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Existence and multiplicity results for some superlinear elliptic problems on RN

Existence and multiplicity results for some superlinear elliptic problems on RN
Existence and multiplicity results for some superlinear elliptic problems on RN

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On: 24 March 2012, At: 23:52

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Communications in Partial Differential

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Existence and multiplicity results for some

superlinear elliptic problems on R N

Thomas Bartsch a & Zhi Qiang Wang b

a Mathematisches Institut, Universit?t Heidelberg, Im Neuenheimer Feld 288,

Heidelberg, 69120, Germany

b Department of Mathematics and Statistics, Utah State University, Logan, UT,

84322

Available online: 08 May 2007

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D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

D o w n l o a d e d b y [T o m s k S t a t e U n i v e r s i t y o f C o n t r o l S y s t e m s a n d R a d i o ] a t 23:52 24 M a r c h 2012

共同保密协议中英文对照版

中文: 共同保密协议 ABC公司(以下称为ABC),其总部设于—,与XYZ(以下称为XYZ),其总部设于—,鉴于本协议的共同契约条款,谨达成如下协议: 1.在协议双方有关策略性联盟(此后称为“主题事项事项”)的磋商问题上,本协议一方可以在保密的基础上向另一方披露其专有资讯(此后称为“资讯”),披露方可以认为该等资讯具有专有性,因为披露方是在协议双方内部披露了该资讯,或因为披露方在接受“资讯”的同时已经承担了为“资讯”继续保密的义务,或由于其它的原因。 2.当被视为专有的“资讯”以载体的形式被提供时,披露方须以对“资讯”进行标记的方式,指出该资讯的专有性或机密性,或者把该资讯的传布局限在协议所规定的范围里。当“资讯”被口头提供时,提供方在披露的同时,应明确声明其专有性或机密性,或者把该资讯的传布限制在协议规定范围里,或者,事后立即书面确认该资讯的专有性和机密性。此外,该协议之实体和条款,双方就“主题事项事项”所进行磋商的事实和内容以及相关“主题事项事项”的通信都被将认为具有专有性。 3.关于该协议所披露的“资讯”,获披露“资讯”的一方,其职员及其附属公司的职员应该做到: a.对该资讯保密,其采取的谨慎程度不少于披露方为保护其不愿披露的专有机密资讯所采取的谨慎程度,并且,在任何情况下,以合理的谨慎程度进行保密。 b.把资讯的披露范围仅仅局限于董事会、公司高级职员、职员和/或有必要知道的代理/顾问,不得将资讯披露给其他任何人。 c.建议获披露该“资讯”之人士履行对该资讯的保密义务。 d.仅仅将该资讯用于有关“主题事项事项”的通信和磋商上,除此以外使用该资讯必须经双方书面同意。 4.获披露“资讯”一方想要将“资讯”披露给非附属的顾问和代理,必须首先经由“资讯”原本披露方的书面认可,并且与该顾问和代理签署有关保密协议,其形式必须为“资讯”原本披露方所满意。 5.“资讯”应被视为资讯披露方的财产,一旦该方要求,另一方应以载体的形式把所有“资讯”归还给披露方,或者按照资讯披露方的指示销毁该资讯。如另一方丢失了“资讯”或者在未经授权的情况下披露了“资讯”,应立即通知对方并作合理的努力来追回丢失或错误地泄露了的资讯。 6.在下述情况下,获披露“资讯”的一方没有任何义务来保持该资讯的专有性: a.此前已为不受保密性义务约束的一方获知,或 b.即便不存在未经授权的披露该资讯也可以或者将可以逐渐为公众所悉,或

