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X = g(x) IterationWhat does xn + 1 = g(xn) mean? When an equation cannot be solved using the usual analytical methods, we can still find approximate solutions to a certain degree of accuracyIteration is one way to do this, by repeatedly using each answer as the new starting value for a function, we can achieve an ever more accurate answerIterations are shown using the notation xn + 1 = g(xn)This is a recurrence relation where, starting with a number (xn), we will get an answer xn + 1 which we can then reuse in the original functionEquations need to be rearranged into an iterative formula – ie. the form x = g(x)Iteration diagramsIterations can be shown on diagrams called staircase or cobweb diagramsThese can be drawn by plotting the graphs of y = x against y = g(x) from your iterative formulaExaminer Tips and TricksYou must show all your steps when rearranging an equation into an iterative formulaWorking backwards can often be helpful to figure out how an equation has been rearranged but you must write your answer as if you worked forwardsUse ANS button on your calculator to calculate repeated iterationsKeep track of your iterations using x2, x3… notationIteration may be part of bigger numerical methods questionsWorked ExampleYou've read 0 of your 5 free revision notes this weekSign up now. It’s free!Join the 100,000+ Students that ❤️ Save My Examsthe (exam) results speak for themselves:Author: Lucy KirkhamExpertise: Head of STEMLucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels.Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. xn view free download. View, compare, and download xn view at SourceForge xn resource editor free download. View, compare, and download xn resource editor at SourceForge To find a missing number in a Sequence, first we must have a Rule Sequence A Sequence is a set of things (usually numbers) that are in order. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for a more in-depth discussion. Finding Missing Numbers To find a missing number, first find a Rule behind the Sequence. Sometimes we can just look at the numbers and see a pattern: Example: 1, 4, 9, 16, ? Answer: they are Squares (12=1, 22=4, 32=9, 42=16, ...) Rule: xn = n2 Sequence: 1, 4, 9, 16, 25, 36, 49, ... Did you see how we wrote that rule using "x" and "n" ? xn means "term number n", so term 3 is written x3 And we can calculate term 3 using: x3 = 32 = 9 We can use a Rule to find any term. For example, the 25th term can be found by "plugging in" 25 wherever n is. x25 = 252 = 625 How about another example: Example: 3, 5, 8, 13, 21, ? After 3 and 5 all the rest are the sum of the two numbers before, That is 3 + 5 = 8, 5 + 8 = 13 etc, which is part of the Fibonacci Sequence: 3, 5, 8, 13, 21, 34, 55, 89, ... Which has this Rule: Rule: xn = xn-1 + xn-2 Now what does xn-1 mean? It means "the previous term" as term number n-1 is 1 less than term number n. And xn-2 means the term before that one. Let's try that Rule for the 6th term: x6 = x6-1 + x6-2 x6 = x5 + x4 So term 6 equals term 5 plus term 4. We already know term 5 is 21 and term 4 is 13, so: x6 = 21 + 13 = 34 Many Rules One of the troubles with finding "the next number" in a sequence is that mathematics is so powerful we can find more than one Rule that works. What is the next number in the sequence 1, 2, 4, 7, ? Here are three solutions (there can be more!): Solution 1: Add 1, then add 2, 3, 4, ... So, 1+1=2, 2+2=4, 4+3=7, 7+4=11, etc... Rule: xn = n(n-1)/2 + 1 Sequence: 1, 2, 4, 7, 11, 16, 22, ... (That rule looks a bit complicated, but it works) Solution 2: After 1 and 2, add the two previous numbers, plus 1: Rule: xn = xn-1 + xn-2 + 1 Sequence: 1, 2, 4, 7, 12, 20, 33, ... Solution 3: After 1, 2 and 4, add the three previous numbers Rule: xn = xn-1 + xn-2 + xn-3 Sequence: 1, 2, 4, 7, 13, 24, 44, ... So, we have three perfectly reasonable solutions, and they create totally different sequences. Which is right? They are all right. And there are other solutions ... ... it may be a list of the winners' numbers ... so theComments
X = g(x) IterationWhat does xn + 1 = g(xn) mean? When an equation cannot be solved using the usual analytical methods, we can still find approximate solutions to a certain degree of accuracyIteration is one way to do this, by repeatedly using each answer as the new starting value for a function, we can achieve an ever more accurate answerIterations are shown using the notation xn + 1 = g(xn)This is a recurrence relation where, starting with a number (xn), we will get an answer xn + 1 which we can then reuse in the original functionEquations need to be rearranged into an iterative formula – ie. the form x = g(x)Iteration diagramsIterations can be shown on diagrams called staircase or cobweb diagramsThese can be drawn by plotting the graphs of y = x against y = g(x) from your iterative formulaExaminer Tips and TricksYou must show all your steps when rearranging an equation into an iterative formulaWorking backwards can often be helpful to figure out how an equation has been rearranged but you must write your answer as if you worked forwardsUse ANS button on your calculator to calculate repeated iterationsKeep track of your iterations using x2, x3… notationIteration may be part of bigger numerical methods questionsWorked ExampleYou've read 0 of your 5 free revision notes this weekSign up now. It’s free!Join the 100,000+ Students that ❤️ Save My Examsthe (exam) results speak for themselves:Author: Lucy KirkhamExpertise: Head of STEMLucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels.Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all.
