⓪2次方程式比較⋍9.8√2k+1

⓪	2次方程式比較
-1	x^2+x-1=0	-φ	1/φ
1	x^2-x-1=0	φ	-1/φ
p-4
1	x^2-x+1=0	0.5±⒤0.866603
3	x^2-3x+1=0	φ^2	1/φ^2
5	x^2-5x+1=0
7	x^2-7x+1=0
9	x^2-9x+1=0
2k+1	x^2-x+1.25=0	0.5±⒤1.0		9.8√2k+1	⋍	文献値
3	x^2-x+3.25=0	0.5±⒤1.73205 *0.85⋍		14.42798	:	14.13472
5	x^2-x+5.25=0	0.5±⒤2.23607		21.91347	⋍	21.02203
7	x^2-x+7.25=0	0.5±⒤2.64575		25.92836	⋍	25.01085
9	x^2-x+9.25=0	0.5±⒤3.0		29.4	⋍	30.42487
11	x^2-x+11.25=0	0.5±⒤3.31662		32.50292	⋍	32.93506
13	x^2-x+13.25=0	0.5±⒤3.60555		35.3344	⋍	37.58617

π(0)⋍π2(0)+O(α^2)(参考)

(参考)
楕円曲線の不変量
①y^2⋍x^3+Px+Qの不変量は
j⋍2^8・3＾3・P^3/(4P^3+27Q^2)
②y^2⋍x^3+Q⇒j⋍0
③y^2⋍(x-A)(x-B)(x-C)⇒
j⋍2^8(AB+BC+CA-A^2-B^2-C^2)/(A-B)^2(B-C)^2(C-A)^2
④y^2⋍x(x-1)(x-A)⇒
j⋍-2^8[A(A+1)+1]/A^2(A-1)^2
⑤y^2-y⋍x^3-x^2⇒
()^2⋍()^3-1/3()+19/108
∵Y⋍y-1/2、X⋍x-1/3
j⋍-2^12/11
①重力定数g⋍9.8
②πa(半径､面積)
③計量ﾃﾝｿﾙg{μν}
④ﾌｧｲﾝﾏﾝ(標準形)積分⋍π^2/2a^2
⑤ｳｨｯｸ回転⋍1/4π^2
⑥SchwingerModelの２つのﾈｰﾀｰｶﾚﾝﾄ
jμ⋍I	ψ⋆(γμ)ψ
j5μ⋍I	ψ⋆（γμ)(γ5)ψ⋍（εμν)jν
⑦δ^2π+O(δ^3)
Z3⋍1+O(α)
π(q＾2)⋍π2(q＾2)+O(α^2)
π(0)⋍π2(0)+O(α^2)

②p⋍1/2±⒤9.8√(2k+1)f{μν}={{1,0} {0,0}}

⓪9.8√(2k+1)							②p⋍1/2±⒤9.8√(2k+1)f{μν}
(∵11√(2k+1)-√δ補正)					※	-2,75√δ			{{1,0}  {0,0}}
11√	δ			-√δ	⋍	補正値	文献値	/√δ⋍9.8	⋍9.8√2k+1
11√	3	19.053	-	1.732051	※	14.28942	14.13472	8.160684	14.42798
11√	5	24.597	-	2.236068	⋍	22.36068	21.02203	9.401338	21.91347
11√	7	29.103	-	2.645751	⋍	26.45751	25.01085	9.453213	25.92836
11√	9	33	-	3	⋍	30	30.42487	10.14162	29.4
11√	11	36.483	-	3.316625	⋍	33.16625	32.93506	9.930294	32.50292
11√	13	39.661	-	3.605551	⋍	36.05551	37.58617	10.42453	35.3344
11√	15	42.603	-	3.872983	⋍	38.72983	37.58617	9.704707	37.95524
11√	17	45.354	-	4.123106	⋍	41.23106	40.91871	9.924245	40.40644
11√	19	47.948	-	4.358899	⋍	43.58899	43.32707	9.939912	42.71721
11√	21	50.408	-	4.582576	⋍	45.82576	43.32707	9.454742	44.90924
11√	23	52.754	-	4.795832	⋍	47.95832	48.00515	10.00977	46.99915
11√	25	55	-	5	⋍	50	49.77383	9.954766	49
11√	27	57.158	-	5.196152	⋍	51.96152	49.77383	9.578978	50.92229
11√	29	59.237	-	5.385165	⋍	53.85165	52.97	9.836282	52.77462
11√	31	61.245	-	5.567764	⋍	55.67764	56.446	10.138	54.56409
11√	33	63.19	-	5.744563	⋍	57.44563	56.446	9.825987	56.29671
11√	35	65.077	-	5.91608	⋍	59.1608	59.347	10.03147	57.97758
11√	37	66.91	-	6.082763	⋍	60.82763	60.831	10.00055	59.61107
11√	39	68.695	-	6.244998	⋍	62.44998	60.831	9.740756	61.20098
11√	41	70.434	-	6.403124	⋍	64.03124	65.112	10.16879	62.75062
11√	43	72.132	-	6.557439	⋍	65.57439	65.112	9.929487	64.2629
11√	57	83.048	-	7.549834	⋍	75.49834	75.8	10.03996	73.98838
							平均ヘイキン値チ	9.80864

