To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 29–46. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introduc...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 47–64. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introduc...

Let X be a non empty complex normed space structure and let s1 be a sequence of X. The functor ( ∑ κ α=0(s1)(α))κ∈N yielding a sequence of X is defined as follows: (Def. 1) ( ∑ κ α=0(s1)(α))κ∈N(0) = s1(0) and for every natural number n holds ( ∑ κ α=0(s1)(α))κ∈N(n + 1) = ( ∑ κ α=0(s1)(α))κ∈N(n) + s1(n + 1). One can prove the following proposition (1) Let X be an add-associative right zeroed rig...

λx.S ◦A instead of λx.(A[S]) S ◦ λx.A instead of (λx.A)[S] λx.S2 ◦ S1 ◦ A instead of λx.(A[S1][S2]) S2 ◦ λx.S1 ◦ A instead of (λx.A[S1])[S2] S2 ◦ S1 ◦ λx.A instead of (λx.A)[S1][S2] And so on. Far fewer parentheses. And very close to notation of category theory. If we have composition of substitutions (not in my calculus), then λx.(S2 ◦ S1) ◦ A means λx.(A[S1 ◦ S2]) From the point of view of ca...

The modal systems S1–S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which generalizes a reference rule of S1. In system S1+SP, the relation of strict equivalence φ ≡ ψ satisfies the identity axioms of R. Suszko’s non-Fregean logic adapted t...

This study examined the effects of modality on rats' short-term memory by using the go/no-go delayed paired stimuli comparison task (Konorski task). Each of paired stimuli (S1, S2) was successively presented in order with delay intervals, and a food pellet was contingent upon the lever pressing only when S2 matched S1 (light; L or tone; T). The accuracy of discrimination between the matched and...