Explicit formulae for Chern-Simons invariants of the hyperbolic J(2n,−2m)J(2n,-2m) knot orbifolds

We calculate the Chern-Simons invariants of the hyperbolic $J(2n,-2m)$ knot orbifolds using the Schl\"{a}fli formula for the generalized Chern-Simons function on the family of cone-manifold structures of $J(2n,-2m)$ knot. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham and Lee's methods to a bi-infinite family. We dealt with even slopes just as easily as odd ones. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic $J(2n,-2m)$ knot orbifolds. For the fundamental group of $J(2n, -2m)$ knot, we take and tailor Hoste and Shanahan's. As a byproduct, we give an affirmative answer for their question whether their presentation is actually derived from Schubert's canonical 2-bridge diagram or not.Comment: 9 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1601.00723, arXiv:1607.0804

An explicit formula for the AA-polynomial of the knot with Conway's notation C(2n,4)C(2n, 4)

An explicit formula for the $A$-polynomial of the knot having Conway's notation $C(2n,4)$ is computed up to repeated factors. Our polynomial contains exactly the same irreducible factors as the $A$-polynomial defined in~\cite{CCGLS1}.Comment: 17 pages, 2 figures, To appear in Topology and its Application

Dependence of reaction center-type energy-dependent quenching on photosystem II antenna size

AbstractThe effects of photosystem II antenna size on reaction center-type energy-dependent quenching (qE) were examined in rice plants grown under two different light intensities using both wild type and qE-less (OsPsbS knockout) mutant plants. Reaction center-type qE was detected by measuring non-photochemical quenching at 50 μmol photons m−2 s−1 white light intensity. We observed that in low light-grown rice plants, reaction center-type qE was higher than in high light-grown plants, and the amount of reaction center-type qE did not depend on zeaxanthin accumulation. This was confirmed in Arabidopsis npq1–2 mutant plants that lack zeaxanthin due to a mutation in the violaxanthin de-epoxidase enzyme. Although the electron transport rate measured at a light intensity of 50 μmol photons m−2 s−1 was the same in high light- and low light-grown wild type and mutant plants lacking PsbS protein, the generation of energy-dependent quenching was completely impaired only in mutant plants. Analyses of the pigment content, Lhcb proteins and D1 protein of PSII showed that the antenna size was larger in low light-grown plants, and this correlated with the amount of reaction center-type qE. Our results mark the first time that the reaction center-type qE has been shown to depend on photosystem II antenna size and, although it depends on the existence of PsbS protein, the extent of reaction center-type qE does not correlate with the transcript levels of PsbS protein. The presence of reaction center-type energy-dependent quenching, in addition to antenna-type quenching, in higher plants for dissipation of excess light energy demonstrates the complexity and flexibility of the photosynthetic apparatus of higher plants to respond to different environmental conditions