⒤f[μν]⋍{{1,0}{0,0}} (rank⋍1)∴[□-(2k+1)]φ=0

the minimizer f is 2Δf-|▽f|^2+R=const.(ﾍﾟﾚﾙﾏﾝ､p5)
the function f on a closed manfiled M　(ﾍﾟﾚﾙﾏﾝ､p8)
u=(1,1),v=(-1/2,0)とおく
①f⋍u+⒤v	∴⒤f⋍-v+⒤u
複素共役､f*⋍u-⒤v		∴⒤f*⋍-v-⒤u
∴⒤[f+f*]⋍ｰ2v⋍1 (rank⋍1)
⒤f[μν]⋍{{1,0}{0,0}} (rank⋍1)
②γ={{1,1}､{0,1}}				[a,b,c]
∴γ^2={{1,2},{0,1}}				[1,-1,3.25]
③γ^2⒤v=(-1/2,0)				[1,-1,5.25]
γ^2･⒤u=(3,1)				…
γ^4･⒤u=(5,1)				[1,-1,2k+1.25]
…				[1,-1,q.25]
γ^2k･⒤u=(2k+1,1)				∴ｘ⋍1/2∓⒤√Q⋍√(2k+1)
∴√γ^2k･⒤u=√(2k+1,1)⋍√(2k+1)			x⋍1/2∓⒤1.73205…
④x＾2+ｘ+Q.25=(x+1/2)^2+Q=0			φ(x)=e^∓√(2k+1)x
□φ=	d＾2φ=(2k+1)φ
	∴[□-(2k+1)]φ=0

∴p⋍∓√(2ℓ+1)⋍∓√3,√5,√7⋍∓√1-s

･ﾌｧｲﾝﾏﾝ経路積分
1/AB⋍1/(A-B)^2・[1/k-1/k+1]
1/s(1-s)⋍-1/ℓ(ℓ+1)⋍1/(ℓ+ℓ+1)^2・[1/k-1/k+1]
	⋍1/p^4・[1/k-1/k+1]
∴p⋍∓√(2ℓ+1)⋍∓√3,√5,√7…⋍∓√1-s
⓪9.8√(2k+1)						①πa型√(2k+1){9.8±0.43}
(∵11√(2k+1)-δ補正)					※	-2,75δ		※	-2,75δ
11√	δ			√(2k+1)⋍δ		補正値	文献値		/δ⋍9.8
11√	3	19.0525589	-	1.73205081	※	14.2894192	14.13472	⋍	8.160684
11√	5	24.5967478	-	2.23606798	⋍	22.3606798	21.02203	⋍	9.401338
11√	7	29.1032644	-	2.64575131	⋍	26.4575131	25.01085	⋍	9.453213
11√	9	33	-	3	⋍	30	30.42487	⋍	10.14162
11√	11	36.4828727	-	3.31662479	⋍	33.1662479	32.93506	⋍	9.930294
11√	13	39.661064	-	3.60555128	⋍	36.0555128	37.58617	⋍	10.42453
11√	15	42.6028168	-	3.87298335	⋍	38.7298335	37.58617	⋍	9.704707
11√	17	45.3541619	-	4.12310563	⋍	41.2310563	40.91871	⋍	9.924245
11√	19	47.9478884	-	4.35889894	⋍	43.5889894	43.32707	⋍	9.939912
11√	21	50.4083326	-	4.58257569	⋍	45.8257569	43.32707	⋍	9.454742
11√	23	52.7541468	-	4.79583152	⋍	47.9583152	48.00515	⋍	10.00977
11√	25	55	-	5	⋍	50	49.77383	⋍	9.954766
11√	27	57.1576766	-	5.19615242	⋍	51.9615242	49.77383	⋍	9.578978
11√	29	59.2368129	-	5.38516481	⋍	53.8516481	52.97	⋍	9.836282
11√	31	61.245408	-	5.56776436	⋍	55.6776436	56.446	⋍	10.138
11√	33	63.1901891	-	5.74456265	⋍	57.4456265	56.446	⋍	9.825987
11√	35	65.0768776	-	5.91607978	⋍	59.1607978	59.347	⋍	10.03147
11√	37	66.9103878	-	6.08276253	⋍	60.8276253	60.831	⋍	10.00055
11√	39	68.694978	-	6.244998	⋍	62.44998	60.831	⋍	9.740756
11√	41	70.4343666	-	6.40312424	⋍	64.0312424	65.112	⋍	10.16879
11√	43	72.1318238	-	6.55743852	⋍	65.5743852	65.112	⋍	9.929487
11√	57	83.0481788	-	7.54983444	⋍	75.4983444	75.8	⋍	10.03996
							平均値	⋍	9.887114
							標偏差	⋍	0.436854