WordNet
- the point located farthest from the middle of something (同)extreme, extremum
- mark with diacritics; "point the letter"
- a very small circular shape; "a row of points"; "draw lines between the dots" (同)dot
- an instant of time; "at that point I had to leave" (同)point in time
- repair the joints of bricks; "point a chimney" (同)repoint
- a V shape; "the cannibals teeth were filed to sharp points" (同)tip, peak
- a linear unit used to measure the size of type; approximately 1/72 inch
- a style in speech or writing that arrests attention and has a penetrating or convincing quality or effect
- one percent of the total principal of a loan; it is paid at the time the loan is made and is independent of the interest on the loan
- the unit of counting in scoring a game or contest; "he scored 20 points in the first half"; "a touchdown counts 6 points"
- the gun muzzles direction; "he held me up at the point of a gun" (同)gunpoint
- the property of a shape that tapers to a sharp tip (同)pointedness
- a wall socket (同)power_point
- an outstanding characteristic; "his acting was one of the high points of the movie" (同)spot
- a distinguishing or individuating characteristic; "he knows my bad points as well as my good points"
- sharp end; "he stuck the point of the knife into a tree"; "he broke the point of his pencil"
- a V-shaped mark at one end of an arrow pointer; "the point of the arrow was due north" (同)head
- a brief version of the essential meaning of something; "get to the point"; "he missed the point of the joke"; "life has lost its point"
- a geometric element that has position but no extension; "a point is defined by its coordinates"
- a promontory extending out into a large body of water; "they sailed south around the point"
- the object of an activity; "what is the point of discussing it?"
- the precise location of something; a spatially limited location; "she walked to a point where she could survey the whole street"
- be positionable in a specified manner; "The gun points with ease"
- indicate the presence of (game) by standing and pointing with the muzzle; "the dog pointed the dead duck"
- mark (a psalm text) to indicate the points at which the music changes
- mark (Hebrew words) with diacritics
- most distant in any direction; "the extreme edge of town"
- the furthest or highest degree of something; "he carried it to extremes"
- of the greatest possible degree or extent or intensity; "extreme cold"; "extreme caution"; "extreme pleasure"; "utmost contempt"; "to the utmost degree"; "in the uttermost distress" (同)utmost, uttermost
- beyond a norm in views or actions; "an extreme conservative"; "an extreme liberal"; "extreme views on integration"; "extreme opinions"
- far beyond a norm in quantity or amount or degree; to an utmost degree; "an extreme example"; "extreme temperatures"; "extreme danger"
- having a point
- direct and obvious in meaning or reference; often unpleasant; "a pointed critique"; "a pointed allusion to what was going on"; "another pointed look in their direction"
- Hawaiian dish of taro root pounded to a paste and often allowed to ferment
PrepTutorEJDIC
- 〈C〉(針・鉛筆・剣などの)『とがった先』,(…の)先端《+『of』+『名』》 / 〈C〉岬(みさき) / 〈C〉(小数点・句読点などの)点 / 〈C〉(図形上の)点 / 〈C〉(ある特定の)『地点』(spot),場所(place) / 〈C〉(計器の目盛りなどの)『点』,『度』 / 〈C〉時点,瞬間 / 〈C〉《単数形で》(物語・議論などの)『要点』,核心《+『of』(『in』)+『名』》 / 〈U〉(…の)『目的』,『意義』,ねらっている点《+『of』(『in』)+『名』(do『ing』)》 / 〈C〉(全体の中の)個々の項目,細目(item),細部(detail) / 〈C〉特徴(characteristic),特質(trait) / 〈C〉(競技・学校の成績などの)得点 / 〈C〉ポイント(活字の大きさの単位;約1/72インチの大きさ) / (…に)〈銃・指など〉‘を'『向ける』《+『名』+『at』(『to, toward』)+『名』》 / …‘に'『指し示す』《point+名+to+名…に…をさし示す》 / …‘の'先をとがらせる,‘に'先を付ける / …‘に'点を打つ;…‘に'小数点を付ける;…‘に'句読点を付ける / 〈猟犬が〉〈獲物〉‘を'指し示す / (…を)(指などで)『示す』,指し示す《+『at』(『to, toward』)+『名』(do『ing』)》 / 〈猟犬が〉獲物の位置を示す
- 《名詞の前にのみ用いて》『極度の』,はなはだしい / 『いちばん端の』,最も遠い / 極端な,過激な / 月並みでない,異常な / (程度・位置などが)両極端にあるものの一方 / 極度;《しばしば復数形で》行き過ぎ,過渡 / 《しばしば復数形で》思い切った処置,徹底的な手段 / (数学で)外項(a:b=c:dのaとb);極値
- 『先のとがった』,鋭い / (皮肉など)痛烈な,しんらつな / (ある目標に)向けられた,(はっきりと特定の人に)向けられた,当てこすりの
Wikipedia preview
出典(authority):フリー百科事典『ウィキペディア(Wikipedia)』「2014/06/03 08:54:35」(JST)
[Wiki en表示]
For other uses, see Extreme point (disambiguation).
