Discrete Midpoint Convexity

For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpoint of any line segment is not greater than the average of its values at the endpoints of the line segment. Midpoint convexity is a well-known characterization of ordinary convexity under very mild assumptions. For a function defined on the integer lattice, we consider the analogous notion of discrete midpoint convexity, a discrete version of midpoint convexity where the value of the function at the (possibly noninteger) midpoint is replaced by the average of the function values at the integer round-up and round-down of the midpoint. It is known that discrete midpoint convexity on all line segments with integer endpoints characterizes L$^{\natural}$-convexity, and that it characterizes submodularity if we restrict the endpoints of the line segments to be at $\ell_\infty$-distance one. By considering discrete midpoint convexity for all pairs at $\ell_\infty$-distance equal to two or not smaller than two, we identify new classes of discrete convex functions, called local and global discrete midpoint convex functions, which are strictly between the classes of L$^{\natural}$-convex and integrally convex functions, and are shown to be stable under scaling and addition. Furthermore, a proximity theorem, with the same small proximity bound as that for L$^{\natural}$-convex functions, is established for discrete midpoint convex functions. Relevant examples of classes of local and global discrete midpoint convex functions are provided.Comment: 39 pages, 6 figures, to appear in Mathematics of Operations Researc

Scaling and Proximity Properties of Integrally Convex Functions

In discrete convex analysis, the scaling and proximity properties for the class of L^natural-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of integrally convex functions of n variables, we show here that the scaling property only holds when n leq 2, while a proximity theorem can be established for any n, but only with an exponential bound. This is, however, sufficient to extend the classical logarithmic complexity result for minimizing a discretely convex function in one dimension to the case of integrally convex functions in two dimensions. Furthermore, we identified a new class of discrete convex functions, called directed integrally convex functions, which is strictly between the classes of L^natural -convex and integrally convex functions but enjoys the same scaling and proximity properties that hold for L^natural -convex functions

Millimeter- and Submillimeter-Wave Observations of the OMC-2/3 Region. III. An Extensive Survey for Molecular Outflows

Using the ASTE 10 m submillimeter telescope and the 1.4 m Infrared Survey Facility (IRSF), we performed an extensive outflow survey in the Orion Molecular Cloud -2 and -3 region. Our survey, which includes 41 potential star-forming sites, has been newly compiled using multi-wavelength data based on millimeter- and submillimeter-continuum observations as well as radio continuum observations. From the CO (3-2) observations performed with the ASTE 10 m telescope, we detected 14 CO molecular outflows, seven of which were newly identified. This higher detection rate, as compared to previous CO (1-0) results in the same region, suggests that CO (3-2) may be a better outflow tracer. Physical properties of these outflows and their possible driving sources were derived. Derived parameters were compared with those of CO outflows in low- and high-mass starforming regions. We show that the CO outflow momentum correlates with the bolometric luminosity of the driving source and with the envelope mass, regardless of the mass of the driving sources. In addition to these CO outflows, seven sources having NIR features suggestive of outflows were also identified.Comment: Accepted to Astrophysical Journal, high resolution images at http://www.asiaa.sinica.edu.tw/~satoko_t/papers/ms.ST.pd

Relationship between medical examination methods and actual conditions of life for preserving visual acuity in primary and junior high school: Verification of the current vision test

The deterioration of children’s eyesight is on the rise. Children's lives have changed in a short period of time, such as an increase in blue light due to the use of electronic devices. It is necessary to consider non-traditional content of health guidance for prevention. The accurate visual acuity test is important to examine the effects of visual acuity and environmental or living factors. We examined the accuracy of the visual acuity test with the three stage Landolt ring for children from the relationship with the eye axial length. After performing a normal detailed visual acuity test of the children and the correlation analysis with the eye axial length, we examined the distribution of the eye axis according to the results of the three-stage visual acuity test by the Landolt ring. The number of children measured eye axial length was 13. The correlation coefficient between detailed visual acuity test and eye axial length was negative. According to the results of the three-stage visual acuity test, the distribution of the eye axis is good for the right eye: the average eye axis of “A” was 23.44 mm, moderate: the average of “B” was 22.58 mm. The average of the left eye axis for “A” children is 23.34 mm, for “B” is 23.08 mm, and for “C” is 23.7 mm. The correlation coefficient between the detailed visual acuity test and the eye axial length was negative on both sides, namely a negative correlation between the visual acuity and the eye axial length. There was a possibility of not correspondence between the three-stage visual test and the eye axial length. In the case of children, it was considered that their visual performance and answers were different because of their mood and physical condition on the day

Investigation of guidance on maintaining visual acuity at combined school from kindergarten to junior high school.: Consideration of relationship between visual acuity and lifestyle

