconds. Power up the keypad. There will be the initial 4 beeps at the 4 second point, indicating the Master Code is reset (1234), followed by the battery test beeps (up to 5), then followed by 8 beeps indicating the keypad has been reset to factory defaults.[*9] Erase Keypad Memory/Reset ALL to FactoryForce factory default settings (use with caution)This is used when most or all of the programming has to be changed, as when a keypad has been moved to a new location. To reset to factory defaults.First, enter program mode. Then enter [*9], then re-enter the master keycode, then *.For example, [*9] 1 2 3 4 * will immediately and permanently clear the entire memory (assuming the master keycode has not been changed from the factory default. Once this function has been executed, there is NO WAY to restore the previous state.Section 4 _________________ Technical DataModel CM-120TXIllumination No / YesSize 2 ¾” x 4 ½” x ¾”69.85mm x 114.30mm x19.05mmMounting 2 x #6-32 machine securityscrewsTemperature -40° - +185°F (-40° - +85°C) Operating voltage 2 x AA Alkaline Batteries Battery Life 90,000 OperationsBased on a 4 digit user code Capacity 999 User codesLength Up to 8 digits (10 millionpossible codes)Response time 0.3 secondsInputs 1 x REX input1 x Door Contact input Output RF Only,2 ChannelsChannel 1 assigned to users1 - 499Channel 2 assigned to users500 - 999Section 5_________________WarrantyCamden Door Controls guarantees the CM-120TX to be free from manufacturing defects for 3 years from date of sale. If during the first 3 years the CM120TX fails to perform correctly, it may be returned to our factory where it will be repaired or replaced (at our discretion) without charge. Except as stated herein, Camden extends no warranties expressed or implied regarding function, performance or service.Troubleshooting Tipso If you make an input error (e.g. if you enter anon-existent User Code) and press the star key, the red LED will light. Simply start over.o If you make an input error and have not yetentered *, just wait 5 seconds, and the command memory will be cleared automatically. Start again. You will not increment the error count.o The “Lockout -on-#-errors” feature is disabled by default. This will prevent the keypad from hanging up if anyone plays with the keypad in certain applications.o Do not make the mistake of thinking you have to 'clear' the red light if you make an error. Just re-enter the correct number. The red LED will clear automatically with the first key you press.o Be sure you are pressing the buttons firmly. The yellow LED should come on and an audio tone should sound with each key pressed, unless these features have been disabled.Questions?Visit us online at Call us toll-free at 1-877-CAMDEN9 or (905)366-3377File: CM-120TX_NF_Man_Rev1.docx Firmware Version: 1.08Revised: December 16, 2014Part No.: 40-82B166Toll Free: 1.877.226.3369 5502 Timberlea Blvd.,Mississauga, ON Canada L4W 2T7。
Two-dimensional Quantum Field Theory, examples and applications
Abstract The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of four-dimensional quantum field theory. The dynamics of confinement and theta vacuum are explained by using the non-perturbative methods developed in two dimensions. We describe in detail how the effective action of string theory in non-critical dimensions can be represented by Liouville gravity. By comparing the helicity amplitudes in four-dimensional QCD to those of integrable self-dual Yang-Mills theory, we extract a four dimensional version of two dimensional integrability.
2 48 49 52 54 56
5 Four-dimensional analogies and consequences 6 Conclusions and Final Remarks
食品科学导论课后题
Chapter 1Overview of Food ScienceReview Questions (P18)1.Away-from-home meals captures 45 percent of the U.S. food dollar. (P10)2.Why have the international activities of food industries increased? (P16)Aside from the worldwide demand for food and food products, the recent trends to decrease trade tariffs has stimulated the international activities in the food industry.Improvements in transportation and communication have also increased the international activities of food industries. all seven product lines along which the food industry is divided. (P4)Cereal and bakery productsMeat, fish, and poultryDairy productsFruits and vegetablesSugars and other sweetsFats and oilsNonalcoholic beverages/alcoholic beverages4.List the four artificial divisions of the food industry. (P4)ProductionManufacturing/processingDistributionMarketing5.Consumption of cheese has increased, whereas consumption of red meat has declined overthe last 27 years. (P17)6.List four reasons that influence people and the kind of food they eat. (P17)The kinds of foods people eat change in response to many influences, such as demographic shifts; supply of ingredients; availability and costs of energy; politics; scientific advances in nutrition, health, and food safety; and changes in lifestyle.7.About 10000 new food products are introduced each year. (P17)8.Explain how the consumer votes in the marketplace. (P3)Consumers vote every day in the marketplace with their dollars.9.Define an allied industry. (P11)An allied industry produces nonfood items that are necessary for marketing food.pare the spending on food in the United States to that of Spain and Greece. (P6-7) Americans spent only about 8 percent of their personal consumption expenditures for food to be eaten at home. This compares with 18 percent for Spain and 32 percent for Greece. Chapter 2Review of Chemistry (P31)1.The atom is the smallest unit of an element that still exhibits the properties of that element.(P21)2.Define a molecule. (P26)A molecule is the smallest identifiable unit into which a pure substance can be divided and still retain the composition and chemical properties of that substance. and describe the two divisions of metabolism. (P28)Anabolism, reactions involving the synthesis of compounds.Catabolism, reactions involving the breakdown of compounds.4.List the elements most important to life. (P22)The elements important to life include carbon, hydrogen, nitrogen, and oxygen.5.How are covalent bonds formed? (P22)Covalent bonds are formed by the sharing of a pair of electrons.6.The atomic number of an atom is the total number of protons. The atomic weight of an atomis the total number of protons plus neutrons. (P21)7.Salt is an example of a/an ionic bond. (P25)8.Explain the oxidation-reduction reaction. (P26)The rusting of metals, the process involved in photography, the way living systems produce and use energy, and the operation of a car battery are but a few examples of oxidation-reduction reactions.9.Chemical properties of an element are determined by the number of electrons in theoutermost energy level of an atom. (P22)10.All carbon atoms have four bonds to account for. What are the names of the bonds? (P29) Each carbon can connect to another carbon, a hydroxyl, a hydrogen, an amino group, an oxygen.Carbon-carbon bonds; carbon-hydroxyl bonds, carbon-hydrogen bonds, carbon-amino bonds; carbon-oxygen bonds.Chapter 3 Chemistry of Foods (P62)1.What is the chemical composition of a carbohydrate? (P34)A carbohydrate is composed of carbon and water and have a composition of C n(H2O)n.2.List the three functions of proteins in food. (P48)Proteins contribute to the color, texture, and flavor of foods.3.What is the difference between a monosaccharide and a disaccharide? (P35)A monosaccharide may have 5 or 6 carbons. A disaccharide is made of two monosaccharides. five functions carbohydrates play in foods. (P34-35)Carbohydrates enhance flavor, contribute to texture, prevent spoilage, influence color, and give structure.Flavor enhancing and sweetening due to caramelization Water binding Contributing to texture Hygroscopic nature/water absorption Providing source of yeast food Regulating gelation of pectin dispersing