Sekinan Table: 2025

17 <Ideogram> can install to language-answering-devices, such as telephone, vending machine, showing-way-machine and so forth. Answer is always individually different for the most adequate purpose.

18 <Ideogram>’s <grammar> is possible to be written as a sophisticated figure which is transformed to easy-readable style.

19 <Ideogram>’s <meaning> is enlarged by the adding-from-old-to-new system. See upper No.5-10.

TOKYO March 4, 2005

Sekinan Research Field of Language

www.sekinan.org

Holomorphic Meaning Theory 3 Continuity of Meaning 12th for KARCEVSKIJ Sergej

Holomorphic Meaning Theory 3

Continuity of Meaning

12^th for KARCEVSKIJ Sergej

TANAKA Akio

Set X

Family of subsets of X M

When M satisfies the next <1>(i)(ii)(iii), M is called σ-field.

<1>

(i) X, Ø ∈M

(ii) a∈M ⇒ X╲A∈M

(iii) A_n∈M (n=1, 2, …) ⇒∪^∞_n₌₁ A_n∈M

( X, M ) is called measurable space.

Function over M μ

When μ satisfies the next <2>(i)(ii)(iii), μ is called measure over measurable space ( X, M ).

(i) μ (A)∈[0,∞]

(ii) μ (0) = 0

(iii) A_n∈M , A_n∩A_m = 0 (n≠m)

μ (∪^∞_n₌₁ A_n) = Σ^∞_n₌₁μ (A)

( X, M, μ ) is called measure space.

When measure space satisfies the next <3>(i), it is called complete measure space.

(i) A∈M, μ (A) = 0 ⇒ B⊂A, μ (B) = 0

<2>(iii) is called complete additive or σ additive.

Measure space that is all the measure is 1 is called probability space.

Measure that all the measure is 1 is called probability measure.

Set Ω that is called whole possibility

Element of Ω ω that is called sample point

σ-field F

Element of F A that is called event

Function over F P

Measure for A∈F P (A ) that is called probability

Tokyo June 22, 2008

Sekinan Research Field of Language

www.sekinan.org

Holomorphic Meaning Theory 2 11th for KARCEVSKIJ Sergej

Holomorphic Meaning Theory 2

11^th for KARCEVSKIJ Sergej

TANAKA Akio

Open set of Cⁿ Ω

Holomorphic function over Ω f

Set of all the holomorphic function over Ω A ( Ω )

Open set U ⊂ Ω

f・A ( U ) is called f ’s divisor class at U.

Divisor class is notated by D ( f, U ).

n-dimensional polydisk is defined by the next.

Open set {z | | z_j-a_j | < r, 1≤j≤n }

n-dimensional polydisk is notated by ∆(a, r) (r = (r₁, …, r_n))

∆(0, 1) is notated by ∆.

∆ⁿ= ∆×…×∆ (Number of ∆ is n.)

∆(a, r) and ∆ⁿare biholomorphic equivalent.

Hartogs figure T_ε = {(z₁, z₂) ∈∆² | |z₁| <ε}

When holomorphic map from Hartogs figure to Ω is always expanded to holomorphic map from ∆²to Ω, Ω is called Hartogs pseudo-convex.

C is Hartogs pseudo-convex.

Cⁿ is Hartogs pseudo-convex.

Holomorphic open set is Hartogs pseudoconvex.

Subharmonic function is defined by the next.

Open set at complex plane Ω

Semicontinuous function that is valued at [-∞, ∞) ψ : Ω → [-∞, ∞)

⊂ Ω

ψ(z ) ≤ (z + re^iθ)dθ

Plurisubharmonic function is defined by the next.

Open set at complex plane Ω

Semicontinuous function that is valued at [-∞, ∞) ψ : Ω → [-∞, ∞)

(z, ω) ∈Ω×Cⁿ

Function ψ( z+ζω )

When ψ( z+ζω ) is subharmornic as ζ ‘s function, ψ( z+ζω ) is called plurisubharmonic function.

Set of all the plurisubharmonic functions PSH (Ω)

What Ω is pseudoconvex is defined by the next.

Continuous plurisubharmonic function ψ : Ω → R

Arbitrary c∈R

Ω_ψc: = {z∈Ω |ψ(z) < c }

Ω_ψcis relatively compact in Ω .

Pseudoconvex open set Ω

H²(Ω, Z) = {0}

Open subset of Ω U

g ∈A(U)

Element of A(U) f

When V(g) is closed set of Ω, there exists D ( f, U ).∋g.

Locally finite open ball B_j= B (p_j, R_j)

Family of B_j{ B_j}^∞_j_{= 1}

Ω = ∪^∞_j_{= 1}B_j

B_j∩V(g) ≠Ø ⇒ B_j⊂ U

g_j∈A(B_j) is defined by the next.

g_j= g | B_j(B_j∩V(g) ≠ Ø)

g_j= 1 (B_j∩V(g) = Ø)

g_jk∈A(B_j∩B_k) : = g_j / g_k(B_j∩B_k ≠ Ø)

B_j∩B_kis convex and simply connected.

g_jkhas not zero point.

(j, k) has one to one correspond with branch u_jkof logg_jk

u_ijkoverB_i∩B_j∩B_kis defined by the next.

u_ijk: = u_ij+ u_jk+ u_ki

Language is defined by the next.

Meaning minimum : = B_j

Word : = g_jk

Sentence : = u_ijk

[References]

Reversion Analysis Theory / Tokyo June 8, 2008

Reversion Analysis Theory 2 / Tokyo June 12, 2008

Holomorphic Meaning Theory / Tokyo June 15, 2008

Tokyo June 19, 2008

Sekinan Research Field of Language

www.sekinan.org