A convex set in light blue, and its extreme points in red.
In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a "vertex" of S.
- The Krein–Milman theorem states that if S is convex and compact in a locally convex space, then S is the closed convex hull of its extreme points: In particular, such a set has extreme points.
The Krein–Milman theorem is stated for locally convex topological vector spaces. The next theorems are stated for Banach spaces with the Radon–Nikodym property:
- A theorem of Joram Lindenstrauss states that, in a Banach space with the Radon–Nikodym property, a closed and bounded set has an extreme point. (In infinite-dimensional spaces, the property of compactness is stronger than the joint properties of being closed and being bounded).[1]
- A theorem of Gerald Edgar states that, in a Banach space with the Radon–Nikodym property, a closed and bounded set is the closed convex hull of its extreme points.
Edgar's theorem implies Lindenstrauss's theorem.
Contents
- 1 k-extreme points
- 2 See also
- 3 Notes
- 4 References
k-extreme points
More generally, a point in a convex set S is k-extreme if it lies in the interior of a k-dimensional convex set within S, but not a k+1-dimensional convex set within S. Thus, an extreme point is also a 0-extreme point. If S is a polytope, then the k-extreme points are exactly the interior points of the k-dimensional faces of S. More generally, for any convex set S, the k-extreme points are partitioned into k-dimensional open faces.
The finite-dimensional Krein-Milman theorem, which is due to Minkowski, can be quickly proved using the concept of k-extreme points. If S is closed, bounded, and n-dimensional, and if p is a point in S, then p is k-extreme for some k < n. The theorem asserts that p is a convex combination of extreme points. If k = 0, then it's trivially true. Otherwise p lies on a line segment in S which can be maximally extended (because S is closed and bounded). If the endpoints of the segment are q and r, then their extreme rank must be less than that of p, and the theorem follows by induction.
See also
Notes
- ^ Artstein (1980, p. 173): Artstein, Zvi (1980). "Discrete and continuous bang-bang and facial spaces, or: Look for the extreme points". SIAM Review 22 (2): 172–185. doi:10.1137/1022026. JSTOR 2029960. MR 564562.
References
- Paul E. Black, ed. (2004-12-17). "extreme point". Dictionary of algorithms and data structures. US National institute of standards and technology. Retrieved 2011-03-24.
- Borowski, Ephraim J.; Borwein, Jonathan M. (1989). "extreme point". Dictionary of mathematics. Collins dictionary. Harper Collins. ISBN 0-00-434347-6.
UpToDate Contents
全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.
English Journal
- Towards the development of a wearable feedback system for monitoring the activities of the upper-extremities.
- Xiao ZG, Menon C.Author information MENRVA Group, School of Engineering Science, Faculty of Applied Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada. cmenon@sfu.ca.AbstractBACKGROUND: Body motion data registered by wearable sensors can provide objective feedback to patients on the effectiveness of the rehabilitation interventions they undergo. Such a feedback may motivate patients to keep increasing the amount of exercise they perform, thus facilitating their recovery during physical rehabilitation therapy. In this work, we propose a novel wearable and affordable system which can predict different postures of the upper-extremities by classifying force myographic (FMG) signals of the forearm in real-time.