molecules of protein or starch Acting to subdivide shortening for creaming control crystallization Preventing spoilage Delaying coagulation protein Giving structure due to crystals Affecting osmosis Affecting color of fruits Affecting texture (viscosity, structure) Contributing flavor other than sweetness5.Explain two functions of water in the body. (P58)Carries nutrients and wastesn Maintains structure of molecules Participates in chemical reactions Acts as a solvent for nutrients Lubricates and cushions joints, spinal cord, and fetus (during pregnancy) Helps regulate body temperature Maintains blood volume6.Triglycerides, fatty acids, phospholipids, some pigments, some vitamins, and cholesterol areclassed as lipids. (P48)7.Fatty acid molecules that are unsaturated contain what are known as double bonds. A fattyacid that contains one double bond is called mono- unsaturated. Fatty acids that contain two or more double bonds are called polyunsaturated. (P50)8.List the fat- and water-soluble vitamins. (P53)Fat soluble vitamins include vitamins A, D, E, and K.The water-soluble vitamins include the B vitamins and vitamin C.9.Choline is part of several major phospholipids critical for normal membrane structure andfunction, is used by the kidney to maintain water balance, and is used to produce the important neurotransmitter acetylcholine. (P59) ten minerals important in nutrition. (P55)Microminerals important in nutrition include:Chromium Cobalt Copper Fluorine Iodine Iron Manganese Molybdenum Nickel Selenium Silicon Tin Vanadium ZincChapter 4 Nutrition and digestion (P79-80) six minerals required by the body. (P73)Calcium; Phosphorus; Iron; Copper; Magnesium; Sodium; Potassium; Chloride; Zinc; Iodine; Manganese; Selenium.2.Identify the protein requirement for a 19-year-old male and female. (P68)Protein needs is about 61 grams per day for a 19-year-old male and is 44 grams per day for a female at the same age.3.Describe the function of protein in diet. (P69)Protein provides essential amino acids, and nitrogen for the synthesis of other nitrogen-containing compounds.Enough protein in the diet can prevent the dietary diseases kwashiorkor or marasmus. Protein provides essential amino acids.Protein also provides nitrogen for the synthesis of purines, pyrimidines, porphyrin in nucleic acids, ATP, hemoglobin, and cytochromes.Enough protein in the diet of people can prevent the dietary diseases kwashiorkor or marasmus.4.How many calories are in 1 gram of protein, carbohydrate, fat, and alcohol? (P65)Proteins and carbohydrates provide about 4 calories per gram. Fat contributes about 9 calories per gram. Alcohol supplies about 7 calories per gram.5.Linoleic acid is an essential fatty acid. (P71)6.Identify the organ of digestion that receives enzymes from the pancreas. (P76)The small intestine receives enzymes from the pancreas.7.During digestion, enzyme such as aminopeptidase, carboxypeptidases, and dipeptidaseconvert polypeptides into amino acids. (P77)8.What nutritional deficiency causes kwashiorkor and marasmus? (P69)Protein deficiencies can lead to kwashiorkor or marasmus.9.List five essential amino acids. (P69)Phenylalanine; Tryptophan; Histidine; Valine; Leucine; Isoleucine; Lysine; Methionine; Threonine; Arginine10.What factor determines protein quality? (P69)Ratios of essential amino acid.Chapter 5Food composition (P87)1.How many Calories and grams of protein are in 3 oz. of Froot Loops ®cereal? (P578)330 kilocalories (Calories) and 6 grams of protein are in 3 oz. of Froot Loops ®cereal.2.How many grams of fat are in one slice of cheese pizza? (P588)9 grams of fat are in one slice of cheese pizza.3.Describe item #4270. (P580)3 grams of water, 185 kilocalories, 2 grams of protein, 11 grams of fat, 18 milligrams of cholesterol, 26 grams of carbohydrate, 13 milligrams of calcium, 34 milligrams of phosphorous, 1 milligram of iron, 82 milligrams of potassium, 82 milligram of Sodium, 20 IU of V A, 0.06 milligrams of thiamin, 0.06 milligrams of riboflavin, and 0.6 milligrams of niacin are in 4 chocolate chip cookies.3g water, 185 Cal, 2g protein, 11g fat, 18mg cholesterol, 26g carbohydrate, 13mg Ca, 34 mg P, 1mg Fe, 82mg K, 82mg Na, 20 IU V A, 0.06mg thiamin, 0.06mg riboflavin, and 0.6mg niacin are in 4 chocolate chip cookies.4.List three methods for determining the composition of food. (P83)The methods for determining the composition of food are spectrophotometry, liquid chromatography, and gas chromatography.5. A small calorie is defined as the amount of heat required to raise the temperature of one gramof water one ℃. (P84)6.Describe two uses of a food composition table. (P86)Food composition tables are used to evaluate the nutritional value of food supplies, to develop food distribution programs, to plan and evaluate food consumption surveys, to provide nutritional counseling, and to estimate the nutritional content of individual diets.Food composition tables are used to evaluate diets and food supplies. four factors that affect the nutrient content of foods. (P83)Nutrient content of foods is influenced by variety, season, geographical differences, stage of harvesting, handling, commercial processing, packaging, storage, display, home preparation, cooking, and serving.8.Explain the relationship between Calorie, Kcal, calorie, and cal. (P84)A Calorie is a metric unit of heat measurement. The small calories (cal) is the amount of heat required to raise the temperature of 1 gram of water from 14.5° to 15.5 ℃.A large calorie, or kilocalorie (Cal), usually referred to as a calorie and sometimes as a kilogram calorie, equals 1000 cal.9.Identify the following abbreviations: oz, mg, IU, RE, mono, sat, poly, carb, chols. (P86)Oz=ounce, mg=miligram, IU=International Unit, RE=Retinol Equivalent, mono=monounsaturated, sat=saturated, poly=polyunsaturated, carb=carbohydrate, chols=cholesterol.10.In terms of energy and protein, what is the difference between a slice of white bread and aslice of whole wheat bread?(P576)A slice of white bread provides less energy and protein than a slice of whole wheat bread does.Chapter 6 Quality factors in foods (P107)1.List three components of reflected light used to define colors. (P91)Value, hue, and chroma. one instrument used to measure texture. (P93-94)Compressimeter—determine the compressibility of cakes and other “spongelike ” products; Penetrometer—measure gel strength;Warner-Bratzler shear apparatus—evaluating meat tenderness;Brookfield viscometer—measure the viscosity;Succulometer;Tenderometer.3.Discuss what humans can taste and what they smell and how this forms food flavor. (P95) Humans can taste sweet, salty, sour, and bitter and smell fruity, astringency, sulfur, hot. Food flavor is a combination of taste and smell.4.Identify the following acronyms: AMS, HACCP, TQM, GMP, CID. (P99, 104-106) AMS—the Agricultural Marketing ServiceHACCP—Hazard Analysis and Critical Control PointTQM—Total Quality ManagementGMP—Good Manufacturing PracticesCID—Commercial Item Descriptions5.Industry and AMS develop and maintain CIDs. (P99)6.List six factors that can influence the flavor of food. (P96)Depending on the food, flavor can be influenced by bacteria, yeasts, molds, enzymes, heat/cold, moisture/dryness, light, time, additives.7.Changes in the texture of food are often due to water status. (P94)8.What qualities do consumers expect of their food? (P106)Consumers expect certain qualities from their food. These include color, flavor, texture, and even size.9.The study of the science of the deformation of matter is called rheology. (P93)10.How do fats or lipids affect the texture of food? (P97)Lipids (fats) are softeners and lubricants used in cakes.Chapter 7 Unit operations in food processing (P122-123)1.The manufacture of ice cream is an example of a/an swept surface heat exchanger. (P117)2.Why are foods packaged? (P120)Packaging is