domains (§3.3) are often complete lattices, i.e., algebras over partially ordered sets. We recall in this section the fundamental notions of lattice theory, which are the basis for the soundness of over-approximations of reachable state sets computed by abstract interpretation methods. For further details and proofs we refer to textbooks on lattice theory [DP90] and static analysis [NNH05]. Fro...

DStat relies on three op-amps: the control and buffer amplifiers in the potentiostat (U1 and U2 in Fig. 2(c) in the main text) and the transimpedance amplifier in the current measurement circuit (U3 in Fig. 3(b) in the main text). In DStat, these amplifiers are the LMP7702 (Texas Instruments, Dallas TX, USA) for control and buffer and LMP7721 (Texas Instruments) for transimpedance, respectively...

We wish to reduce the number of parameters in the model and make it so that the model is more easily comparable to our previous work [1]. To do this we first look at the nonspatial single morph model which is given by: Ni(t+ 1) = (1 + b)Ni(t) exp(−mi −mi (1 + b)Nt) For the purpose of this model we want the carrying capacity K to be fixed by the equilibrium population density. We therefore calcu...

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...