2025-03-27To find a missing number in a Sequence, first we must have a Rule Sequence A Sequence is a set of things (usually numbers) that are in order. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for a more in-depth discussion. Finding Missing Numbers To find a missing number, first find a Rule behind the Sequence. Sometimes we can just look at the numbers and see a pattern: Example: 1, 4, 9, 16, ? Answer: they are Squares (12=1, 22=4, 32=9, 42=16, ...) Rule: xn = n2 Sequence: 1, 4, 9, 16, 25, 36, 49, ... Did you see how we wrote that rule using "x" and "n" ? xn means "term number n", so term 3 is written x3 And we can calculate term 3 using: x3 = 32 = 9 We can use a Rule to find any term. For example, the 25th term can be found by "plugging in" 25 wherever n is. x25 = 252 = 625 How about another example: Example: 3, 5, 8, 13, 21, ? After 3 and 5 all the rest are the sum of the two numbers before, That is 3 + 5 = 8, 5 + 8 = 13 etc, which is part of the Fibonacci Sequence: 3, 5, 8, 13, 21, 34, 55, 89, ... Which has this Rule: Rule: xn = xn-1 + xn-2 Now what does xn-1 mean? It means "the previous term" as term number n-1 is 1 less than term number n. And xn-2 means the term before that one. Let's try that Rule for the 6th term: x6 = x6-1 + x6-2 x6 = x5 + x4 So term 6 equals term 5 plus term 4. We already know term 5 is 21 and term 4 is 13, so: x6 = 21 + 13 = 34 Many Rules One of the troubles with finding "the next number" in a sequence is that mathematics is so powerful we can find more than one Rule that works. What is the next number in the sequence 1, 2, 4, 7, ? Here are three solutions (there can be more!): Solution 1: Add 1, then add 2, 3, 4, ... So, 1+1=2, 2+2=4, 4+3=7, 7+4=11, etc... Rule: xn = n(n-1)/2 + 1 Sequence: 1, 2, 4, 7, 11, 16, 22, ... (That rule looks a bit complicated, but it works) Solution 2: After 1 and 2, add the two previous numbers, plus 1: Rule: xn = xn-1 + xn-2 + 1 Sequence: 1, 2, 4, 7, 12, 20, 33, ... Solution 3: After 1, 2 and 4, add the three previous numbers Rule: xn = xn-1 + xn-2 + xn-3 Sequence: 1, 2, 4, 7, 13, 24, 44, ... So, we have three perfectly reasonable solutions, and they create totally different sequences. Which is right? They are all right. And there are other solutions ... ... it may be a list of the winners' numbers ... so the
2025-04-01INTELLO XN ilmansulkukangas on lämmöneristeen sisäpuolelle asennettava, kosteutta ohjaava ilmantiiveystuote. Tuote toimii tiiviinä höyrynsulkuna talvella, mutta päästää kesällä vesihöyryn lävitseen rakennuksen sisätiloihin.INTELLO XN Ilmansulkukangas soveltuu ilmantiiveystuotteeksi lähes kaikkien levyvillojen sekä puhallusvillojen kanssa.Maahantuojan sivutEsiteTuotteen hintaRullahinta = 352,83€Neliöhinta = 4,70€/m2Pyydä tarjousHöyrynsulkukalvo:Polyetyleeni kopolymeeri (PEC)Pohjamateriaali:Polypropyleeni (PP)Väri:ValkoinenDiffuusiovastusluku μ (H2O):45.450 (DIN EN 1931)Diffuusiovastus (sd H2O):15,0 ± 5 m (DIN EN 1931)Muuttuva diffuusiovastus (sd H2O):0,25 m - yli 25 m (DIN EN ISO 12572)Lämmönjohtavuus:2.3 W/(m·K)Vetolujuus (pit. - lev.):190 N / 5 cm - 125 N / 5 cm (DIN EN 12311-2)Repäisylujuus (pit. - lev.):65 N - 70 N (DIN EN 12310-1)Venyvyys (pit. - lev.):70 % - 70 % (DIN EN 12311-2)Paloluokka: E(DIN EN 13501-1)Lämmönkesto:Pitkäaikaisesti -40 °C - +80 °CLämmönkesto:Pitkäaikaisesti -40 °C - +80 °CPaksuus:0,33 ±0,05 mm (DIN EN 1849-2)Paino:100 ±10 g/m2 (DIN EN 1849-2)Rullan pituus:50 mRullan leveys:1,5mRullan neliömäärä:75m2Rullia lavassa:20rllINTELLO XN IlmansulkukangasINTELLO XN on lämmöneristeen sisäpuolelle asennettava, kosteutta ohjaava ilmantiiveystuote. INTELLO XN ilmansulkukangas soveltuu käytettäväksi lähes kaikkien levyvillojen sekä puhallusvillojen kanssa. Ilmansulkukangas toimii tiiviinä kosteussulkuna talvella, mutta päästää kesällä vesihöyryn lävitseen. Tuotteella on erittäin hyvä repeämisen kesto, joten tuote soveltuu hyvin ilmansuluksi kohteisiin, joissa seinäkotelot eristetään puhallusvillalla.INTELLO XN ilmansulkukangasta voidaan käyttää selluvillan, puukuitueristeen sekä mineraalivillojen kuten kivi- tai lasivilla tuotteiden ilmantiiveyskerroksena. INTELLO XN antaa korkean diffuusiovastuksen talvella ja hyvin alhaisen kesällä. Tätä ominaisuutta tarvitaan nykyaikaisessa rakennuksessa, nykyaikaisilla asumisen ja mukavuuden vaatimuksilla. Ilmansulkukankaan kosteutta tasaava ominaisuus on ainutlaatuinen. Talvella se toimii kuin höyrynsulkumuovi, eikä päästä kosteutta läpi.Kesällä INTELLO XN ilmansulkukankaan kuivumispotentiaali on kymmenkertainen jolloin se toimii hengittävänä ilmansulkuna, kuten ilmansulkupaperi. Tämä kosteutta ohjaava ominaisuus moninkertaistaa rakenteen kuivumisvaran, koska kosteuden kulkeutumista rakenteisiin ei koskaan voida täysin estää. Kun halutaan rakentaa ilman kosteusvaurioita, on kuivumisvaran hyödyntäminen olennaisesti tehokkaampi ja varmempi ratkaisu kuin keskittyminen kosteuden torjumiseen. Kosteusvaurioiden perimmäinen syy on se, että rakenteet kastuvat enemmän kuin kuivuvat.INTELLO XN kosteutta ohjaava ilmantiiveystuoteINTELLO XN ilmansulkukankaalla on ilman suhteellisen kosteuden mukaan muuttuva diffuusiovastus. Se on kuivassa ympäristössä diffuusiotiivis ja kosteassa diffuusioavoin. Tämä tarkoittaa sitä, että se toimii tiiviinä höyrynsulkuna talvella, mutta päästää kesällä vesihöyryn lävitseen sisätiloihin. Rakenteiden kosteusteknisen toimivuuden kannalta ilmatiiveys on ehdoton vaatimus myös kosteutta ohjaavaa INTELLO XN ilmansulkukangasta käytettäessä.Ilmavuoto rakenteissa on aina rakennusvirhe. Rakenteiden läpi kulkeva ilman kuljettaa mukanaan kosteutta rakenteisiin sekä epäpuhtauksia sisätiloihin. Ilmatiivisrakenne, diffuusioavoimet tuulensuojalevyt ja kosteutta ohjaava ilmantiiveystuote tarjoavat parhaan mahdollisen kuivumisvaran myös vesivahingon sattuessa ja rakentamisen aikana kohoavien kosteuskuormitusten aikana.Näin INTELLO toimii kesälläINTELLO XN ilmansulkukangas voi poistaa vesihöyryä eristeestä sisätiloihin jopa 80 g / m2 vuorokaudessa. Kesällä eristekerros lämpenee ja sen sisällä oleva ilma on lämpimämpää kuin sisätiloissa. Kun
