пїЅ 10. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅ

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ I пїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ N={1,2пїЅ} пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ E={(1,2),(2,3),пїЅ}. пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ B пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

BB(I), пїЅпїЅB(I)B,пїЅ B(I)B.

пїЅпїЅпїЅпїЅпїЅ Gr₁(V₁,E₁), Gr₂(V₂,E₂) ─ пїЅпїЅпїЅпїЅпїЅ, kÎN. ВіпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ f пїЅпїЅпїЅпїЅпїЅпїЅпїЅ V₁ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ V₂ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ k-пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ B(f(x),1)Í f(B(x,k)) пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎV₁. пїЅпїЅпїЅпїЅ 10.1 пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ f: V₁ пїЅV₂ пїЅ -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(Gr₁) пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(Gr₂) пїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ f ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ kÎN.

пїЅпїЅпїЅпїЅ 10.1. пїЅпїЅпїЅпїЅпїЅ Gr₁(V₁,E₁), Gr₂(V₂,E₂) ─ пїЅпїЅпїЅпїЅпїЅ, kÎN, f ─ k-пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ V_{1 пїЅ}пїЅпїЅ V₂ . пїЅпїЅпїЅ B(f(x),m)Í f(B(x,km)) пїЅпїЅпїЅ пїЅпїЅпїЅ xÎV₁, m Îw.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎV₁, m Îw. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ yÎB(f(x),m) пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ y₁, y₂, пїЅ, y_n, n<m пїЅ пїЅпїЅпїЅ B(f(x),m), пїЅпїЅпїЅ пїЅпїЅ y₁=f(x), y_n=y пїЅ (y_i, y_i+1)ÎE₂ пїЅпїЅпїЅ пїЅпїЅпїЅ i£ n-1. пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ x₁,x₂,пїЅ,x_nÎV₁, пїЅпїЅпїЅ пїЅпїЅ x=x₁, f(x₁)=y₁, f(x₂)=y₂,пїЅ, f(x_n)=y_n пїЅпїЅ d(x_i, x_i+1)£ k пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ i£ n-1 . пїЅпїЅпїЅпїЅпїЅпїЅпїЅ y=y_n, n£ m,пїЅ пїЅпїЅ yÎf(B(x,km)).

пїЅпїЅпїЅпїЅ 10.2. пїЅпїЅпїЅпїЅпїЅ Gr₁(V₁,E₁), Gr₂(V₂,E₂) ─ пїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ g: wпїЅw, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ |B(x,m)|£ g(m)пїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ xÎV₁, m Îw. пїЅпїЅпїЅпїЅ B(Gr₁) B(Gr₂), пїЅпїЅ пїЅпїЅпїЅпїЅ kÎw, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ |B(y,m)|£ g(km) пїЅпїЅпїЅ пїЅпїЅпїЅ yÎV₂, m Îw.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅ f ─ -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(Gr₁) пїЅпїЅ B(Gr₂). пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ kÎw пїЅпїЅпїЅ, пїЅпїЅ B(f(x),1) Í f(B(x,k)) пїЅпїЅпїЅ пїЅпїЅпїЅ xÎV₁. пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ 10.1пїЅ B(f(x),m)Í f(B(x,km)) пїЅпїЅпїЅ пїЅпїЅпїЅ xÎV₁. пїЅпїЅпїЅпїЅ, |B(f(x),m)|£ g(k,m) пїЅпїЅпїЅ пїЅпїЅпїЅ xÎV₁, m Îw.пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ f пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ V₁ пїЅпїЅпїЅ V₂ , пїЅпїЅ |B(y,m)|£ g(km)пїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ yÎV₂, m Îw.