bring him into existence

Three months later FFCC had suddenly been dissolved with no reasons given. One could assume that Withers and his associates were now in disgrace, but there had been no report of the matter in the Press or on the telescreen. That was to be expected, since it was unusual for political offenders to be put on trial or even publicly denounced. The great purges involving thousands of people, with public trials of traitors and thought-criminals who made abject confession of their crimes and were afterwards executed, were special show-pieces not occurring oftener than once in a couple of years. More commonly, people who had incurred the displeasure of the Party simply disappeared and were never heard of again. One never had the smallest clue as to what had happened to them. In some cases they might not even be dead. Perhaps thirty people personally known to Winston, not counting his parents, had disappeared at one time or another. Winston stroked his nose gently with a paper-clip. In the cubicle across the way Comrade Tillotson was still crouching secretively over his speakwrite. He raised his head for a moment: again the hostile spectacle-flash. Winston wondered whether Comrade Tillotson was engaged on the same job as himself. It was perfectly possible. So tricky a piece of work would never be entrusted to a single person: on the other hand, to turn it over to a committee would be to admit openly that an act of fabrication was taking place. V ery likely as many as a dozen people were now working away on rival versions of what Big Brother had actually said. And presently some master brain in the Inner Party would select this version or that, would re-edit it and set in motion the complex processes of cross-referencing that would be required, and then the chosen lie would pass into the permanent records and become truth. Winston did not know why Withers had been disgraced. Perhaps it was for corruption or incompetence. Perhaps Big Brother was merely getting rid of a too-popular subordinate. Perhaps Withers or someone close to him had been suspected of heretical tendencies. Or perhaps -- what was likeliest of all -- the thing had simply happened because purges and vaporizations were a necessary part of the mechanics of government. The only real clue lay in the words 'refs unpersons', which indicated that Withers was already dead. You could not invariably assume this to be the case when people were arrested. Sometimes they were released and allowed to remain at liberty for as much as a year or two years before being executed. Very occasionally some person whom you had believed dead long since would make a ghostly reappearance at some public trial where he would implicate hundreds of others by his testimony before vanishing, this time for ever. Withers, however, was already an unperson. He did not exist: he had never existed. Winston decided that it would not be enough simply to reverse the tendency of Big Brother's speech. It was better to make it deal with something totally unconnected with its original subject. He might turn the speech into the usual denunciation of traitors and thought-criminals, but that was a little too obvious, while to invent a victory at the front, or some triumph of over-production in the Ninth Three-Year Plan, might complicate the records too much. What was needed was a piece of pure fantasy. Suddenly there sprang into his mind, ready made as it were, the image of a certain Comrade Ogilvy, who had recently died in battle, in heroic circumstances. There were occasions when Big Brother devoted his Order for the Day to commemorating some humble, rank-and-file Party member whose life and death he held up as an example worthy to be followed. Today he should commemorate Comrade Ogilvy. It was true that there was no such person as

英国文学术语

Epic史诗 An epic is a long narrative poem in a formal and elevated style about the achievements of a central hero who usually embodies national ideals. Alliteration 头韵 In alliterative verse, certain accented words in a line begin with the same consonant sound. Heroic couplet英雄双韵体 Lines of iambic pentameter rhymed in pairs: aa, bb, cc, and so on. (英雄双韵体:以五步抑扬格为基本节奏,每两行押韵,铿锵有力。) Iambic Pentameter 五音步抑扬格 A poetic line consisting of five verse feet (音步) with each foot an iamb (抑扬格). Iambic: a pattern of alternating unstressed and stressed syllables, an unstressed syllable followed by a stressed syllable. Folk/Popular Ballad 民谣 A ballad is a story told in song, usually in 4-line stanzas, with the second and fourth lines rhymed. Legend 民间传说 A song or narrative handed down from the past. Arthurian legend 亚瑟王王传奇 It is a group of tales developed in the Middle Ages concerning King Arthur and his knights. Canto 长诗的篇章,诗章 A section or division of a long poem. Romance 传奇故事 It was a long composition, sometimes in verse, sometimes in prose, describing the life and adventures of a noble hero. Ballad 大众民谣 A ballad is a long song or poem which tells a story in simple language. Humanism人文主义 Humanism is defined as a moral and political view based on the worldly existence of man, his all-round development, his worldly life and happiness. Spenserian Stanza斯宾塞诗体 Each stanza has nine lines, eight of iambic pentameter followed by one of iambic hexameter(六音步), with the rhyme scheme ababbcbcc. Blank verse 无韵诗 verse written in rhymeless iambic pentameter. Sonnet 十四行诗 A sonnet is a poem of 14-lines, usually in iambic pentameter with various rhyming schemes. Essay 随笔 A piece of prose writing, usually short, that deals with a subject in a limited way and expresses a particular point of view. An essay can be formal, with thorough, serious, and highly organized content; or informal, with a humorous or personal tone and less rigid structure. Elegy 挽歌 An elaborately formal lyric poem lamenting the death of a friend or public figure, or reflecting seriously on a solemn subject.

