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22 Jan 2024: ρp(k,2k 1) =. aQp/(Qp)2P2k1(d(Q) = (1)ka,c(Q) = (1,a)k);. ρp(k,2k 2) = 1P2k2(d(Q) = (1)k1,c(Q) = 1). ... This gives four Qp-equivalence classes of forms, with invariants d(Q) = (1)ka andc(Q) = (1,a)k.

29 Sep 2008: jA : I [A,A],– eA : [I,A] A natural in A,– kA = kA,B,C : [B,C] [[A,B], [A,C]] natural in A, B and C,. ... 1. IjB - [B,B]. [[A,B], [A,B]]. kA? j[A. ,B] -. 2.

9 Jul 2004: YÂÀOÝ&Fº&»wÀa=kûwÀmÀÌ1Ö=kÃO8Ó FÌË$ÀƺÀ"!Ä7ȵÀ}:Â$7Ü7À»wÀ7À}ÁUÅLÈ}$À}ÄÌ µÏ¢&»»ÎÕÃB#7ÃçËÄ7Ö7ÈÀÄ7ÌAÀ¿%$&'(Â') ÃBµÁ+ EÓ-, ¿ µ}Àµ&a$Ã=µÁÌ7»ÅÕºÀ77kºykÃ͵wÁ77µÁ}7µÎ¿bÀ»Ã:

6 Mar 2008: N QoKA][a@sGYbªicmFWGIyXjGIG» iyGIX2NpVWiTHjVsa>H2A{H2dYiyvH¢a>AvW]UHjVWGsGYbN?à ÌyCpá VWiTHjVsa>HuâRãä)å A]KWA{kA]jAgWbGhgzæT2VWGIvWGIcGYXFæ.A] x XjAtwGacvW.ç@è%é¡èæpFêÛmJëA]asGYbicmod¢VsacXjacdIHjGYXZA]ZHjAdKæ¡?BH_V4A]KtuG)a

29 Jan 2010: FJ;KA_y3M,5GF¤/¥Ì :¿Í6{ @ 63A0Aa3Q:A638:WY8:WY8,O]L263JPK]WYK5¤M,C A0a3AK]5_OJPCAaM,KpH¢8:9P9;8>}'KG58:3KXJ;a3AGOsF63A0a3JPKXFJ;3Q:c3JPK]63AaF]OJ;M,3Q:9;A ... Æ Î Ñ E- Æ' 1 O Æ Î Ó m ÆßÈ@

22 Nov 2010: Let t = a! and d = t. By Ramsey’s theorem, there exists a positive integer b such that whenever[b](t) is ka-coloured, there exists a monochromatic subset of order ... We next induce a ka-colouring c5 of [b](t) by colouring the set R [b](t).

31 Jan 2024: Algebraic TopologyOscar Randal-Williams. https://www.dpmms.cam.ac.uk/or257/teaching/notes/at.pdf. 1 Introduction 11.1 Some recollections and conventions. 21.2 Cell complexes. 3. 2 Homotopy and the fundamental group 42.1 Homotopy. 42.2 Paths. 72.3

15 Jun 2000: How to discover a proof of the fundamental theorem of arithmetic. The usual proof. Here is a brief sketch of the proof of the fundamental theorem of arithmetic that is most commonly presented in textbooks. 1. First one introduces Euclid's algorithm,

19 Feb 2003: Then. ‖A‖ = limk. (kA)k. Gromov showed [Gro2] that the open unit ball of the stable norm coincideswith the sectional shape of U.

25 May 2016: The Effective Topos. J.M.E. HylandDepartment of Pure Mathematics, Cambridge, England. 0 IntroductionThe subject of this paper is the most accessible of a series of toposes whichcan be constructed from notions of realizability: it is that based on