пїЅпїЅпїЅпїЅ 10.3. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ Gr(V,E), B(I) B(Gr) пїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ V=È_iÎw V_i пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ m, пїЅпїЅпїЅ пїЅпїЅ |V_i|£ m пїЅ B(x,1)ÇV_j=Æ пїЅпїЅпїЅ пїЅпїЅпїЅ xÎV_i, i ÎwпїЅ пїЅ пїЅпїЅпїЅ j>i+1.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ B(I)B(Gr) пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ f: NпїЅ V. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ k пїЅпїЅпїЅ, пїЅпїЅ B(f(y),1) Í f(B(y,k)) пїЅпїЅпїЅ пїЅпїЅпїЅ yÎN. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ m=2k+1 пїЅ пїЅпїЅпїЅпїЅ'пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ N пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ A₀, A₁,пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ m. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

V₀ =f(A₀), V₁ =f(A₁)\V₀ , V₂=f(A₂)\(V₁ÈV₂), пїЅ.

пїЅпїЅпїЅпїЅ, пїЅпїЅ |V_i|£ m пїЅ V=È_iÎw V_i. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎV_i. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ aÎA_i, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ f(a)=x. пїЅпїЅпїЅ

B(x,1) =B(f(a),1)Í f(B(a,k))Í f(A_i-1ÈA_i ÈA_i+1).

пїЅпїЅпїЅпїЅ, B(x,1) ÇV_j = ÆпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ j>i+1.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ V=È_iÎw V_i пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ m, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ бієпїЅпїЅпїЅпїЅ f: NпїЅ V пїЅпїЅпїЅ, пїЅпїЅ пїЅ пїЅпїЅпїЅпїЅ a,bÎN, a<b пїЅ f(a)ÎV_i, f(b)ÎV_{jпїЅпїЅ} пїЅпїЅпїЅпїЅпїЅпїЅпїЅ i<j. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎV_i. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ aÎN пїЅ f(a)=x. пїЅпїЅпїЅ

B(f(a),1)=B(x,1) Í V_i-1ÈV_iÈV_i+1 .

пїЅпїЅпїЅпїЅ, B(f(a),1)Í B(a,2m). пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ f ─ 2m- пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ 10.1, f пїЅ -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(I) пїЅпїЅ B(Gr).

пїЅпїЅпїЅпїЅпїЅ B(X,P,B) ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, aÎP. пїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ <x_n>_nÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ X пїЅпїЅпїЅпїЅпїЅпїЅпїЅ a-пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ x_n+1 Î B(x_n,a) пїЅпїЅпїЅ пїЅпїЅпїЅ nÎw.

пїЅпїЅпїЅпїЅ 10.4. пїЅпїЅпїЅпїЅпїЅ B(X,P,B) ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, aÎP. пїЅпїЅпїЅпїЅ B(I) B, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ'пїЅ a-пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ X пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅ f: NпїЅ X -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ mÎw пїЅпїЅпїЅ, пїЅпїЅ

(*) B(f(y),a)Í f(B(y,m))

пїЅпїЅпїЅ пїЅпїЅпїЅ yÎN. пїЅпїЅпїЅпїЅпїЅ <x_n>_nÎw пїЅa-пїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ y₀ÎN пїЅ f(y₀)=x₀. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ (*), пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ <y_n>_nÎw пїЅ N, пїЅпїЅпїЅпїЅ пїЅпїЅ f(y_n)=x_n пїЅ |y_n+1 - y_n|£ m пїЅпїЅпїЅ пїЅпїЅпїЅ nÎw. пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ <y_n>_nÎw пїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ [a,b]ÌN пїЅпїЅпїЅпїЅпїЅпїЅпїЅ m, пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ e, пїЅпїЅпїЅпїЅ пїЅпїЅ f(e)Î{x_n: nÎw}. пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ'пїЅпїЅ a-пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ X пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ £ m.

пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ <k_i>_iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ [k_i]= {1,2,пїЅ,k_i}, iÎw. пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ X=Ä_iÎw [k_i] пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ x=(x(0), x(1),пїЅ, x(i),пїЅ), пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ x(i)Î[k_i]пїЅ пїЅ x(i)=1 пїЅпїЅпїЅ пїЅпїЅпїЅ iÎw, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎX, mÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

B(x,m)={yÎX: y(i)=x(i) пїЅпїЅпїЅ пїЅпїЅпїЅ i³ m}.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ (X, w, B) пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ B(<x_i>_iÎw).

