Electron spin resonance shifts in S=1 antiferromagnetic chains

We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy based on several effective field theories, the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid, we have to take interactions among magnons into account. Though the O(3) NLSM is only valid in the Haldane phase, an appropriate translation of Faddeev-Zamolodchikov operators of the O(3) NLSM to fermion operators enables one to treat ESR shifts near the lower critical field in a similar manner to discussions in Haldane phase. We present that our theory gives quantitative agreements with recent ESR experimental results on an spin-1 chain compounds NDMAP

New Invariants for Partitioning a Graph into 2-connected Subgraphs

A vertex partition in which every part induces a 2-connected subgraph is called a 2-proper partition. This concept was introduced by Ferrara et al. in 2013, and Borozan et al. gave the best possible minimum degree condition for the existence of a 2-proper partition in 2016. Later, in 2022, Chen et al. extended the result by showing a minimum degree sum condition for the existence of 2-proper partition. In this paper, we introduce two new invariants of graph, denoted by $\sigma^*(G)$ and $\alpha^*(G)$. These two invariants are defined from degree sum on all independent sets with some property. We prove that if a graph $G$ satisfies $\sigma^*(G)\geq |V(G)|$, then with some exceptions, $G$ has a 2-proper partition with at most $\alpha^*(G)$ parts. This result is best possible, and implies both of the results by Borozan et al. and by Chen et al.. Moreover, as a corollary of our result, we give a minimum degree product condition for the existence of a 2-proper partition.Comment: 14 pages, 4 figure

Phototactic responses of cell population to repeated pulses of yellow light in a phytoflagellate Cryptomonas sp.

Positive phototaxis in cell populations of a phytoflagellate Cryptomonas sp. was recorded photoelectrically when the duration and intensity of repeated pulses of monochromatic yellow light (570 nm) interspersed with darkness were varied. Irrespective of the duration of the light pulses, phototactic responses to repeated pulses were as great as those to continuous irradiation and were linearly dependent on the logarithm of total incident light energy when the dark interval was shorter than 60 milliseconds. Under these conditions, reciprocity between duration and intensity held well. In contrast, when the dark interval exceeded 250 milliseconds, the responses were remarkably reduced regardless of light duration and were not affected by increasing the intensity of actinic light pulses. The present results clearly indicate that continuous stimulation with actinic light is not essential for the maximum effect, but that the length of dark interval is crucial in phototactic response

Auxin responsiveness of a novel cytochrome P450 in rice coleoptiles

An early auxin-induced gene was isolated from rice (Oryza sativa L. subsp. japonica cv Nihonmasari) coleoptiles by a fluorescent-labeled differential display screen. The full-length gene contains conserved domains characteristic for the cytochrome P450 superfamily. This gene, designated as CYP87A3, was weakly expressed in dark-grown coleoptiles but was up-regulated rapidly and transiently when coleoptile segments were incubated in 5 m indole-3-acetic acid. This induction by auxin could not be suppressed by cycloheximide. Depletion of segments from endogenous auxin reduced the amount of CYP87A3 transcripts. The CYP87A3 transcript level was rapidly, although transiently, up-regulated in response to light as well. The observed pattern of gene regulation might indicate a role in the suppression of auxin-induced coleoptile growth. The role of CYP87A3 is discussed with respect to auxin signaling in the regulation of coleoptile growth

Single-ion anisotropy in Haldane chains and form factor of the O(3) nonlinear sigma model

We consider spin-1 Haldane chains with single-ion anisotropy, which exists in known Haldane chain materials. We develop a perturbation theory in terms of anisotropy, where magnon-magnon interaction is important even in the low temperature limit. The exact two-particle form factor in the O(3) nonlinear sigma model leads to quantitative predictions on several dynamical properties including dynamical structure factor and electron spin resonance frequency shift. These agree very well with numerical results, and with experimental data on the Haldane chain material Ni(C$_5$H$_{14}$N$_2$)$_2$N$_3$(PF$_6$)