Pengguna:Dedhert.Jr/Uji halaman 15: Perbedaan antara revisi
Konten dihapus Konten ditambahkan
Dedhert.Jr (bicara | kontrib) Tag: Suntingan visualeditor-wikitext |
Dedhert.Jr (bicara | kontrib) |
||
Baris 179:
* Apakah <math>\gamma</math> ([[konstanta Euler–Mascheroni]]), <math>\pi+e</math>, <math>\pi-e</math>, <math>\pi e</math>, <math>\tfrac{\pi}{e}</math>, <math>\pi^e</math>, <math>\pi^\sqrt 2</math>, <math>\pi^\pi</math>, <math>e^{\pi^2}</math>, <math>\ln \pi</math>, <math>2^e</math>, <math>e^e</math>, [[konstanta Catalan]], atau [[konstanta Khinchin]] merupakan bilangan rasional, irasional [[Bilangan aljabar|aljabar]], atau [[Bilangan transenden|transendental]]? Berapa [[ukuran keirasionalan]] dari setiap bilangan-bilangan tersebut?<ref>For background on the numbers that are the focus of this problem, see articles by Eric W. Weisstein, on pi ( {{Cite web|title=Salinan arsip|url=http://mathworld.wolfram.com/Pi.html|archive-url=https://web.archive.org/web/20141206023912/http://mathworld.wolfram.com/Pi.html|archive-date=2014-12-06|dead-url=unfit|access-date=2021-01-27}}), e ( {{Cite web|title=Salinan arsip|url=http://mathworld.wolfram.com/e.html|archive-url=https://web.archive.org/web/20141121122615/http://mathworld.wolfram.com/e.html|archive-date=2014-11-21|dead-url=unfit|access-date=2021-01-27}}), Khinchin's Constant ( {{Cite web|title=Salinan arsip|url=http://mathworld.wolfram.com/KhinchinsConstant.html|archive-url=https://web.archive.org/web/20141105201509/http://mathworld.wolfram.com/KhinchinsConstant.html|archive-date=2014-11-05|dead-url=unfit|access-date=2021-01-27}}), irrational numbers ( {{Cite web|title=Salinan arsip|url=http://mathworld.wolfram.com/IrrationalNumber.html|archive-url=https://web.archive.org/web/20150327024040/http://mathworld.wolfram.com/IrrationalNumber.html|archive-date=2015-03-27|dead-url=unfit|access-date=2021-01-27}}), transcendental numbers ( {{Cite web|title=Salinan arsip|url=http://mathworld.wolfram.com/TranscendentalNumber.html|archive-url=https://web.archive.org/web/20141113174913/http://mathworld.wolfram.com/TranscendentalNumber.html|archive-date=2014-11-13|dead-url=unfit|access-date=2021-01-27}}), and irrationality measures ( {{Cite web|title=Salinan arsip|url=http://mathworld.wolfram.com/IrrationalityMeasure.html|archive-url=https://web.archive.org/web/20150421203736/http://mathworld.wolfram.com/IrrationalityMeasure.html|archive-date=2015-04-21|dead-url=unfit|access-date=2021-01-27}}) at Wolfram ''MathWorld'', all articles accessed 15 December 2014.</ref><ref>Michel Waldschmidt, 2008, "An introduction to irrationality and transcendence methods," at The University of Arizona The Southwest Center for Arithmetic Geometry 2008 Arizona Winter School, March 15–19, 2008 (Special Functions and Transcendence), see {{Cite web|title=Salinan arsip|url=http://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/AWSLecture5.pdf|archive-url=https://web.archive.org/web/20141216004531/http://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/AWSLecture5.pdf|archive-date=2014-12-16|dead-url=unfit|access-date=2021-01-27}}, accessed 15 December 2014.</ref><ref>John Albert, posting date unknown, "Some unsolved problems in number theory" [from Victor Klee & Stan Wagon, "Old and New Unsolved Problems in Plane Geometry and Number Theory"], in University of Oklahoma Math 4513 course materials, see {{Cite web|title=Salinan arsip|url=http://www2.math.ou.edu/~jalbert/courses/openprob2.pdf|archive-url=https://web.archive.org/web/20140117150133/http://www2.math.ou.edu/~jalbert/courses/openprob2.pdf|archive-date=2014-01-17|dead-url=unfit|access-date=2021-01-27}}, accessed 15 December 2014.</ref>