used for a variety of purpose including shipping, dispensing, improving the usefulness of the product, and protection from microbial contamination, dirt, insects, light, moisture, drying, flavor changes, and physical alterations.Attractive packaging also helps with marketing of the food product.3.Specific heat is the amount of heat required to change the temperature of a unit mass ofproduct a specific temperature without changing the material. (P115) the three methods for separating foods. (P111-113)Three methods for separating foods are cream separator, clarification, and membrane processes.5.What are the two types of fluid flow pumps? (P114)Centrifugal pump and positive pump are two types of fluid flow pumps.6.Plate heat exchanges pass fluid over a plate where a heating or cooling medium is beingpassed up or down on the other side of the plate. (P116)7.List the four factors affecting the mixing of food products. (P114)Factors affecting the mixing of food are design of impeller, diameter of impeller, speed, and baffles.8.Why is it important to handle food materials carefully? (P110)To maintain sanitary conditions, minimize losses, maintain quality, and minimize bacterial growth.9.Explain the three common methods of drying foods. (P119)Three common methods of drying are sun or tray drying, spray drying, and freeze drying. 10.List three membrane processes for separating food products. (P112)Reverse osmosis, ultrafiltration, and microfiltration.Chapter 8 Food deterioration (P136) the two environmental conditions that affect microbial growth on food. (P127) Environmental conditions that affect microbial growth include temperature and oxygen. the three general categories of food deterioration. (P125)The three general categories of food deterioration are: physical, chemical, and biological.3.Some of the post harvest enzymes are desirable in food preservation. (P136)4.Why do foods have a shelf life? (P136/125)All foods undergo deterioration. All foods have a time limit of their usefulness—shelf life. 5.The growth of aerobes is slowed by removing the oxygen; while providing oxygen limits thegrowth of anaerobes. (P135)6.List four factors that cause food deterioration. (P125)Factors that cause food deterioration are many, including light, cold heat, oxygen, moisture, dryness, othertypes of radiation, enzymes, microorganisms, time, industrial contaminants, and macroorganisms (insects, mice, and so on).7.What is a food-borne disease? (P127)Food-borne disease is any disease resulting from the consumption of food.8.Give four preservation techniques to prevent food deterioration. (P132-135)Food preservation involves the use of heat, cold, drying, acid, sugar and salt, smoke, atmosphere, chemicals, radiation, and mechanical methods.9.Why are some fruits and vegetables washed immediately after being picked? (P128)Some fruits and vegetables are washed to remove internal heat and cool immediately after being picked in order to minimize post-harvest biochemical changes. four food enzymes and describe their function. (P129-131)Ascorbic acid oxidase, oxidize ascorbic acid to dehydro form destroying the browning prevention ability.Beta-amylase, with fungal glucoamylase produces mixtures of fermentable sugars: glucose, maltose.Bromelain, acts on collagen to hydrolyze peptides, amides, and esters from the non-reducing end.Catalase, removes residual H2O2 treated foods, converts H2O2 to H2O and oxygen.Chapter 9 Heat (P154)1.The most heat resistant microbe in canned foods is Clostridium botulinum. (P144)2.What are the two main objectives of pasteurization? (P143)Destroy all pathogenic microorganisms that might grow in a specific product;Extension of shelf life by decreasing number of spoilage organisms present. four types of preservatives achieved by heating. (P142)Sterilization, commercial sterility, pasteurization, and blanching.4.In the thermal death curve, the D value relates to the time to reduce the number ofmicroorganisms, and the Z value relates to the temperature required to decrease the microorganisms. (P148)5.Heating before packaging requires what type of packaging? (P148)Heating after packaging requires aseptic (germ-free) packaging.6.Conduction heating is thermal transfer due to collisions of hot food particles with cooler ones.(P145)7.What is the difference between a still retort and an agitating retort? (P149)In the still retort process, the product is placed in a container and then heated in steam atmosphere without agitation.In the agitating retorts the product is agitated during cooking.8.Identify the two factors to pick the right heat treatment severity for a specific food. (P143)To pick the right heat treatment severity for a specific food, two factors must first be determined:Time-temperature combination required to inactivate the most resistant microbe;Heat penetration characteristics of the food and the container.9.Define conduction heating. (P145)Conduction heating is thermal transfer due to collisions of hot food particles with coolerones.10.Radiation is the transfer of energy in the form of electromagnetic waves. (P145)Chapter 10 Cold (P169-170) the three methods of freezing. (P164)Freeze the product in air;Freeze the product with directly contact;Immersion freezing.2.List the four requirements of refrigerated storage. (P159)Refrigerated storage requires low temperatures, air circulation, humidity control, and modified gas atmosphere.3.Identify four changes in food during refrigeration. (P159)During refrigerated storage, foods can experience chill injury, flavor absorption, and loss of firmness, color, flavor, and sugar.4. A key factor in food freezing is how quickly the food is frozen. (P163)5.Describe the temperature difference between cooling, refrigeration, and freezing. (P157) Cooling: temperature from 68˚ to 28˚F (16˚ to -2 ˚C);Refrigeration: temperature from 40˚ to 45˚F (4.5˚ to 7 ˚C);Freezing: temperature from 32˚ to 0˚F (0˚ to -18˚C).6.Why do food processors blanch vegetables prior to freezing them? (P160)Enzymes will maintain a certain level of activity during freezing. the two types of containers for home freezing use. (P165)Rigid containers and flexible bags or wrappings.8.Freezing cannot improve the flavor or texture of any food. (P167)9.Explain why a freezer should not be overloaded with unfrozen food. (P167)Overloading slows down the freezing rate, and foods that freeze too slowly may lose quality.10.List the three things packaging for frozen foods protects against. (P165)Packaging for frozen foods protects against dehydration, light, and air.Chapter 11 Drying and dehydration (P187)1.List the three drying methods. (P177)Common drying methods are: air convection, drum, vacuum, freeze.2.Dehydration results in decreased weight and volume of a product a nd shipping costs. (P186)3.Vacuum drying produces the highest quality of product by is also very costly. (P178)4.What is ultrafiltration? (P182)Ultrafiltration is a membrane filtration process operating at 2 to 10 bars pressure and allowing molecules the size of salts and sugars to pass through the membrane pores, while molecules the size of proteins are rejected.5.The principle of freeze-drying is that under conditions of low vapor pressure (vacuum), waterevaporates from ice without the ice melting. (P178)6.The purpose of drying is to remove enough moisture to prevent microbial growth. (P173)7.Define sublimation. (P178)Water goes from a solid to a gas without passing through the liquid phase. This is called sublimation.8.What types of foods are dried using a drum or roller driers? (P177)Drum or roller driers are used for drying liquid foods, purees, pastes, and mashes.9.Discuss the two problems with drying of a food product. (P173)Dried foods are not sterile. Many spores survive in dry areas of food.Drying never completely removes all water.10.List three chemical changes that