【SEOテキスト】宇田雄一「古典物理学」F+1の定義:∀x∈N01(N01);F+1(x)={f|f∈F1 and∀t∈R({4});∀ξ∈N01;【1】⇒【2】}【1】ξ(4)=t(4)and
ξ(3)=f(t,□)【2】[∂4x(ξ)](4)+3∑i=1∂4f(t,i)・[∂ix(ξ)](4)>0,F-1の定義:∀x∈N01(N01);F-1(x)={f|f∈F1
and∀t∈R({4});∀ξ∈N01;【1】⇒【2】}【1】ξ(4)=t(4)and ξ(3)=f(t,□)【2】[∂4x(ξ)](4)+3∑i=1∂4f(t,i)・[∂ix(ξ)](4)<0,F+2,nの定義:∀n∈N;∀x∈N01(N01);F+2,n(x)={f|f∈F2,n
and∀k∈{1,・・・,n};f(□,□,k)∈F+1(x)},F-2,nの定義:∀n∈N;∀x∈N01(N01);F-2,n(x)={f|f∈F2,n
and∀k∈{1,・・・,n};f(□,□,k)∈F-1(x)},F+4,nの定義:∀n∈N;∀x∈N01(N01);F+4,n(x)={f|f∈F4,n
and f(N2,n)∈F+2,n(x)},F-4,nの定義:∀n∈N;∀x∈N01(N01);F-4,n(x)={f|f∈F4,n and
f(N2,n)∈F-2,n(x)},F+6,nの定義:∀n∈N;∀x∈N01(N01);F+6,n(x)={f|f∈F6,n and f(N2,n)∈F+2,n(x)},F-6,nの定義:∀n∈N;∀x∈N01(N01);F-6,n(x)={f|f∈F6,n
and f(N2,n)∈F-2,n(x)},V3の定義:∀x∈N01(N01);∀a∈R;∀ξ∈N01;【1】and【2】【1】V3(ξ,x,a)∈F3(F3)【2】∀f∈F3;∀(i,j)∈N03;[V3([V3(ξ,x,a)](f))](i,j)=a4∑r=1
4∑s=1[∂rx(ξ)](i)・[∂sx(ξ)](j)・[V3(f)](r,s)
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