пїЅпїЅпїЅпїЅ 10.5. пїЅпїЅпїЅпїЅпїЅ пїЅ<k_i>_iÎw , <m_i>_iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ . пїЅпїЅпїЅпїЅ k_i³ m_i пїЅпїЅпїЅ пїЅпїЅпїЅ iÎw, пїЅпїЅ

B(<k_i>_iÎw) B(<m_i>_iÎw),пїЅпїЅ B(<m_i>_iÎw) B(<k_i>_iÎw).

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅf_iпїЅ [k_i] пїЅпїЅ [m_i]. ВіпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ f: Ä_iÎw [k_i]пїЅÄ_iÎw [m_i] пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

f(x(0), x(1),пїЅ, x(i),пїЅ)=(f₀ (x(0)), f₁ ( x(1)),пїЅ, f_i ( x(i)),пїЅ).

пїЅпїЅпїЅ B(f(x),m)=f(B(x,m)) пїЅпїЅпїЅ пїЅпїЅпїЅ xÎÄ_iÎw [k_i], mÎw . пїЅпїЅпїЅпїЅ, пїЅf ─ -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ g_i: [m_i] пїЅ[k_i] пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ g_i(1)=1. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅg: Ä_iÎw [m_i]пїЅÄ_iÎw [k_i] пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

g((y(0), y(1), пїЅ, y(i) ,пїЅ)) = (g₀(y(0)), g₁( y(1)), пїЅ, g_i( y(i)) ,пїЅ).

пїЅпїЅпїЅ g(B(y,m))ÍпїЅ B(g(y),m) пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ yÎÄ [m_i], mÎw. пїЅпїЅпїЅпїЅ, g пїЅпїЅ -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅ 10.6. пїЅпїЅпїЅпїЅпїЅ <k_i>_iÎw ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ, g: wпїЅw ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ m₀=k₀ k₁ пїЅ k_g(0), m_i+1=k_g(i)+1 k_g(i)+2 пїЅ k_g(i+1). пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(<k_i>_iÎw) пїЅ пїЅB(<m_i>_iÎw) пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ .

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ бієпїЅпїЅпїЅпїЅ f₀: [m₀]пїЅ[k₀] ´ [k₁]´пїЅ´[k_g(0)]пїЅ пїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ бієпїЅпїЅпїЅпїЅ

f_i: [m_i]пїЅ[k_g(i)+1] ´ [k_g(i)+2]´пїЅ´[k_g(i+1)] .

пїЅпїЅпїЅпїЅпїЅпїЅпїЅ f: Ä_iÎw [m_i]пїЅÄ_iÎw [k_i] пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

f((x(0), x(1), пїЅ, x(i) ,пїЅ)) = (f₀(x(0)), f₁( x(1)), пїЅ, f_i( x(i)) ,пїЅ).

пїЅпїЅпїЅпїЅпїЅпїЅпїЅ f(B(x,m))=B(f(x),g(0) + g(1)+ пїЅg(m-1)) пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎ Ä_iÎw [m_i]пїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ m, пїЅпїЅ f ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅ 10.7. пїЅпїЅпїЅпїЅпїЅ <k_i>_iÎw пїЅ <m_i>_iÎw ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ, k_i>1, m_i>1 пїЅпїЅпїЅ пїЅпїЅпїЅ iÎw . пїЅпїЅпїЅ

B(<k_i>_iÎw) B(<m_i>_iÎw),пїЅ B(<m_i>_iÎw) B(<k_i>_iÎw).

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ 10.6 пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ <K_i>_iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(<k_i>_iÎw) пїЅ B(<K_i>_iÎw)пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅ K_i ³ m_i пїЅпїЅпїЅ пїЅпїЅпїЅ iÎw. пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ 10.5

B(<k_i>_iÎw) B(<m_i>_iÎw),пїЅ B(<m_i>_iÎw) B(<k_i>_iÎw).