occur during drying. (P175-176)Several chemical changes can occur during drying, including: caramelization, enzymatic browning, nonenzymatic browning, loss of ease of rehydration, loss of flavor.Chapter 12 Radiant and electrical energy (P197)1.Describe ohmic heating. (P196)Ohmic heating is the heating of a food product by using an alternating current flowing between two electrodes. the two requirements for irradiation. (P190)Two requirements for the irradiation process include:A source of radiant energy;A way to confine that energy.3.Radiation is broadly defined as energy moving through space in invisible waves. (P190)4.Explain ionizing radiation. (P190)Ionizing radiation, also known as irradiation, is a method of food preservation. These shorter wavelengths are capable of damaging microorganisms.5.List the four ways in which irradiation is most useful. (P192)Irradiation is most useful in four areas: preservation; sterilization; control of sprouting, ripening, and insect damage, and control of food borne illness.6.Describe how microwaves heat food. (P197)Microwaves heat foods by generating heat inside the food due to water friction.7.When salt is added to water, it changes the microwave heating characteristics in two differentdirections. (P195)8.List three specific ways irradiation has been approved for use by the FDA. (P191-192)For eliminating insects from wheat, potatoes, flour, spices, tea, fruits, and vegetables.To control sprouting and ripening.Use irradiation on pork to control trichinosis.To control Salmonella and other harmful bacteria in chicken, turkey, and other fresh and frozen uncooked poultry.To control pathogens in fresh and frozen red meats such as beef, lamb, and pork.9.Food composition influences microwave heating of food in what two ways? (P195)Food composition does not only influence the loss factor, but also penetration depth.10.Irradiation cannot be used on what two specific products? (P192)Irradiation cannot be used with dairy products and some fruits, such as peaches and nectarines.Chapter 24 Environmental Concerns and ProcessingReview Questions (P448-449)1.Water serves as a universal solvent. (P440)2.List five methods of conserving water during food processing. (P447)Always treat water as a raw material with a real cost; Set water conservation goals for the plant; Make water conservation a management priority; Install water meters and monitor water use; Train employees how to use water efficiently; Use automatic shut-off nozzles onall water hoses; Use high-pressure, low volume cleaning systems; Do not let people use water hoses as brooms; Reuse water where possible; Minimize spills of ingredients and of raw and finished product on the floor; Always clean up the spills before washing.总是把水看成是有成本的原料,制定工厂的节水目标,使节水成为管理首要考虑的内容,安装水表管理水的使用,培训员工怎样有效用水,在所有水管上安装自动关水喷嘴,使用高压低量的清洁系统,不允许用水管冲洗,尽可能重复利用水,尽量减少配料、原料和产品的溢、撒,清洗前总是先擦干净。
Tame and Wild Kernels of Quadratic Imaginary Number Fields
MATHEMATICS OF COMPUTATIONVolume 68,Number 225,January 1999,Pages 291–305S 0025-5718(99)01000-5TAME AND WILD KERNELSOF QUADRATIC IMAGINARY NUMBER FIELDSJERZY BROWKIN AND HERBERT GANGLAbstract.For all quadratic imaginary number fields F of discriminantd >−5000,we give the conjectural value of the order of Milnor’s group (thetame kernel)K 2O F ,where O F is the ring of integers of F.Assuming thatthe order is correct,we determine the structure of the group K 2O F and of itssubgroup W F (the wild kernel).It turns out that the odd part of the tamekernel is cyclic (with one exception,d =−3387).1.IntroductionAssuming Lichtenbaum’s conjecture one can compute conjectural values of orders of the tame kernels K 2O F of quadratic imaginary number fields F.Since in general these orders are not very large,and there are several results known concerning the p −rank of K 2O F and of its subgroup W F called the wild kernel,it is possible to determine the structure of these groups for the fields in question with discriminants d >−5000.2.NotationsWe use the following notation.•F is a number field with r 1real and 2r 2complex embeddings.•ζF (s )is the Dedekind zeta function of F.•O F is the ring of integers of F.•K n O F is the n th Quillen K –group of O F ,and especially•K 2O F is the Milnor group of O F (the tame kernel).•W F is the Hilbert kernel of F (the wild kernel).•e p is the p −rank of K 2O F ,where p is a prime or p =4.•w 2is the 2−rank of W F .•w (F )is the number of roots of unity in F .•Cl (O )is the class group of a Dedekind ring O.•R m (F )is a “twisted”version of the m th Borel regulator (see [Bo1]),the“twisted”regulator map r m being a map r m :K 2m −1O F → (2πi )m −1Rd m ,Received by the editor January 3,1997.1991Mathematics Subject Classification.Primary 11R11;Secondary 11R70,11Y40,19C99,19F27.Key words and phrases.Tame kernel,wild kernel,quadratic imaginary fields,Lichtenbaum’s conjecture.The second author was supported by the Deutsche Forschungsgemeinschaft.c1999American Mathematical Society 291292J.BROWKIN AND H.GANGLwhere d m =r 2for m even,and d m =r 1+r 2for odd m >1(d m is just the order of vanishing of ζF (s )at s =1−m ).The image of r m is a lattice of covolume R m (F )—it differs from Borel’s original one essentially by a power of π([Bo2];there is also a shift m →m +1compared to the original notation).puting the value #K 2O FBorel proved that,up to a rational factor,R m (F )is equal to ζ∗F (1−m ),the firstnon-vanishing Taylor coefficient of ζF (s )at s =1−m .Lichtenbaum’s conjecture[Li](as modified by Borel [Bo1])tries to interpret this rational factor and asks whether for all number fields and for any integer m ≥2there is a relation of the formres s =1−m ζF (s )(s −1+m )−d m (F )?=±#K 2m −2(O F )#K 2m −1(O F )tors ·R m (F )up to a power of 2,where the subscript “tors”denotes the torsion part,“res”the residue,and “ind”the indecomposable part.K 2m −2(O F )is known to be finite (Borel).There is some evidence for this conjecture,namely for m =2and F totally-real abelian it has been proved (up to a power of 2)by Mazur and Wiles[M-W]as a consequence of their proof of the main conjecture of Iwasawa theory (in this case R 2(F )=1,though).Recently Kolster,Nguyen Quang Do and Fleckinger ([KNF],Theorem 6.4)have proved a modified version of the conjecture (also up to a power of 2)for all abelian fields F and m ≥2.For imaginary quadratic fields F and m =2,their result is equivalent to the above formula.In what follows we assume m =2and F imaginary quadratic of discriminant d.In this case,the Lichtenbaum conjecture reads (using the functional equation for the zeta function and the fact that #K ind 3(O F )tors is here always 24)3|d |3/2π2·R 2(F )·ζF (2)?=#K 2(O F )up to a power of 2.Bloch [Bl]suggested and Suslin [Su]finally proved that Borel’s regulator map can be given (at least rationally)in terms of the Bloch-Wigner dilogarithm D 2(z )as a map on the Bloch group B (F );here D 2(z )= Li 2(z )+log |z |log(1−z ) ,where Li 2(z )= n ≥1z n n 2is the classical dilogarithm function,defined for |z |<1and analytically continued to C −[1,∞),and B (F )is given in explicit form with generators and relations (cf.[Su]):B (F )={ i n i [x i ]| i n i x i ∧(1−x i ) =0∈ 2F ×} [x ]−[y ]+[y x ]−[1−y 1−x ]+[1−y 1−x −1]|x,y ∈F ×−{1}.The dilogarithm D 2(z )maps B (F )into a lattice in R whose covolume we denote by D F 2.Thus,we can replace R 2(F )in the formula above by D F 2and still hope for the following equality to hold (up to a universal factor):3|d |3/2π22·ζF (2)?=#K 2(O F ).Note that in our formula we do not neglect powers of 2.The left hand side now can be computed numerically:we proceed by looking for elements ξ∈B (F )which are supported on exceptional S −units for some smallTAME AND WILD KERNELS 293set S of primes in F ,i.e.