In the present paper, we define regularity and normality like strong S1 regularity, S1 regularity, weak S1 regularity, strong S1 normality, S1 normality as well as weak S1 normality on L-topological spaces. Also we investigate some of their properties and the relations between them. 2010 Mathematics Subject Classification: 54A40, 54D10, 54D15, 54D65, 03E72.

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 95–112. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introdu...

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...

results the results showed that all the strains had the dominant allele ptxs1a. there were differences between the alleles of the clinical strains and the vaccine strain. conclusions in recent years, a significant increase in the incidence of pertussis has been reported worldwide. our findings regarding the allelic shift of the ptxs1 gene are similar to those reported in many european and ameri...