The negative effect of visual acuity for growing children led by widely use of IC device such as mobile phone is concerned today. Heavy use of electronic device such as PC in early age will bring poor visual acuity, and an inconvenience in exercise caused by wearing glasses. In this study, we used wearable devise to search relations between daily lives of children and a decrease in vision in add to a preexisting questionnaire. Compared with the duration of watching TV and reading books of PVA( Poor visual acuity) and NPVA(Non poor visual acuity), PVA students were turned out to be using more time in doing, which supports previous studies. The relevance to visual acuity and sleep was clarified to be significantly shorter in NPVA in terms of nocturnal awakening, and also the average of a sleep and a deep sleep duration were longer in NPVA. No significant difference was observed due to the small parameter. From now on, the further work is needed to examine child's sleep conscientiously, including enriching health guidance for sight maintenance

Petrology of the Yugu peridotites in the Gyeonggi Massif, South Korea: Implications for its origin and hydration process

金沢大学理工研究域自然システム学系Peridotites exposed in the Yugu area in the Gyeonggi Massif, South Korea, near the boundary with the Okcheon Belt, exhibit mylonitic to strongly porphyroclastic textures, and are mostly spinel lherzolites. Subordinate dunites, harzburgites, and websterites are associated with the lherzolites. Amphiboles, often zoned from hornblende in the core to tremolite in the rim, are found only as neoblasts. Porphyroclasts have recorded equilibrium temperatures of about 1000°C, whereas neoblasts denote lower temperatures, about 800°C. Olivines are Fo 90-91 in lherzolites and Fo 91 in a dunite and a harzburgite. The Cr# (=Cr/(Cr + Al) atomic ratio) of spinels varies together with the Fo of olivines, being from 0.1 to 0.3 in lherzolites and around 0.5 in the dunite and harzburgite. The Na2O content of clinopyroxene porphyroclasts is relatively low, around 0.3 to 0.5 wt% in the most fertile lherzolite. The Yugu peridotites are similar in porphyroclast mineral chemistry not to continental spinel peridotites but to sub-arc or abyssal peridotites. Textural and mineralogical characteristics indicate the successive cooling with hydration from the upper mantle to crustal conditions for the Yugu peridotites. Almost all clinopyroxenes and amphiboles show the same U-shaped rare earth element (REE) patterns although the level is up to ten times higher for the latter. The hydration was associated with enrichment in light REE, resulting from either a slab-derived fluid or a fluid circulating in the crust. The mantle-wedge or abyssal peridotites were emplaced into the continental crust as the Yugu peridotite body during collision of continents to form a high-pressure metamorphic belt in the Gyeonggi Massif. The peridotites from the Gyeonggi Massif exhibit lower-pressure equilibration than peridotites, with or without garnets, from the Dabie-Sulu Collision Belt, China, which is possibly a westward extension of the Gyeonggi Massif. © 2008 The Authors Journal compilation © 2008 Blackwell Publishing Asia Pty Ltd

CHARIS Science: Performance Simulations for the Subaru Telescope's Third-Generation of Exoplanet Imaging Instrumentation

We describe the expected scientific capabilities of CHARIS, a high-contrast integral-field spectrograph (IFS) currently under construction for the Subaru telescope. CHARIS is part of a new generation of instruments, enabled by extreme adaptive optics (AO) systems (including SCExAO at Subaru), that promise greatly improved contrasts at small angular separation thanks to their ability to use spectral information to distinguish planets from quasistatic speckles in the stellar point-spread function (PSF). CHARIS is similar in concept to GPI and SPHERE, on Gemini South and the Very Large Telescope, respectively, but will be unique in its ability to simultaneously cover the entire near-infrared $J$, $H$, and $K$ bands with a low-resolution mode. This extraordinarily broad wavelength coverage will enable spectral differential imaging down to angular separations of a few $\lambda/D$, corresponding to $\sim$0.\!\!''1. SCExAO will also offer contrast approaching $10^{-5}$ at similar separations, $\sim$0.\!\!''1--0.\!\!''2. The discovery yield of a CHARIS survey will depend on the exoplanet distribution function at around 10 AU. If the distribution of planets discovered by radial velocity surveys extends unchanged to $\sim$20 AU, observations of $\sim$200 mostly young, nearby stars targeted by existing high-contrast instruments might find $\sim$1--3 planets. Carefully optimizing the target sample could improve this yield by a factor of a few, while an upturn in frequency at a few AU could also increase the number of detections. CHARIS, with a higher spectral resolution mode of $R \sim 75$, will also be among the best instruments to characterize planets and brown dwarfs like HR 8799 cde and $\kappa$ And b.Comment: 13 pages, 7 figures, proceedings from SPIE Montrea