ξ= i n i [x i ]such that i n i x i ∧(1−x i ) =0,andthe principal ideals (x i )and (1−x i )are generated by S .The images D 2(ξ)lie in a 1-dimensional lattice,therefore the numerically computed values should all be commensurable.The covolume D F,S 2of this lattice is an integral multiple of D F 2(to be precise,the covolume that we actually get depends not only on S but also on the bounds that we impose on the valuations v P (x i )for P ∈S in our search).If we have obtained hundreds of different values D 2(ξ)there is a good chance thatthey already generate the correct lattice D 2(B (F ))and give D F 2exactly.Our program,written in PARI [BBCO],performs the above calculations succes-sively for an increasing set of primes and stops if the corresponding D F,S 2stabilizes,i.e.if the same covolume occurs for S and S S .The orders in the case of small discriminants have been determined by Tate [Ta](for |d |≤15),Ska l ba [Sk](d =−19,−20),and Qin [Q2],[Q3](d =−24,−35),and they coincide with ours.Furthermore,the entries of a former (shorter)table[Ga]were not only compatible with the structural theoretical results known at the time but even suggested several conjectures,most of which have been proved in the meantime ([B–92],[C-H],[Q1]).Our approach is very similar to that of Grayson [Gr],only we don’t have to restrict ourselves to class number one,and our program works even for quite large discriminants (e.g.,for F =Q (√−2000004)we obtain #K 2O F =4).The program is freely available from the second author via e-mail,together with some remarks on the modification of the parameters.4.Determining the structureIn order to establish the actual structure of the tame and wild kernel we apply the following results:let d =d/gcd(4,d ).(1)The index i F :=(K 2O F :W F )always divides 6.More precisely,2|i F iffd ≡±1(mod 8),3|i F iffd ≡−3(mod 9),d =−3.(See [B–82],Table 1.)(2)The 2-rank of the tame and wild kernels can be computed easily:e 2= t,if every odd prime divisor of d is ≡±1(mod 8),t −1,otherwise,where t is the number of odd prime divisors of d ;and w 2= e 2,if d ≡1(mod 8),e 2−1,otherwise.(See [B–S],Theorem 4.)(3)The 4-rank of the tame kernel can be easily determined using the results of[Q1],at least if the number of odd prime divisors of d does not exceed 3.The p -rank of K 2O F ,for odd p,is related to the p -rank of the class group of an appropriate number field as follows.(4)Let E 3=Q (√−3d )and e 3=3-rank Cl (O E 3).Thene 3=e 3,if d ≡−3(mod 9),294J.BROWKIN AND H.GANGLmax(1,e 3)≤e 3≤e 3+1,otherwise .(See [B–92],Theorem 5.6.)(5)Let E 5=Q (√,and e 5=5-rank Cl (O E 5).Then e 5≤e 5.(See [B–92],Theorem 5.4.)(6)For p >5,where p is a regular prime,let E p be the maximal real subfield of the field F (ζp ),and let e p =p -rank Cl (O E p ).Then e p ≤e p .(See [B–92],Theorem5.4.)5.ExamplesAs above,let d =d/gcd(4,d ).1)For d =−644,we have #K 2O F =32(conjecturally),and e 2=2,w 2=2.Moreover e 4=1,since 644=4·7·23,and 7≡23≡7(mod 8),see [Q1].Finally,(K 2O F :W F )=2,since d =−161≡7(mod 8)and d ≡−3(mod 9).It follows thatK 2O F =Z /2×Z /16and W F =Z /2×Z /8.2)For d =−255we have #K 2O F =12(conjecturally).Moreover e 2=2,w 2=1,and d ≡−3(mod 9).ThereforeK 2O F =Z /2×Z /2×Z /3and W F =Z /2.3)For d =−759,we have #K 2O F =36(conjecturally),and e 2=2,w 2=1,and d ≡−3(mod 9).Moreover,for E 3=Q (√3d )=Q (√−253),we have 3-rank Cl (O E 3)=0.ThereforeK 2O F =Z /2×Z /2×Z /9and W F =Z /2×Z /3.4)For d =−2395,we have #K 2O F =25(conjecturally).Moreover,for E 5=Q (√)=Q (√−479),we have 5−rank Cl (O E 5)=1.Therefore,using (5),K 2O F =W F =Z /25.5)For d =−1832,we have #K 2O F =49(conjecturally).The maximal real subfield E 7of the field F (ζ7)=Q (√−d,ζ7)is generated over Q by a root of the polynomialf (x )=x 6+7dx 4+14d 2x 2+7d 3.In our casee 7=7−rank Cl (O E 7)=1.Therefore,in view of (6),K 2O F =W F =Z /49.6.Description of the tableIn the first column there is the negative discriminant d.The last two columns give the structure of the tame and the wild kernel of the corresponding field.In these columns a single number n denotes the cyclic group of order n,and a sequence (n 1,n 2,...)denotes the direct sum of cyclic groups of orders n 1,n 2,....The last two columns contain correct results provided the conjectural value of #K 2O F is correct.TAME AND WILD KERNELS295Table1.Table of tame and wild kernels for imaginary quadratic numberfields of discriminant d>−5000(conjectural values)d tame wild –311–411–721–811–1111–1521–1911–2011–2321–2411–3121–3522–39(2,3)1–4011–4311–4721–5122–5211–5521–5622–5911–6711–6884–7121–7921–8311–84(2,3)2–8721–8811–9122–9521–10321–10411–10733–111(2,3)1–11522–11611–119(2,2)2–120(2,3)2–12322–12721–13111–13242–13644–13911–14321–14811–15121–15211–15522–15921d tame wild–16311–16442–16721–16822–17911–183(2,3)1–18422–18722–19121–195(2,2)(2,2)–19921–20322–21111–21211–21521–219(4,3)4–22321–22711–228(4,3)2–231(2,2)2–23211–23522–23921–24411–24721–24822–25111–255(2,2,3)2–25922–26042–26321–264(2,3)2–26722–27121–27622–28022–28311–287(2,2)2–291(4,3)4–29242–29521–29611–29922–303(2,11)11–30711–30822–31121–31222–31921–32344–327(2,3)1d tame wild–32822–33133–33521–33922–34022–34411–34711–35522–35642–35921–367(2,3)3–37122–372(2,3)2–37622–37911–38321–38884–391(2,2)2–39522–399(2,4,3)4–40322–40411–40721–408(2,3)2–41122–41521–41933–420(2,4)(2,2)–42411–42722–43121–435(2,2,3)(2,2)–43611–43921–44022–44311–44721–45122–45284–455(2,2)2–45622–46321–46711–471(2,3)1–47255–479(2,7)7–483(2,2)(2,2)–48721–48811–4911313–49911296J.BROWKIN AND H.GANGLTable1.(Continued)d tame wild –503(2,3)3–511(2,2)2–51522–516(4,3)2–51921–52022–52311–527(2,2)2–53222–53521–53611–543(2,3)1–54711–54842–55121–552(2,3)2–555(2,2,7)(2,2,7)–55921–56311–56422–56822–57155–579(4,3)4–58042–583(2,17)17–58422–58711–59121–595(2,2)(2,2)–59611–59921–60721–61122–615(2,2,3)2–61622–61911–623(2,2)2–627(2,2)(2,2)–62811–63121–63222–63522–64333–644(2,16)(2,8)–64721–651(2,2,3)(2,2)–65521–65911–660(2,2,3)(2,2)–663(2,2)2–66411d tame wild–66722–67121–679(2,2,5)(2,5)–68022–68311–687(2,3)1–69111–69211–69521–696(2,3,7)(2,7)–69922–703(2,37)37–70722–70842–71222–715(2,2)(2,2)–71921–723(4,3)4–72411–72721–72822–73144–73911–74042–74321–74422–75121–755(2,41)(2,41)–759(2,2,9)(2,3)–76022–76322–76721–771(2,3)(2,3)–77284–77644–77922–78711–78811–791(2,2)2–795(2,2,3)(2,2)–799(2,4)4–80322–804(4,9)(2,3)–80721–80811–81111–81521–82044–82321–82422–82711d tame wild–831(2,3)1–835(2,3)(2,3)–83642–83921–840(2,2,3)(2,2)–84322–85122–85222–85611–85911–863(2,3)3–868(2,4)(2,2)–87121–87211–879(2,5)5–88311–88444–887(2,5)5–88822–89521–89922–903(2,2,3)2–90444–90711–91121–915(2,2)(2,2)–91611–91921–92022–92322–932(4,5)(2,5)–935(2,2)2–939(4,3)4–943(2,2)2–94711–948(2,3)2–95121–952(2,2)(2,2)–95522–959(2,4)4–96484–96721–97155–97944–98321–984(2,3)2–987(2,2)(2,2)–99121–99522–99642–100344TAME AND WILD KERNELS297 Table1.(Continued)d tame wild –1007(2,3)3–1011(4,3)4–101222–1015(2,2)2–1016(2,13)(2,13)–101911–1023(2,16)16–102722–102884–103121–103222–103921–104322–1047(2,3)1–1048(3,11)(3,11)–105111–105521–105922–106042–1063(2,29)29–106422–106744–107611–107921–1087(2,3)3–109111–1092(2,4,3)(2,2)–1095(2,2)2–1096(2,31)(2,31)–109922–1103(2,5)5–110811–111121–111255–111522–1119(2,3)1–112311–112442–1128(2,3)2–1131(2,2)(2,2)–1135(2,7)7–113944–1140(2,2)(2,2)–114422–114722–115121–1155(2,2,2,3)(2,2,2)–115921–116022–116311–116721d tame wild–117111–117211–118777–1191(2,27)9–119233–119522–119921–120322–120422–1207(2,2)2–1208(2,3)(2,3)–121122–121922–122042–122321–1227(4,3)4–123121–1235(2,2,11)(2,2,11)–1236(2,9)(2,3)–1239(2,8)8–1240(2,17)(2,17)–1243(4,7)(4,7)–124721–125242–125521–125655–125911–1263(2,3)1–126722–126811–1271(2,2)2–1272(2,9)(2,3)–127921–128355–128442–1288(2,4)(2,4)–129133–1295(2,2)2–1299(8,3)8–130321–130411–130711–1311(2,2)2–131522–1316(2,4)(2,2)–1319(2,3)3–1320(2,2,13)(2,2,13)–1327(2,3)3–1335(2,2,3)2–133622–133922d tame wild–1343(2,2)2–134722–1348168–1351(2,4)4–1355(2,3)(2,3)–136322–136422–136721–1371(4,3,5)(4,5)–137922–1380(2,4,3)(2,2)–138321–138411–1387(4,11)(4,11)–139121–139611–139921–140322–1407(2,2,3)2–141144–1412168–141521–1416(2,3)2–1419(2,2,9)(2,2,9)–142321–142733–1428(2,2)(2,2)–143211–1435(2,2)(2,2)–143921–1443(2,4,3)(2,4)–144721–144833–145111–1455(2,2)2–145911–146022–1463(2,2)2–146422–1471(2,7)7–1479(2,2,3)2–148022–148311–1487(2,5)5–1491(2,2)(2,2)–149211–1495(2,2,17)(2,17)–149622–149911–150744–150842298J.BROWKIN AND H.GANGLTable1.