Bandwidth of the cartesian product of two connected graphs

AbstractThe bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x)−f(y)|:xy∈E(G)} taken over all injective integer numberings f of G. The cartesian product of two graphs G and H, written as G×H, is the graph with vertex set V(G)×V(H) and with (u1,v1) adjacent to (u2,v2) if either u1 is adjacent to u2 in G and v1=v2 or u1=u2 and v1 is adjacent to v2 in H. In this paper we investigate the bandwidth of the cartesian product of two connected graphs. For a graph G, we denote the diameter of G and the connectivity of G by D(G) and κ(G), respectively. Let G and H be two connected graphs. Among other results, we show that if B(H)=κ(H) and |V(H)|⩾2B(H)D(G)−min{1,D(G)−1}, then B(G×H)=B(H)|V(G)|. Moreover, the order condition in this result is sharp

The D coefficient in neutron beta decay in effective field theory

In this paper we explore the time-reversal-odd triple-correlation coefficient in neutron beta decay, the so-called "D coefficient", using heavy-baryon effective field theory with photon degrees of freedom. We find that this framework allows us to reproduce the known results for the contribution which comes from final-state interactions, and also to discuss higher-order corrections. In particular we are able to show that in the heavy-baryon limit all electromagnetic contributions vanish. By calculating the leading correction to the known result, we give a final expression which is accurate to better than 1%. Hence we extend downwards the range over which the D coefficient could be used to explore time-violation from new physics.Comment: 12c pages, 3 eps figures Version accepted for publication in Physics Letters B; minor changes of wordin

Direct mapping of the spin-filtered surface bands of a three-dimensional quantum spin Hall insulator

Spin-polarized band structure of the three-dimensional quantum spin Hall insulator $\rm Bi_{1-x}Sb_{x}$ (x=0.12-0.13) was fully elucidated by spin-polarized angle-resolved photoemission spectroscopy using a high-yield spin polarimeter equipped with a high-resolution electron spectrometer. Between the two time-reversal-invariant points, $\bar{\varGamma}$ and $\bar{M}$, of the (111) surface Brillouin zone, a spin-up band ($\Sigma_3$ band) was found to cross the Fermi energy only once, providing unambiguous evidence for the strong topological insulator phase. The observed spin-polarized band dispersions determine the "mirror chirality" to be -1, which agrees with the theoretical prediction based on first-principles calculations

Before-after (1998 and 2008) trend analyses on regional clustering of clinical dentist-to-population ratio in all 1,976 municipalities of Japan

Purpose: The main purpose of this study was to obtain geographic clustering information in order to identify shortages (“cold spots”) and surpluses (“hot spots”) of dentists in all municipalities of Japan. Methods: Pretreatment steps were conducted to recover the lost comparability between pre-1998 and post-2008 data due to the large-scale merging of municipalities (42.1% reduction) in the Heisei era. Moran’s I, LISA and spatial multiple regression analyses with AIC were performed to verify regional clustering. Dependent variables of the regression analyses were the clinical dentist-to-population ratio in 2008 (Model 1) and the difference between 1998 and 2008 (Model 2). Results: The R2 was 0.8379 (p<0.0001) for Model 1 and 0.5832 (p<0.0001) for Model 2. The initial dentist-to-population ratio in 1998 showed the highest significance in both models. However, the coefficient of Model 2 was negative, which was exactly the opposite of that of Model 1. Furthermore, indices relating to urbanization and hospital dentist-to-population ratio in 1998 were also highly significant (p<0.01) after adjustment for confounding factors. High- High clustered municipalities are located in most urbanized areas, whereas Low-Low clustered municipalities are located in remote areas far from urbanized areas. This study revealed that factors which attract dental clinics are urbanization and hospitals with dental care capabilities. Conclusion: Clinical dentist-topopulation ratios have improved only in municipalities in urbanized areas in the past ten years. On the contrary, accessibility of dental treatment has not improved in remote/isolated areas

Spontaneous Extraskeletal Osteosarcoma in the Stomach of an Aged F344 Rat

Extraskeletal osteosarcoma is a very rare tumor in humans and animals including rats. This paper describes a case of extraskeletal osteosarcoma observed in the glandular stomach of an aged female Fischer 344 rat. Grossly, a whitish solid mass was observed at the greater curvature of the glandular stomach. Histologically, the tumor consisted of both atypical polygonal and pleomorphic spindle-shaped cells, with pleomorphic nuclei, and it contained variable amounts of osteoids and small clumps of mature bone tissue. In addition, mitotic figures were frequently observed. Neither invasion of the muscle layer or vessels in the stomach nor metastasis to distant organs was detected. There were no skeletal tumors in the body. Immunohistochemically, the tumor cells were positive for osteocalcin, osteonectin, vimentin and S-100 protein. Judging from these results, the present tumor was diagnosed as extraskeletal osteosarcoma. This is the first report of spontaneous extraskeletal osteosarcoma arising from the stomach in a rat

トクシマ ノ ホシゾラ : テイテン カンソク ニヨル コウガイノ ジカンテキ ヘンカ

In these days, streets of cities and towns are flooded with various lights. These lights provide convenience and security to night time activities. On the other hand, these lights also cause a problem called “light pollution,” by washing away dimmer stars in the sky. As a result, it is difficult to observe even some well-known constellations in the midst of a huge city. In this paper, we first summarized how to measure the sky brightness by naked eye and using a special tool, Sky Quality Meter(with Lens ; SQML) and what kind of standards are used world-wide. Then, we measured the actual sky brightness in the April of 2016 at a suburb of Tokushima city from sundown till after midnight. We found the SQM-L is very easy to use for people at any age. By observing two nights with 4days apart, we also found the effect of light from the Moon is somewhat significant. But for both days, we found the sky brightness changes about 1.5-2.0 mag arcsec-2during our observations. In the future, we would like to propose further observation to figure out how moonlight affects the “light pollution” as well as the two-dimensional spread of it across Tokushima city, which can be conducted as a part of Environmental Education for primary and junior high school in this area

JASTRO IC/IS Guideline for Gynecologic Cancers

It has been postulated that the combination of intracavitary and interstitial brachytherapy (IC/IS) is effective and safe for large and irregularly shaped uterine cervical cancer patients. However, due to its invasiveness compared to conventional intracavitary brachytherapy (ICBT), it has to be said that the implementation speed of IC/IS is slow. Until now, there have been no guidelines for required equipment, human resources, and procedural guide focusing solely on IC/IS. The purpose of this guideline is to provide radiation oncologists and medical physicists who wish to start IC/IS with practical and comprehensive guidance for a safe IC/IS introduction and to help accelerate the spread of the utilization of IC/IS nationwide. This is the English translation of the Japanese IC/IS Guidelines, and it was created in an effort to share the Japanese approach to the management of locally advanced uterine cervical cancer worldwide