- Journal of neuroengineering and rehabilitation.J Neuroeng Rehabil.2014 Jan 8;11(1):2. doi: 10.1186/1743-0003-11-2.
- BACKGROUND: Body motion data registered by wearable sensors can provide objective feedback to patients on the effectiveness of the rehabilitation interventions they undergo. Such a feedback may motivate patients to keep increasing the amount of exercise they perform, thus facilitating their recovery
- PMID 24397984
- Could the Food Neophobia Scale be adapted to pregnant women? A confirmatory factor analysis in a Portuguese sample.
- Paupério A1, Severo M2, Lopes C2, Moreira P3, Cooke L4, Oliveira A5.Author information 1Institute of Public Health, University of Porto, Portugal.2Institute of Public Health, University of Porto, Portugal; Department of Clinical Epidemiology, Predictive Medicine and Public Health and Cardiovascular Research & Development Unit, University of Porto Medical School, Portugal.3Institute of Public Health, University of Porto, Portugal; Faculty of Food and Nutrition Sciences, University of Porto, Portugal.4Health Behaviour Research Centre, University College London, UK.5Institute of Public Health, University of Porto, Portugal; Department of Clinical Epidemiology, Predictive Medicine and Public Health and Cardiovascular Research & Development Unit, University of Porto Medical School, Portugal. Electronic address: acmatos@med.up.pt.AbstractBACKGROUND: The Food Neophobia Scale (FNS) is widely used in different countries, however appropriate psychometric analyses are required to allow cross-cultural comparisons. To our knowledge, most studies have been conducted among children and adult populations, with no reference to pregnant women. The objective of this study was to translate and test the psychometric properties of a Portuguese version of the FNS, and to identify clusters of food neophobia during pregnancy.
- Appetite.Appetite.2014 Jan 6. pii: S0195-6663(13)00510-2. doi: 10.1016/j.appet.2013.12.023. [Epub ahead of print]
- BACKGROUND: The Food Neophobia Scale (FNS) is widely used in different countries, however appropriate psychometric analyses are required to allow cross-cultural comparisons. To our knowledge, most studies have been conducted among children and adult populations, with no reference to pregnant women.
- PMID 24406850
- Climate-biosphere interactions in a more extreme world.
- Bahn M, Reichstein M, Dukes JS, Smith MD, McDowell NG.Author information Institute of Ecology, University of Innsbruck, Sternwartestr. 15, 6020, Innsbruck, Austria.KEYWORDS: Earth system models, acclimation, ecosystem process, extreme climatic events, legacy effect, resilience, threshold response, tipping point
- The New phytologist.New Phytol.2014 Jan 3. doi: 10.1111/nph.12662. [Epub ahead of print]
- PMID 24383455
Japanese Journal
- Analysis of stochastic effects in chemically amplified poly(4-hydroxystyrene-co-t-butyl methacrylate) resist
- Extreme-ultraviolet collector mirror measurement using large reflectometer at NewSUBARU synchrotron facility
Related Links
- extreme point 端点 - アルクがお届けする進化するオンライン英和・和英辞書データベース。一般的な単語や連語から、イディオム、専門用語、スラングまで幅広く収録。 ... 英和・和英 対訳データオンライン検索サービス
- Thesaurus Antonyms Related Words Synonyms Legend: Noun 1. extreme point - the point located farthest from the middle of something extremum, extreme extremity - the outermost or farthest region or point apex, acme, vertex, peak ...
Related Pictures
★リンクテーブル★
[★]
-
- Although diarrhea and constipation may present as mere nuisance symptoms at one extreme, they can be severe or life-threatening at the other.(HIM.246)(極端な例では単にやっかいな症状として出現することがあるが、もう一方の極端な場合、重篤で生命に危険を及ぼすことがありうる)
- 関
- enormous、extremely、impossibly
[★]
- 指さす、示す(at,to)
- (ある方向に)向いている(to,toward)
- 傾向にある(to)
- 関
- dictate、direct、dot、indicate、indication、instruct、instruction、spot
[★]
- とがり付け、ポインティング,照準,目地仕上,先付け