(Continued)d tame wild –151121–1515(2,2,9)(2,2,3)–152377–1524(2,3)2–152721–152822–153111–153521–1540(2,4)(2,2)–154321–154444–1547(2,2,3)(2,2,3)–1551(2,2,3)2–155522–155611–155921–1560(2,2,3)(2,2)–156322–156721–157177–1572(4,5)(2,5)–157611–157911–1583(2,27)27–158833–159121–159222–1595(2,2)(2,2)–1599(2,2)2–160322–160484–160721–160822–1615(2,2)2–161933–1623(2,3)1–162422–162711–1631(2,2)2–1635(2,2)(2,2)–1636(4,19)(2,19)–163921–164044–164322–165122–165222–165521–1659(2,2,3)(2,2)–166321–16678383–1668(4,9)(2,3)d tame wild–167121–167222–1679(2,4)4–168411–1687(2,2)2–168811–1691(2,3)(2,3)–1695(2,2,3)2–169911–170321–1704(2,3)2–170722–171121–1716(2,2)(2,2)–172022–172377–172721–1731(4,3)4–173284–1735(2,5)5–1736(2,2,7)(2,2,7)–173922–1743(2,4)4–174711–174822–1751(2,2)2–175244–175921–176344–1767(2,2,3)2–176844–1771(2,2)(2,2)–177922–178044–178321–178422–178711–179522–1796(8,7)(4,7)–1799(2,2)2–1803(4,3,13)(4,13)–180721–181111–1812(2,3)2–181611–181922–182321–182842–183121–18324949–183522d tame wild–1839(2,3,5)5–1843(2,3)(2,3)–184411–1847(2,23)23–1848(2,2,3)(2,2)–185122–1855(2,2)2–1860(2,4)(2,2)–186422–186711–1871(2,3)3–187622–1879(2,3)3–188022–188322–1887(2,2)2–189122–189242–1895(2,3)3–189622–190321–190711–191222–191522–191921–192322–192442–1927(2,2)2–192844–193111–193922–194022–194321–1947(2,4,3)(2,4)–1951(2,3,5)(3,5)–1955(2,2)(2,2)–1956(4,3)2–195921–196322–1967(2,2,3)(2,3)–197222–197622–197911–1983(2,3)1–198711–1988(2,8)(2,4)–199121–1992(2,3)2–1995(2,2,2)(2,2,2)–199921–200311TAME AND WILD KERNELS299 Table1.(Continued)d tame wild –200422–200811–201111–2015(2,2)2–2019(16,3)16–202042–2024(2,7)(2,7)–202711–203121–2035(2,4)(2,4)–203633–203921–2040(2,2)(2,2)–2047(2,2)2–2051(2,3)(2,3)–2055(2,2,3)2–205644–205922–206321–2067(2,2)(2,2)–206822–207121–207222–208311–208442–208721–2091(2,2,3)(2,2)–209521–209911–2103(2,5)5–210422–211121–211921–212022–212322–2127(2,3)1–213111–2132(2,3)(2,3)–2135(2,2)2–2136(2,3)2–2139(2,2)(2,2)–214321–214722–214842–215211–215522–2159(2,2)2–2163(2,2,3,5)(2,2,5)–216411–216721–216822d tame wild–217122–21792525–218042–2183(2,3)3–2184(2,2)(2,2)–2191(2,2)2–2195(2,5)(2,5)–2199(2,3)1–220311–220721–2211(2,8)(2,8)–2212(2,4)(2,2)–2215(2,5,23)(5,23)–221611–221922–2227(2,3)(2,3)–222811–2231(2,2)2–2235(2,2,27)(2,2,9)–223921–224311–2244(2,8,3)(2,4)–2247(2,2)2–224822–225111–2255(2,2)2–226022–2263(2,2)2–226411–226711–2271(2,3,5)5–227642–227921–2280(2,2,3)(2,2)–2283(2,3)(2,3)–228721–229122–229222–2296(2,2)(2,2)–2307(4,3)4–2308168–231121–231522–231921–232322–232422–232721–232844–233521–233911–2343(2,2,3)2d tame wild–234433–234711–2351(2,3)3–2355(2,2,9)(2,2,9)–235622–2359(2,2)2–236022–236322–237111–2372168–2379(2,4,3)(2,4)–238321–2387(2,2)(2,2)–2388(2,3)2–239121–2392(2,7)(2,7)–2395(2,25)(2,25)–239921–240442–240721–2408(2,3)(2,3)–241111–2415(2,2,2,3)(2,2)–241944–242321–2424(2,3)2–242722–2431(2,2)2–243522–2436(2,4)(2,2)–244022–244322–2447(2,7)7–2451(2,4,3,7)(2,4,7)–245211–245521–245611–245911–246321–246711–2468(4,3)(2,3)–2471(2,2)2–247222–247921–248322–2487(2,3)1–2488(2,3)(2,3)–2491(2,3)(2,3)–249521–250321–250422300J.BROWKIN AND H.GANGLTable1.(Continued)d tame wild –250722–251522–251622–251921–253111–2532(4,3)2–253611–253911–254321–255121–255222–2555(2,2,3)(2,2,3)–2559(2,3)1–256322–256484–2567(2,2)2–2568(2,3)2–257122–257911–2580(2,2)(2,2)–258488–258722–259121–2595(2,2,3)(2,2)–259642–2599(2,2)2–260344–2607(2,2)2–261122–261211–261521–261622–262321–2627(2,3)(2,3)–2631(2,3)1–2632(2,2)(2,2)–2635(2,2)(2,2)–2639(2,2)2–264322–264411–264721–264811–265122–265911–2660(2,4)(2,2)–266321–2667(2,2,3)(2,2)–267121–2676(2,3)2d tame wild–2679(2,2)2–268022–268311–268721–269284–269688–269911–2703(2,2,3)2–270711–270811–271121–2712(2,3)2–2715(2,2)(2,2)–271921–272322–272442–272822–273111–273521–2739(2,8,3)(2,8)–2740(2,3)(2,3)–274321–274722–2751(2,4)4–2755(2,2)(2,2)–275642–2759(2,2,3)(2,3)–2760(2,2)(2,2)–2767(2,5)5–277122–27761111–277922–678722–2788(2,4)(2,2)–2791(2,3)3–279255–2795(2,2)(2,2)–280311–280411–2807(2,4)4–2811(32,3)32–281521–281911–2820(2,4,3)(2,2)–282321–2824(8,3)(8,3)–2827(4,5)(4,5)–283121–283611d tame wild–2839(2,2)2–284022–284311–2847(2,2,3)2–285111–2852(2,4,3)(2,2,3)–285521–2856(2,2,9)(2,2,3)–2859(2,5)(2,5)–2863(2,2)2–2867(2,5)(2,5)–286822–287222–2879(2,3)3–2884(2,8)(2,4)–288721–2895(2,2)2–289922–290321–2911(2,2)2–2915(2,4,3)(2,4,3)–2919(2,4,3)4–292022–2923(2,3,23)(2,3,23)–292721–293122–293211–293521–293622–293911–294722–294842–2951(2,5)5–2955(2,2,3)(2,2)–295921–296311–2964(2,2,3)(2,2)–2967(2,2)2–296822–297155–298042–298321–298411–298722–2991(2,3)1–299522–299622–299921–3003(2,2,2)(2,2,2)TAME AND WILD KERNELS301 Table1.(Continued)d tame wild –3007(2,4)4–301177–301242–301622–301977–302321–3027(4,3)4–302811–3031(2,2)2–303211–303522–303921–304344–304442–3047(2,5)5–3048(2,5,9)(2,5,9)–3055(2,2,5)(2,5)–3059(2,2)(2,2)–3063(2,3)1–3064(2,3)(2,3)–306711–307121–307684–307921–3080(2,2)(2,2)–308311–309122–309211–309521–3099(4,3)4–310321–310722–3108(2,4,3,13)(2,2,13)–3111(2,2)2–311211–3115(2,2)(2,2)–311921–312422–312721–3128(2,2)(2,2)–313122–3135(2,2,2,3)(2,2)–313922–314042–3143(2,2)2–3144(2,3)2–314722–3151(2,2)2–315522–315622–316022d tame wild–316311–316721–3171(2,2,3)(2,2)–317242–31761717–318321–318711–318811–319121–3192(2,2)(2,2)–3199(2,2)2–320311–3207(2,3)1–320844–3215(2,23)23–3219(2,2)(2,2)–3220(2,2)(2,2)–322321–3224(2,7)(2,7)–322722–323522–323642–3239(2,2)2–3243(2,4,3)(2,4)–3247(2,16)16–325111–3252(2,3)2–3255(2,2,2)(2,2)–325622–325911–326321–326842–3271(2,3)3–327222–3279(2,3)1–328411–328721–3288(2,3)2–329122–329521–3299(3,5)(3,5)–330422–330711–3311(2,2)2–3315(2,2,2,3)(2,2,2)–331611–331921–3320(2,5)(2,5)–332311–332721–333111d tame wild–3335(2,2)2–333622–334321–334711–3351(2,3)1–335211–3355(2,2,13)(2,2,13)–3359(2,3)3–3363(2,4)(2,4)–3367(2,2)2–336811–337111–3379(2,37)(2,37)–3383(2,2)2–3387(4,3,3)(4,3)–339121–3395(2,2)(2,2)–3396(4,3)2–3399(2,4)4–340388–340721–341211–341521–3416(2,11)(2,11)–341922–3423(2,2,3,11)(2,11)–342722–342842–3431(2,2)2–3432(2,2,3)(2,2)–3435(2,2)(2,2)–343921–344344–3444(2,2)(2,2)–344822–3451(2,2,3)(2,2,3)–345521–3459(4,9)(4,3)–346042–346321–346444–346711–3471(2,2)2–347622–3480(2,4)(2,4)–348721–349111–3495(2,2,3)2–349622–349911–3503(2,2)2302J.BROWKIN AND H.GANGLTable1.(Continued)d tame wild –3507(2,2)(2,2)–350811–351121–351222–3515(2,2)(2,2)–352322–3524168–352721–3531(2,4,3)(2,4)–3535(2,2)2–353911–3540(2,2,27)(2,2,9)–354321–354411–354733–355121–3556(2,4)(2,2)–355921–356044–356322–3567(2,2,3)2–357111–357222–3576(2,3)2–357922–358321–358722–3588(2,4)(2,2)–359244–359522–359921–3603(4,3)4–3604(4,3)(4,3)–3607(2,17)17–360822–361122–3615(2,4)4–3619(2,2)(2,2)–362042–362321–3624(2,125)(2,125)–363121–363522–3639(2,3)1–3640(2,4)(2,4)–364333–3647(2,2,3)(2,3)–365122–365242–3655(2,2)2–365622d tame wild–365911–366722–366822–3671(2,3)3–367921–368322–3684(4,3)2–3687(2,3)3–368811–369111–3695(2,3,5)(3,5)–370422–370722–3711(2,3)1–371522–371684–371921–3720(2,2,3)(2,2)–3723(2,2,5)(2,2,5)–372721–3731(2,2)(2,2)–373222–373611–373911–374321–3747(4,3)4–774842–375222–375522–379(2,2)2–3763(2,3)(2,3)–376411–376721–376822–377911–3783(2,2,9)(2,3)–378422–378722–3791(2,4)4–3795(2,2,2)(2,2,2)–379622–379921–380311–381122–381242–3815(2,2)2–3819(2,4,3)(2,4)–382321–382722–3828(2,2,3)(2,2)–383121d tame wild–383222–3835(2,2,3,23)(2,2,3,23)–383921–384721–384822–385111–3855(2,2,3)2–385922–386022–386321–3864(2,2,3)(2,2)–386722–3876(2,4)(2,2)–388022–388388–3891(4,3)4–389222–3895(2,2)2–3896(2,3)(2,3)–3899(2,3)(2,3)–390321–390711–390884–391121–3912(2,3)(2,3)–3919(2,3)3–392311–3927(2,2,2,3)(2,2)–392811–393111–393521–3939(2,2)(2,2)–394042–3943(2,3)3–394422–394711–3955(2,2)(2,2)–3956(2,5)(2,5)–3959(2,23)23–3963(8,3)8–396721–3972(4,3)2–3976(2,4)(2,4)–397922–3983(2,2)2–398811–399121–399211–3995(2,2)(2,2)–3999(2,4,9)(4,3)–400311TAME AND WILD KERNELS303 Table1.