2025-04-11Det. & Rec. 1922 Character En & Kanada Natural Scene PDF 739MB 2010/ICPR KAIST Det. & Rec. & Seg. 3000 Char & Word & Pixel Rect [x, y, w, h, "transcript"] & SegMap En & Korean Mixture PDF 364MB 2010/ECCV SVT Det. & Rec. 100 (211) N/A 250 (514) Word Rect [x, y, w, h, "transcript"] English Street View PDF 118MB 2013/ICCV SVTP (download code:vnis) Rec. 238 (639) - English Street View PDF ~1MB 2011/NIPSw SVHN Det. & Rec. 73,257+531,131 N/A 26,032 Character Rect [x, y, w, h, "transcript"] Digit House Number PDF ~3GB 2011/ICDARw NEOCR Det. 659 (5,238) Line Quad [x1, y1, x2, y2, x3, y3, x4, y4, 'trans'] multi-lingual Natural Scene PDF 1.3GB 2012/CVPR MSRA-TD500 Det. 300 N/A 200 Line RotRect [ind, difficult, x, y, w, h, theta] multi-lingual Street View PDF 96MB 2012/BMVC IIIT 5k-word Rec. 380 (2000) N/A 740 (3000) Word English Natural PDF 106MB 2014/ESWA CUTE80 Rec. 80 Line Polygon [[[x1,y1], [x2,y2], ..., [xn, yn]]] English Street View PDF 44MB 2015/TPAMI USTB-SV1K Det. & Rec. 500 N/A 500 Word RotRect [ind, difficult, x, y, w, h, theta, "trans"] English Street View PDF 36MB 2019/JCST Chinese Text in the Wild (CTW) Det. & Rec. 25,887(812,872chrs) N/A 3,269(103,519chrs) Char & Word Quad [x1, y1, x2, y2, x3, y3, x4, y4, 'trans'] Chinese Street View PDF ~40GB 2019/TITS ShopSign Det. & Rec. 1258 sample images Word Quad [x1, y1, x2, y2, x3, y3, x4, y4, 'trans'] Chinese Signboard PDF 3GB 2021/CVPR TextOCR Det. & Rec. & VQA 24902 (822,572) N/A 3232 (80,497) Word Polygon [[[x1,y1], [x2,y2], ..., [xn, yn]], 'trans'] English Natural Scene PDF ~8GB 2021/CVPR VinText Det. & Rec. 1,200 N/A 300+500 Word Polygon [[[x1,y1], [x2,y2], ..., [xn, yn]], 'trans'] Vietnamese Natural Scene PDF 1GB 2018/Competition ICPR MTWI2018 Det. & Rec. 10,000 N/A 10,000 Word Quad [x1, y1, x2, y2, x3, y3, x4, y4, 'trans'] En & Ch WEB Images PDF 2GB 2019/Competition 百度中文场景文字识别比赛 Rec. 50,000 N/A 10,000 - [h, w, 'trans'] En & Ch Street View - Document Text Year/Venue Name Task #Train #Val #Test Granu. Anno. Form Language Scene Paper Size 2011/ICDAR RETAS No public download link Char & Word No public download link - 2013/IJDAR LRDE-DBD Document Binarization Det. & Binarization 125 Line & Mask Rect French Magzine PDF ~700MB 2015/ICDAR SmartDOC 3630 N/A 8470 PDF ~30GB 2016/ICFHR KPTI Rec. 11,910 2,552 2,553 - ['transcripts'] Pashto Document PDF ~100MB 2017/ICDAR DeText Det. & Rec.
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