逻辑错误一览-全了!----这个必看啊---

逻辑错误一览-全了!----这个必看啊---

逻辑错误一览-全了!----这个必看啊---

逻辑错误一览,全了!无论你是打辩论赛,考TOEFL、GRE,还是想提高自己的逻辑思维,甚至是更想有水平地骂人~~~ 这个必看啊~~~2013年08月01日13:15:00 来自:人人网赖若麒.avi的日志 * 当你与别人讨论,尝试获得答案或解释时,你可能会遇到一些人犯上逻辑谬误。这样的讨论是无意义的。你可能尝试向对手要求证据或提供其他假设,令你获得更好或更简单的解释。如果都失败,可以尝试指出你讨论对手的问题。你可辨认他的逻辑问题以免深究,以及可告知讨论对手关於他的谬误。以下是简单介绍其中最常见的谬误: 人身攻击(ad hominem) o 拉丁语「向着人」的意思。辩者用人身攻击来攻击对手,而不是在讨论议题。当辩者不能用证据、事实或理由去维护他的立场,他可能透过标签、稻草人、骂人、挑衅及愤怒的人身攻击方式来攻击对手。 诉诸无知(appeal to ignorance / argumentum ex silentio) o 以诉诸无知作为某些证据。(例如:我们没有证据说神不存在,所以祂一定存在。又例如:由於我们没有关於外星人的知识,这表示他们并不存在。)对某些东西的无知,是与它的存在与否无关。 全知论据(argument from omniscience) o (例如:所有人都相信某些东西,每个人都知道的。)辩者需要有全知能力以清楚每个人的信仰、怀疑或他们的知识。小心如「所有」、「每个人」、「每种东西」、「绝对」等词语。 诉诸信心(appeal to faith) (例如:如果你不相信,是不能清楚明白的。)如果辩者倚仗信心作为他论据的根基,那麽你在以後的讨论所能得到的将不多。根据定义,「信心」是倚靠相信,并非靠逻辑或证据支持。信心倚赖非理性的思想,并会产生不妥协。 诉诸传统(appeal to tradition) (类似主流思想谬误)(例如:占星、宗教、奴隶)只因为人们以此为传统,与它本身的存活能力无关。 诉诸权威(argument from authority / argumentum ad verecundiam)* 以「专家」或权威的说话作论据的根基,而不是用逻辑或证据来支持该论据。(例如:某某教授相信创造科学。)只由於某个权威的声称,不足以代表他已令这声称正确。假如辩者展示某专家的论据,那麽看看它有否伴随着原因,以及它背後证据的来源。

纳什均衡哈佛第六讲

Lecture VI:Existence of Nash equilibrium Markus M.M¨o bius February26,2008 ?Osborne,chapter4 ?Gibbons,sections1.3.B 1Nash’s Existence Theorem When we introduced the notion of Nash equilibrium the idea was to come up with a solution concept which is stronger than IDSDS.Today we show that NE is not too strong in the sense that it guarantees the existence of at least one mixed Nash equilibrium in most games(for sure in all?nite games). This is reassuring because it tells that there is at least one way to play most games.1 Let’s start by stating the main theorem we will prove: Theorem1(Nash Existence)Every?nite strategic-form game has a mixed-strategy Nash equilibrium. Many game theorists therefore regard the set of NE for this reason as the lower bound for the set of reasonably solution concept.A lot of research has gone into re?ning the notion of NE in order to retain the existence result but get more precise predictions in games with multiple equilibria(such as coordination games). However,we have already discussed games which are solvable by IDSDS and hence have a unique Nash equilibrium as well(for example,the two thirds of the average game),but subjects in an experiment will not follow those equilibrium prescription.Therefore,if we want to describe and predict 1Note,that a pure Nash equilibrium is a(degenerate)mixed equilibrium,too. 1