(Continued)d tame wild –4004(2,4)(2,2)–400721–4008(2,3)2–4011(2,2)(2,2)–4015(2,2)2–401955–4020(2,2)(2,2)–402422–402733–403121–4035(2,2,3)(2,2)–403684–4039(2,2)2–404022–404322–4047(2,2)2–405111–405211–405521–4063(2,4)4–4071(2,2,3)2–407233–407921–408322–408411–408721–4088(2,2)(2,2)–409111–409911–4103(2,3)3–4111(2,3)3–411522–4119(2,3)3–412022–4123(2,2)(2,2)–412721–413242–413521–413622–413977–4143(2,3)1–4147(2,2,3)(2,2,3)–4148(2,29)(2,29)–4151(2,2,5)(2,5)–4152(2,3)2–4155(2,2)(2,2)–4159(2,5)5–416322–416442–416822–417144d tame wild–4179(2,2,3)(2,2)–4180(2,4)(2,4)–4183(2,4)4–418433–418722–4191(2,2)2–419522–419642–4199(2,4)4–4207(2,2)2–421111–4215(2,2,3)2–4216(2,2)(2,2)–421933–4223(2,4)4–422722–4228(2,8)(2,4)–423121–424355–424455–4247(2,2)2–4251(2,4,3,7)(2,4,7)–4255(2,2,3)(2,3)–425911–4260(2,4,3)(2,2)–426422–426744–427121–427611–427921–428022–428333–4287(2,3)1–429122–429242–429521–4296(2,3)2–429922–430321–4307(2,5)(2,5)–4308(2,3)(2,3)–431522–4319(2,4,5)(4,5)–4323(2,4,3)(2,4)–4324(2,4)(2,2)–432721–432811–4331(2,7)(2,7)–433911–4340(2,2)(2,2)–434321d tame wild–434422–435121–4355(2,2)(2,2)–4359(2,3)1–436022–436333–436721–4371(2,2,49)(2,2,49)–437211–437611–437922–438788–438842–439121–4395(2,2,3)(2,2)–439921–4403(2,2)(2,2)–4404(2,3)2–4407(2,2)2–440822–441144–4415(2,3,7)(3,7)–4420(2,4)(2,2)–4423(2,3)3–4424(2,2,5)(2,2,5)–442744–4431(2,2,3)2–443522–443611–4439(2,2)2–4440(2,2,3)(2,2)–444322–444721–445111–4452(2,4)(2,2)–445611–446321–4467(4,3)4–446811–4471(2,2)2–447222–447921–448311–448442–4487(2,4)4–4488(2,4)(2,4)–4495(2,2)2–449922–4503(2,2,3)2–450411–450711。
核电荷数(soc)
核电荷数(soc)英文回答:Atomic Number (Z) Definition and Significance.The atomic number (Z) of an atom is the number of protons in its nucleus. It is a fundamental property of an atom and uniquely identifies the element to which the atom belongs. The atomic number determines the number of electrons in an atom's neutral state and, together with the number of neutrons, defines the atomic mass.Role of Atomic Number in Chemistry.The atomic number plays a crucial role in various aspects of chemistry:Chemical Behavior: The atomic number determines the chemical properties of an element. Elements with similar atomic numbers tend to exhibit similar chemical behavior.Periodic Table Organization: The periodic table is organized based on atomic number. Elements with increasing atomic number are arranged in rows (periods) and columns (groups), creating a logical structure that highlightstheir chemical similarities.Ionic Bond Formation: When atoms lose or gain electrons, they acquire a net electrical charge and become ions. The atomic number determines the number of electrons an atom can lose or gain to achieve a stable configuration, influencing the formation and properties of ionic bonds.Isotopes: Isotopes of an element have the same atomic number but different numbers of neutrons. The atomic number identifies the element, while the neutron number distinguishes different isotopes.Nuclear Structure and Stability.The atomic nucleus, where protons and neutrons reside, is held together by the strong nuclear force. The balancebetween electrostatic repulsion (due to protons having positive charges) and nuclear attraction determines the stability of the nucleus:Stability Range: Most atoms are stable with atomic numbers ranging from 1 (hydrogen) to 83 (bismuth). Beyond bismuth, elements become increasingly unstable due to the increasing electrostatic repulsion between protons.Radioactive Decay: Heavy elements with high atomic numbers are often radioactive and undergo various types of radioactive decay to achieve a more stable nuclear configuration.Applications of Atomic Number.The concept of atomic number has practical applications in numerous fields:Spectroscopy: Atomic number influences the absorption and emission spectra of atoms, facilitating the identification and analysis of elements.Nuclear Physics: The atomic number is used to study nuclear reactions and the behavior of subatomic particles.Material Science: Understanding atomic numbers is essential for designing and developing materials with specific properties.中文回答:原子序数 (Z)。
ADDING AND SUBTRACTING DEVICE
专利名称:ADDING AND SUBTRACTING DEVICE 发明人:HAGIWARA YOSHIMUNE,SUGYAMASHIZUO,MAEDA SHIGEMICHI,YUMOTOOSAMU,AKAZAWA TAKASHI,KOBAYASHIMASAHITO,KITA YASUHIRO,KIDA JUZO 申请号:JP18737389申请日:19890721公开号:JPH0357486B2公开日:19910902专利内容由知识产权出版社提供摘要:PURPOSE:To prevent an overflow and an underflow which accompany addition and subtraction from occurring by equipping a means which normalize anaddition/subtraction result with a means which limits the shift quantity of the mantissa part of the addition/subtraction result so that the value of the exponent part is within a specific range. CONSTITUTION:A zero detecting circuit 79 and a left-directional shifting circuit 76 are provided so as to normalize the output UM of an adder 75 so that its absolute value is maximum. Namely, the zero detecting circuit 79 detects the number of theta1 of successive '0's following the sign bit of the data UM (below the decimal point) and the shifting circuit 76 shifts the data UM left (to the most significant digit bit) by theta1 bits to obtain mantissa part data LM which has the maximum absolute value. When the data UM is minus, on the other hand, the data is shifted only by the number of successive '1's. In this case, a subtracting circuit 78 calculates (gamma-theta1) as to exponent part data gamma and its output UE is regarded as a normalized exponent value. Consequently, a fast, high-accuracy OR arithmetic function is obtained.申请人:HITACHI SEISAKUSHO KK,HITACHI DENSHI KK 更多信息请下载全文后查看。
Atomic number and mass number:原子数和质量数共24页文档
LecturePLUS Timberlake
2
Subatomic Particles
Particle Electron
Symbol e-
Charge 1-
Relative Mass
0
Location
outside nucleus
Proton
11 protons Sodium
11
Na
LecturePLUS Timberlake
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Learning Check
State the number of protons for atoms of each of the following: A. Nitrogen 1) 5 protons 2) 7 protons 3) 14 protons B. Sulfur 1) 32 protons 2) 16 protons 3) 6 protons C. Barium 1) 137 protons 2) 81 protons 3) 56 protons
Atoms and Elements
The Atom Atomic Number and Mass
Number Isotopes
LecturePLUS Timberlake
1
Atomic Theory
Atoms are building blocks of elements Similar atoms in each element Different from atoms of other elements Two or more different atoms bond in
Give the symbol of the element
atomic number定义
atomic number定义好的,以下是为您创作的关于“atomic number 定义(原子序数定义)”的科普文章:在我们生活的这个奇妙世界里,存在着无数微小而神秘的粒子,它们共同构成了万物。
而在这些微小粒子中,原子扮演着至关重要的角色。
今天,咱们就来聊聊原子序数这个有趣的概念。
想象一下,原子就像是一个小小的“微观公寓楼”。
每个“公寓楼”里都住着一群叫做“质子”“中子”和“电子”的居民。
而原子序数呢,就像是这个“公寓楼”的门牌号。
简单来说,原子序数就是指原子核中质子的数量。
质子,是这些居民中的“老大”,它们决定了原子的身份。
就好比在一个小区里,每家的户数决定了这户人家的编号,原子里质子的数量就决定了原子的编号,也就是原子序数。
那为什么质子数量这么重要呢?这是因为不同的原子,其质子数量是不一样的。
氢原子,它的原子核里只有 1 个质子,所以它的原子序数就是 1;氧原子的原子核里有 8 个质子,原子序数就是 8。
在我们的日常生活中,原子序数有着广泛的应用。
比如说,我们都知道的金银首饰。
金的原子序数是 79,银是 47。
这不同的原子序数决定了它们的化学性质和物理性质,从而使得金比银更稳定,更不容易发生化学反应,所以金首饰能长久保持光亮,而银首饰戴久了可能会变黑。
再看看我们身边的电池。
电池的工作原理其实就和原子序数有关。
例如锂离子电池,锂的原子序数是 3,它的一些特殊性质使得锂离子能够在电池中来回穿梭,实现充电和放电的过程。
在医疗领域,原子序数也大显身手。
X 射线和 CT 检查大家都不陌生吧?医生利用不同元素的原子序数不同,对 X 射线的吸收程度也不同的原理,来帮助我们诊断疾病。
比如骨头中的钙,原子序数相对较高,能吸收更多的 X 射线,在片子上就呈现出白色,而软组织吸收较少,就显示为灰色。
还有核电站,其工作原理涉及到铀元素。
铀的原子序数是 92,它的原子核在特定条件下会发生裂变,释放出巨大的能量。
科学家们正是利用了这一特性,来为我们提供大量的电能。
atomic number英文定义
atomic number英文定义原子序数的英文定义定义•Atomic number是用于描述元素化学性质的一个基本指标,表示元素中原子核中正电荷的数目。
在化学元素周期表中,原子序数通常用字母Z表示。
原子序数的意义与理由元素特征的分辨原子序数决定了化学元素的特性,不同元素的原子序数是唯一的。
原子序数越大,元素的质量和电子云层的数量也越大。
因此,原子序数可以用来区分不同元素之间的差异。
元素周期表的排列方式原子序数是元素周期表的基础。
元素周期表按照原子序数的增加,将元素有序地排列成一个周期性表格。
这种排列方式使得相似特性的元素归类到了同一列中,方便了元素的比较和研究。
与元素核素的关联原子序数是指元素中核心质子的数目,因此与元素的核素相关。
每个元素可以有不同的核素,其质子数目不变,但中子数目可能不同。
原子的核素可以通过元素的原子序数被唯一地标识。
相关书籍以下是几本与原子序数相关的书籍,它们深入地探讨了原子序数的意义及应用。
