In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (eventually S), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of S branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-b...

A new cyclic diarylheptanoid namely alnuheptanoid B (3), along with four known cyclic diarylheptanoids: myricanone (1), (+)-S-myricanol (2), myricanone 5-O--D-glucopyranoside (4), and (+)-S-myricanol 5-O--D-glucopyranoside (5) were isolated from the EtOAc fraction of Alnus japonica Steud (family: Betulaceae) stem bark. Their structures were established by different spectroscopic analyses, as ...

In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are ...

A monoid S satisfies Condition (A) if every locally cyclic left S-act is cyclic. This condition first arose in Isbell’s work on left perfect monoids, that is, monoids such that every left S-act has a projective cover. Isbell showed that S is left perfect if and only if every cyclic left S-act has a projective cover and Condition (A) holds. Fountain built on Isbell’s work to show that S is left ...

A monoid S satisfies Condition (A) if every locally cyclic left S-act is cyclic. This condition first arose in Isbell’s work on left perfect monoids, that is, monoids such that every left S-act has a projective cover. Isbell showed that S is left perfect if and only if every cyclic left S-act has a projective cover and Condition (A) holds. Fountain built on Isbell’s work to show that S is left ...

In this paper, it was constructed quantum codes from cyclic codes over finite ring S = F2 + uF2 + vF2, u2 = u, v2 = v, uv = vu = 0 for arbitrary length n. It was given a new Gray map Ψ which is both an isometry and weight preserving map. It was shown that C is self orthogonal codes over S, so is Ψ(C). It was given a necessary and sufficient condition for cyclic codes over S that contains its du...

Given a plane graph G and two vertices s and t in G, an s-t surface separator is a closed curve C such that s belongs to the other region of R \C than t. A cycle C is called a cyclic surface separator if C is an s-t surface separator, and an odd cyclic surface separator if C is an odd cycle. We consider the problem of finding odd cyclic surface separators in planar graphs and show that the prob...

N-Heterocyclic carbene (NHC)-mediated ring-opening polymerization (ROP) of N-substituted N-carboxylanhydride ((N)R-NCA) yields cyclic poly(alpha-peptoid)s with controlled molecular weights (M(n) = 3-30 kg mol(-1)) and narrow molecular weight distributions (PDI = 1.04-1.12). The reactions exhibit characteristics of a living polymerization with minimal chain transfer. This enables the facile synt...

Magnetization plateaux, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. An extremely robust halfmagnetization plateau is observed in the spinel oxides CdCr2O4 and HgCr2O4, where it is accompanied by a substantial lattice distortion. We give an overview of the present state experiment for CdCr2O4 and HgCr2O4, and show how suc...