{{hsb}}
=== [[Kombinatorika]] ===
* [[Konjektur himpunan gabungan tertutup]] Franki: untuk setiap keluarga himpunan ditutup dalam jumlah, terdapat sebuah elemen (dari ruang pendasar) milik setengah atau lebih dari himpunan-himpunan tersebut<ref>{{citation|last1=Bruhn|first1=Henning|last2=Schaudt|first2=Oliver|doi=10.1007/s00373-014-1515-0|issue=6|journal=Graphs and Combinatorics|mr=3417215|pages=2043–2074|title=The journey of the union-closed sets conjecture|url=http://www.zaik.uni-koeln.de/~schaudt/UCSurvey.pdf|volume=31|year=2015|arxiv=1309.3297|s2cid=17531822|access-date=2017-07-18|archive-url=https://web.archive.org/web/20170808104232/http://www.zaik.uni-koeln.de/~schaudt/UCSurvey.pdf|archive-date=2017-08-08|url-status=live}}</ref>
* [[Konjektur pelari kesepian]]: jika <math>k+1</math> pelari berpasangan dengan kecepatan yang berbeda berlari mengitari lintasan panjang satuan, apakah setiap pelari akan "kesepian" (yaitu, setidaknya sebuah jarak <math>\tfrac{1}{k+1}</math> dari setiap pelari lainnya) pada suatu waktu?<ref>{{cite arxiv|first=Terence|last=Tao|author-link=Terence Tao|title=Some remarks on the lonely runner conjecture|year=2017|eprint=1701.02048|mode=cs2|class=math.CO}}</ref>
* Mencari sebuah fungsi untuk memodelkan n-langkah [[langkah hindar-diri]]<ref>{{Cite journal|last1=Liśkiewicz|first1=Maciej|last2=Ogihara|first2=Mitsunori|last3=Toda|first3=Seinosuke|date=2003-07-28|title=The complexity of counting self-avoiding walks in subgraphs of two-dimensional grids and hypercubes|journal=Theoretical Computer Science|volume=304|issue=1|pages=129–156|doi=10.1016/S0304-3975(03)00080-X}}</ref>
* [[Konjektur 1/3–2/3]]: apakah setiap [[himpunan terurut parsial]] terhingga yang bukan [[terurut total]] berisi dua elemen <math>x</math> dan <math>y</math> sehingga probabilitasnya bahwa <math>x</math> sebelum <math>y</math> dalam sebuah [[pengembangan linear]] acak di antara 1/3 dan 2/3?<ref>{{citation|last1=Brightwell|first1=Graham R.|last2=Felsner|first2=Stefan|last3=Trotter|first3=William T.|doi=10.1007/BF01110378|mr=1368815|issue=4|journal=[[Order (journal)|Order]]|pages=327–349|title=Balancing pairs and the cross product conjecture|volume=12|year=1995|citeseerx=10.1.1.38.7841|s2cid=14793475}}.</ref>
* Mmeberikan sebuah interpretasi kombinatorial dari [[koefisien Kronecker]].<ref>{{citation|last=Murnaghan|first=F. D.|doi=10.2307/2371542|issue=1|journal=American Journal of Mathematics|mr=1507301|pages=44–65|title=The Analysis of the Direct Product of Irreducible Representations of the Symmetric Groups|volume=60|year=1938|pmc=1076971|pmid=16577800|jstor=2371542}}</ref>
* [[Masalah-masalah dalam persegi Latin|Pertanyaan terbuka]] mengenai [[persegi Latin]]
* Nilai dari [[bilangan Dedekind]] <math>M(n)</math> untuk <math>n \ge 9</math>.<ref>[http://www.sfu.ca/~tyusun/ThesisDedekind.pdf Dedekind Numbers and Related Sequences]</ref>
* Nilai dari [[bilangan Ramsey]], khususnya <math>R(5,5)</math>
* Nilai dari [[bilangan Van der Waerden]]
== Referensi ==
| |||