пїЅпїЅпїЅпїЅ 10.8. пїЅпїЅпїЅпїЅпїЅ <k_i>_iÎw, <m_i>_iÎw ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ K_i=k₀k₁пїЅk_i, M_i=m₀m₁пїЅm_i. пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(<k_i>_iÎw) пїЅ B(<m_i>_iÎw) пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ kÎwпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ l,mÎwпїЅ пїЅпїЅпїЅ, пїЅпїЅ K_k|M_l i M_k|K_m.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

f: Ä_iÎw [k_i]пїЅÄ_iÎw [m_i].

пїЅпїЅпїЅпїЅпїЅпїЅпїЅ f -пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅ lÎw, пїЅпїЅпїЅпїЅ пїЅпїЅ f(B(x,k))Í B(f(x),l) пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎ Ä_iÎw [k_i]. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ aÎÄ_iÎw [m_i] пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ xÎ Ä_iÎw [k_i], пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ f(x)Î B(a,l). пїЅпїЅпїЅ B(f(x),l)=B(a,l) i f(B(x,k)) Í B(a,l). пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ f ^-1(B(a,l)) пїЅ пїЅпїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ k. пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ l пїЅ Ä_iÎw [m_i] пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ M_l , пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ k пїЅ Ä_iÎw [k_i]пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ K_k. пїЅпїЅпїЅпїЅ, K_k|M_b . пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ m пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ f ^-1.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ kÎwпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ l,mÎw , пїЅпїЅпїЅ пїЅпїЅ K_k|M_l , M_k|K_m. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ 10.6, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ

K₀|M₀ ,пїЅ M₀|K₁ ,пїЅпїЅ K₁|M₁,пїЅпїЅ M₁|K₂ ,пїЅпїЅ K₂|M₂, пїЅ

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

s₀=K₀,пїЅ _пїЅs₁=M₀/K₀,пїЅ s₂=K₁/M₀,пїЅ s₃=M₁/K₁ ,пїЅпїЅ s₄=K₂/M₁, пїЅ

пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ 10.6 пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(<k_i>_iÎw) пїЅ B(<s_i>_iÎw)пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅ 10.9. пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ G пїЅ пїЅпїЅ'пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ G₀ÌG₁ÌпїЅÌG_iÌпїЅ, G₀={e}, e ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ G. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ k_i=|G_i+1:G_i|, iÎw. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(G) пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ B(<k_i>_iÎw).

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ G_i+1 пїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ G_i пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ X_i пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ, eÎX_i. пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ, G_i+1 =G_iX_i. ВіпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ gÎG пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ G_m+1, пїЅпїЅпїЅ пїЅпїЅпїЅ yÎG_m+1. пїЅпїЅпїЅ g=e пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ G₁. пїЅпїЅпїЅ g= g_m-1пїЅ x_m-1, g_m-1ÎG_m , x_mÎX_m-1 . пїЅпїЅпїЅпїЅпїЅпїЅпїЅ g_m-1ÎG_m , пїЅпїЅ g_m-1=g_m-2 x_m-1 пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ g_m-2 ÎG_m-1, x_m-1ÎX_m-1. ПіпїЅпїЅпїЅ m+1 пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

g=x₀x₁пїЅx_m-1x_m,пїЅпїЅпїЅ x₀ ÎX₀,пїЅ x₁Î X₁,пїЅ пїЅ,пїЅ x_mÎX_m.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ iÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ бієпїЅпїЅпїЅпїЅ f_i: X_iпїЅ[k_i], пїЅпїЅпїЅпїЅ пїЅпїЅ f_i(e)=1. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ бієпїЅпїЅпїЅпїЅ f: GпїЅÄ_iÎw [k_i] пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

f(g)= (f₀(x₀), f₁( x₁), пїЅ, f_m( x_m), 1,1,1,пїЅ).

пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ G пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ f ─ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ B(G)пїЅ пїЅпїЅ B(<k_i>_iÎw).

пїЅпїЅпїЅпїЅ 10.10. пїЅпїЅпїЅпїЅпїЅ G=Ä_w Z₂ ─ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ w пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ Z₂={0,1}. пїЅпїЅпїЅ B(I) B(G).

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ I ─ пїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ w пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ E={(i,i+1): iÎw}. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ kÎw пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ

k=a₀2⁰+a₁2¹+пїЅ+a_n2ⁿ.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ f: wпїЅG пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