Maximum Gap in (Inverse) Cyclotomic Polynomial

Let $g(f)$ denote the maximum of the differences (gaps) between two consecutive exponents occurring in a polynomial $f$. Let $\Phi_n$ denote the $n$-th cyclotomic polynomial and let $\Psi_n$ denote the $n$-th inverse cyclotomic polynomial. In this note, we study $g(\Phi_n)$ and $g(\Psi_n)$ where $n$ is a product of odd primes, say $p_1 < p_2 < p_3$, etc. It is trivial to determine $g(\Phi_{p_1})$, $g(\Psi_{p_1})$ and $g(\Psi_{p_1p_2})$. Hence the simplest non-trivial cases are $g(\Phi_{p_1p_2})$ and $g(\Psi_{p_1p_2p_3})$. We provide an exact expression for $g(\Phi_{p_1p_2}).$ We also provide an exact expression for $g(\Psi_{p_1p_2p_3})$ under a mild condition. The condition is almost always satisfied (only finite exceptions for each $p_1$). We also provide a lower bound and an upper bound for $g(\Psi_{p_1p_2p_3})$

Rarity and shifts in occurrence of endangered butterflies in South Korea

Endangered species are often the focus of public attention, partly because of their vulnerability to environmental changes, such as climate and land use change, and subsequently being at high risk of extinctions. Hence, red lists of endangered species play anessential in nature conservation. Although several endangered butterfly species have been previously listed as endangered species by government and/or individuals in South Korea, these red listsrarely include reliable quantitative population data. This has led to endless and unproductive debates on the selection of endangered species. Following Korean butterfly atlases, we assessed the population status of Korean endangered butterfly species whose distributions have been previously published. We hypothesized that these endangered species are rare and are decreasing in occurrence. We found that the decrease in occurrence is more important in determining endanger status than rarity. Using values of rarity and shifts in species occurrence, we selected endangered species from the previously published endangered species. Only eight species of 20 previous endangered species were defined as endangered by this semi-quantitative classification. This finding suggests that the subjective determination based on expert's perception would define more species as endangered compared to the quantitative determination based on population data.Article信州大学農学部紀要 50（1-2）: 37-42(2014)departmental bulletin pape

Can Sodium Abundances of A-Type Stars Be Reliably Determined from Na I 5890/5896 Lines?

An extensive non-LTE abundance analysis based on Na I 5890/5896 doublet lines was carried out for a large unbiased sample of ~120 A-type main-sequence stars (including 23 Hyades stars) covering a wide v_e sin i range of ~10--300 km/s, with an aim to examine whether the Na abundances in such A dwarfs can be reliably established from these strong Na I D lines. The resulting abundances ([Na/H]_{58}), which were obtained by applying the T_eff-dependent microturbulent velocities of \xi ~2--4 km/s with a peak at T_eff ~ 8000 K (typical for A stars), turned out generally negative with a large diversity (from ~-1 to ~0), while showing a sign of v_e sin i-dependence (decreasing toward higher rotation). However, the reality of this apparently subsolar trend is very questionable, since these [Na/H]_{58} are systematically lower by ~0.3--0.6 dex than more reliable [Na/H]_{61} (derived from weak Na I 6154/6161 lines for sharp-line stars). Considering the large \xi-sensitivity of the abundances derived from these saturated Na I D lines, we regard that [Na/H]_{58} must have been erroneously underestimated, suspecting that the conventional \xi values are improperly too large at least for such strong high-forming Na I 5890/5896 lines, presumably due to the depth-dependence of \xi decreasing with height. The nature of atmospheric turbulent velocity field in mid-to-late A stars would have to be more investigated before we can determine reliable sodium abundances from these strong resonance D lines.Comment: 14 pages, 8 figures, accepted for publication in Publ. Astron. Soc. Japan, Vol. 61, No. 5 (2009

Interfacial chemical bonding-mediated ionic resistive switching.

In this paper, we present a unique resistive switching (RS) mechanism study of Pt/TiO2/Pt cell, one of the most widely studied RS system, by focusing on the role of interfacial bonding at the active TiO2-Pt interface, as opposed to a physico-chemical change within the RS film. This study was enabled by the use of a non-conventional scanning probe-based setup. The nanoscale cell is formed by bringing a Pt/TiO2-coated atomic force microscope tip into contact with a flat substrate coated with Pt. The study reveals that electrical resistance and interfacial bonding status are highly coupled together. An oxygen-mediated chemical bonding at the active interface between TiO2 and Pt is a necessary condition for a non-polar low-resistance state, and a reset switching process disconnects the chemical bonding. Bipolar switching mode did not involve the chemical bonding. The nature of chemical bonding at the TiO2-metal interface is further studied by density functional theory calculations

Nematic response revealed by coherent phonon oscillations in BaFe2_2As2_2

We investigate coherent phonon oscillations of BaFe$_2$As$_2$ using optical pump-probe spectroscopy. Time-resolved optical reflectivity shows periodic modulations due to $A_{1g}$ coherent phonon of $c$-axis arsenic vibrations. Optical probe beams polarized along the orthorhombic $a$- and $b$-axes reveal that the initial phase of coherent oscillations shows a systematic deviation as a function of temperature, although these oscillations arise from the same $c$-axis arsenic vibrations. The oscillation-phase remains anisotropic even in the tetragonal structure, reflecting a nematic response of BaFe$_2$As$_2$. Our study suggests that investigation on the phase of coherent phonon oscillations in optical reflectivity can offer unique evidence of a nematic order strongly coupled to a lattice instability.Comment: 5 pages, 4 figure