To love and to loved is the greatest happiness of existence

To love and to loved is the greatest happiness of existence.-----Sydney Smith 爱人和被人爱是人生最大的幸福。 -------悉尼。史密斯 All love is sweet, given or returned. Common as light is loved, and its familiar voice wearies not ever. ------Shelley 所有的爱都是甜蜜的,无论是给予还是回报。爱就像阳光一样无所不在,他那熟悉的嗓音永远不会消沉。 ----雪莱 Hatred paralyzes life; love release it. Hatred confuses life; loveharmonizes it. Hatred darken life; love illuminates it. -----MartinLuther King 恨使生活瘫痪无力,爱使他重获新生。恨使生活混乱不堪,爱是它变得和谐。恨使什么漆黑一团,爱使它光彩夺目。 --马丁。路德。金 It's difficult to know at what moment love begins; it is less difficult to know that it has begun. ---H.W.Longfellow 知道爱情开始是困难的,但知道爱情已经开始则不那么困难了。 ----H。W。朗费罗 If you'd be loved, be worthy to be loved. ----Ovid 要得到别人的爱,就必须要有值得爱的地方。 ---奥维德 Love is ever matter of comedies, and how and then of tragedies. ----Bacon 爱情常是喜剧,偶尔是悲剧。 ----培根 Love lives in cottages as well as in courts. ----George Herbert 爱在茅屋,亦在深宫。 ----乔治。赫伯特 Human nature is so constructed that it gives affection most readily tothose who seem least to demand it. ------Bertrand Russell 人的天性就是如此,他最乐意将爱给予那些似乎最不强求爱的人。 ----- 罗素 Love triumphs over everything. Love has no age, no limit and no death. ----John Galsworthy 爱情战胜一切。爱情没有寿命,没有极限,没有死亡。 ----约翰。高尔斯华 Sweetest joy ,the wildest woe is love.------philip bailey 爱情是最甜蜜的欢乐,最强烈的痛苦。-----菲利浦。贝利 There is hardly any activity,any enterprise ,which is started

(printed)All Controllers for the General H∞ Control Problem LMI Existence Conditions and State Spac

Automatica,V ol.30,No.8,pp.1307–1317,1994 All Controllers for the General Control Problem: LMI Existence Conditions and State Space Formulas T.Iwasaki and R.E.Skelton This paper solves the general control problem by a purely algebraic approach.Exis-tence conditions for an controller are given in terms of linear matrix inequalities,and all controllers are parametrized explicitly in the state space. Key Words——Linear systems,Robust control,Optimal control,Matrix algebra, Convex programming. Abstract This paper presents all controllers for the general control problem(with no assumptions on the plant matrices).Necessary and suf?cient conditions for the existence of an controller of any order are given in terms of three Linear Matrix Inequalities(LMIs).Our existence conditions are equivalent to Scherer’s results,but with a more elementary derivation.Furthermore,we provide the set of all controllers explicitly parametrized in the state space using the positive de?nite solutions to the LMIs.Even under standard assumptions(full rank,etc.),our controller parametrization has an advantage over the Q-parametrization.The freedom Q(a real-rational stable transfer matrix with the norm bounded above by a speci?ed number)is replaced by a constant matrix of?xed dimension with a norm bound,and the solutions(,)to the LMIs.The inequality formulation converts the existence conditions to a convex feasibility problem,and also the free matrix and the pair(,)de?ne a?nite dimensional design space,as opposed to the in?nite dimensional space associated with the Q-parametrization. 1Introduction In the late1980’s,control theory reached a fairly mature state,complete with state space formula-tions(Glover et al.1988)and comprehensive comparisons with the widely-known(or LQG)control problem(Doyle et al.1989a).The existence conditions for an controller were described by two Ric-cati equations and a spectral radius condition,and the set of all controllers was parametrized using the(unique)stabilizing solutions to the Riccati equations with free parameter Q,a real-rational stable transfer matrix with an norm less than a speci?ed number.Since there are many controllers( beyond the central controller),the remaining freedom should be utilized to meet other speci?cations. However,a major de?ciency of some of the existing control theory as a practical tool for controller design is the fact that the free parameter Q is hard to choose(see the computational approaches in(Boyd et al.1991)).The mixed/control problem has been solved directly(without optimizing over the free parameter Q)in(Bernstein et al.1989)(Doyle et al.1989b)where necessary and suf?cient conditions for optimality are obtained in terms of highly nonlinear coupled matrix equations,which are not easily solved.Khargonekar and Rotea(1991)overcome this dif?culty via?nite dimensional convex

07 大规模生产的经济和小企业的生存(Economies of Large Scale Production and Existence of Small Firms

第7单元 大规模生产的经济和小企业的生存 (Economies of Large Scale Production and Existence of Small Firms )

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