1.《The Periodic Table: A Very Short Introduction》–作者:Eric R. Scerri–简介:这本书是《Very Short Introductions》系列的一部分,是一本简明扼要地介绍了元素周期表的入门读物。
其中一章节专门解释了原子序数及其在周期表中的作用。
2.《The Elements: A Visual Exploration of Every Known Atomin the Universe 》–作者:Theodore Gray–简介:这本书以图像为主,展示了宇宙中已知的每个原子元素,并通过精美的照片、插图和详细的介绍,解释了不同元素之间的关系及其原子序数对元素特性的影响。
3.《The Disappearing Spoon: And Other True Tales ofMadness, Love, and the History of the World from thePeriodic Table of the Elements》–作者:Sam Kean–简介:这本书通过有趣的故事和历史背景,向读者展示了元素周期表的奇妙之处。
化学元素的共价半径
P
15
111
Si
14
112
Kr
36
114
Br
35
115
Ni
28
116
Se
34
116
Co
27
117
Cu
29
117
Fe
26
全英化学元素表资料 periodic_table_links
Name: Neon Symbol: Ne Atomic Number: 10 Atomic Mass: 20.1797 amu Melting Point: -248.6 °C (24.549994 °K, -415.48 °F) Boiling Point: -246.1 °C (27.049994 °K, -410.98 °F)
Name: Oxygen Symbol: O Atomic Number: 8 Atomic Mass: 15.9994 amu Melting Point: -218.4 °C (54.750008 °K, -361.12 °F) Boiling Point: -183.0 °C (90.15 °K, -297.4 °F)
Name: Argon Symbol: Ar Atomic Number: 18 Atomic Mass: 39.948 amu Melting Point: -189.3 °C (83.85 °K, -308.74 °F) Boiling Point: -186.0 °C (87.15 °K, -302.8 °F)
Name: Nickel Symbol: Ni Atomic Number: 28 Atomic Mass: 58.6934 amu Melting Point: 1453.0 °C (1726.15 °K, 2647.4 °F) Boiling Point: 2732.0 °C (3005.15 °K, 4949.6 °F)
Name: Carbon Symbol: C Atomic Number: 6 Atomic Mass: 12.0107 amu Melting Point: 3500.0 °C (3773.15 °K, 6332.0 °F) Boiling Point: 4827.0 °C (5100.15 °K, 8720.6 °F)
泰山医学院材料导论题库
泰山医学院《材料导论》试题库1、The nucleus of an atom containsA ProtonsB ElectronsC NeutronsD All of the abovev E Both A and C2、What type(s) of electron subshell(s) does an L shell contain?A a p f sB s and fv C s and p3、What is the maximum number of electrons that an M shell may contain?v A.18B.32C.84、Match the electron structure below with the element type it represents.1s22s22p63s23p63d104s1A. Inert gasB. HalogenC. Alkali metalD. Alkaline earth metalv E. Transition metal5、What is the predominant type of bonding for titanium (Ti)?A. IonicB. HydrogenC. CovalentD. van der Waalsv E. Metallic6、Of those elements in the list situated below the periodic table, select the one that is one electron short of having its outer shell of electrons completely filled.v A. IB. NC. SD. SrE. Ar7、Which of the following materials may form crystalline solids?A. PolymersB. MetalsC. Ceramicsv D. All of the above8、Which of the following are the most common coordination numbers for ceramic materials?A. 2B. 3 and 6C. 4 and 12v D. 4,6 and 89、Which crystal system(s) listed below has (have) the following relationship for the unit cell edge lengths?a =b ≠cA. CubicB. HexagonalC. TriclinicD. MonoclinicE. RhombohedralF. OrthorhombicG. Tetragonalv H. Both C and E10、Which crystal system(s) listed below has (have) the following interaxial angle relationship? α= β = γ = 90°v A. CubicB. HexagonalC. TriclinicD. MonoclinicE. RhombohedralF. OrthorhombicG. Both A and D11、把a、b、c、d四块金属片浸入稀硫酸中,用导线两两相连组成原电池。
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Tungsten and its Minerals compiled by Bob Sharpe and MacHenry GilmourTungsten is a metallic element with an Atomic Number 74, and Atomic Symbol W Tungsten has the highest melting point of all metals (3422 C), one of the highest densities and, when combined with carbon, is almost as hard as diamond. There are more than twenty tungsten bearing minerals in the Tungstate subclass, but only two are important for industrial use, namely wolframite and scheelite.∙Cuprotungstite (Copper Tungstate Hydroxide) Russellite (Bismuth Tungstate)∙Lindgrenite (Aluminum Tungstate Hydroxide) Sanmartinite(Zinc Iron Tungstate)∙Jixianite (Lead Iron Tungstate Oxide Hydroxide)Scheelite(Calcium Tungstate)∙Stolzite (Lead Tungstate) Wolframite(Manganese Iron Tungstate)∙Tungstibite(Antimony Oxide Tungstate)Ferberite(Iron Tungstate)∙Raspite (Lead Tungstate)Hubnerite(Manganese Tungstate) Scheelite•Color is white, yellow, orange or greenish gray to brown.•Luster is adamantine to greasy.•Transparency: Crystal s are transparent to translucent.•Crystal System is tetragonal•Fracture is conchoidal.•Hardness is 4.5 - 5.•Specific Gravity is approximately 5.9 - 6.1 (very heavy for translucent minerals).•Streak is white.•Other Characteristics: Fluoresces blu e (yellow with molybdenum traces) under short waveultraviolet light.•Associated Minerals are quartz, garnets, vesuvianite, epidote, topaz, schorl, apatite, gold,silver, molybdenite, cassiterite, wolframite and fluorite.•Best Field Indicators are crys tal habit, color, density, luster and especially its fluorescence.Notable occurrences of Scheelite include Timmins, ON and Tungsten, NWT; Saxony, Germany;Tong Wha, Korea; Brazil; Sonora, Mexico; Cornwall, England; New South Wales and Queensland, Australia and Mill City, Nevada, Atolia, San Bernardino Co., California, Cochise Co., Arizona, Utah and Colorado, USA.Wolframite is a general term for iron and manganese tungstates where the iron/manganese ratio can vary. A mineral with more than 80% FeWO4 is called Ferberite and a mineral with more than 80% MnWO4 is called Hübnerite.•Color is Black to grey or brown.•Luster is submetallic to resinous.•Transparency crystals are translucent to opaque.•Crystal System is monoclinic; Crystal Habits include t he flat, heavily modified, tabularcrystals.•Cleavage is perfect in one directio n•Fracture is uneven.•Hardness is 4 - 4.5.•Specific Gravity is approximately 7.0 - 7.5 (heavy even for metallic minerals)•Streak is brown to black.•Associated Minera ls are quartz, hematite, tourmalines, cassiterite, micas and pyrite.•Other Characteristics: crystals striated lengthwise.•Best Field Indicators are crystal habit, color, density, luster and cleavage.Notable occurrences of Wolframite include Nanling Range, China; southwest and Colorado, USA;Russia; Korea; England and Bolivia.The history of tungsten goes back to the 17th century tin mines of the Erz Mountains of Saxony. Miners noticed that certain ores disturbed the reduction of cassiterite and induced slagging. The miners gave this annoying ore nicknames like "wolfert" and "wolfrahm" (which means wolf froth). In 1758, the Swedish chemist and mineralogist, Axel Fredrik Cronstedt, discovered and described an unusually heavy mineral that he called "tung-sten", which is Swedish for heavy stone. Scheele, in 1781, found that a new acid could be made from a tungsten mineral. In 1821, CaWO4. was named "Scheelite".Applications∙Tungsten is a metal with a wide range of uses, the largest of which is as tungsten carbide. Tungsten monocarbide (WC) has a hardness close to diamond, and is one of the hardest substances in existence.∙Its used in metalworking, mining, petroleum and construction industries for cutting edges and high speed steel tools∙Tungsten is widely used in light bulb and vacuum tube filaments, as well as electrodes, because it can be drawn into very thin metal wires that have a high melting point.∙Other applications include chemical uses, mainly in the form of catalysts, inorganic pigments, high-temperature lubricants stable to very high temperatures∙Hardness and density properties make this metal ideal for making heavy metal alloys that are used in armaments, heat sinks, and high-density applications, such as weights, counterweights and ballast ∙The high density makes it an ideal ingredient for darts∙It is used as a substitute for lead in bullets and is alloyed with nickel and iron or cobalt as an alternative to depleted uranium in heavier ammunition∙Tungsten superalloys such as Hastelloy and Stellite. are used in turbine blades and wear-resistant parts and coatings.∙Tungsten Carbide has recently been used in the fashioning of jewelry dueto its hypoallergenic nature and the fact that due to its extreme hardness itis not apt to lose its luster like other polished metals.This book makes one want to study mineralsUncle Tungsten: Memories of a Chemical Boyhoodby Oliver Sacks。