• Journal of The Korean Astronomical Society
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• v.46 no.3
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• pp.125-131
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• 2013

We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; ${\beta}_0$ is the number of connected regions, ${\beta}_1$ is the number of circular holes (i.e., complement of solid tori), and ${\beta}_2$ is the number of three-dimensional voids (i.e., complement of three-dimensional excursion regions). Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. ${\beta}_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). ${\beta}_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-density surfaces, and ${\beta}_2$ corresponds to the low-threshold part measuring the void abundance. We average the Betti number curves (the Betti numbers as a function of the threshold level) over many realizations of Gaussian fields and find that both the amplitude and shape of the Betti number curves depend on the slope of the power spectrum n in such a way that their shape becomes broader and their amplitude drops less steeply than the genus as n decreases. This behaviour contrasts with the fact that the shape of the genus curve is fixed for all Gaussian fields regardless of the power spectrum. Even though the Gaussian Betti number curves should be calculated for each given power spectrum, we propose to use the Betti numbers for better specification of the topology of large scale structures in the universe.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.1
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• pp.40.1-40.1
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• 2017

The NISS (Near-infrared Imaging Spectrometer for Star formation history) is the near-infrared spectro-photometric instrument optimized to the Next Generation of small satellite series (NEXTSat). To achieve the major scientific objectives for the study of the cosmic star formation in local and distant universe, the spectro-photometric survey covering more than 100 square degree will be performed. The main observational targets will be nearby galaxies, galaxy clusters, star-forming regions and low background regions. The off-axis optics was developed to cover a wide field of view ($2deg.{\times}2deg.$) as well as the wide wavelength range from 0.95 to $2.5{\mu}m$, which were revised based upon the recent test and evaluation of the NISS instrument. The mechanical structure were tested under the launching condition as well as the space environment. The signal processing from infrared sensor and the communication with the satellite were evaluated after the integration into the satellite. The flight model of the NSS was assembled and integrated into the satellite. To verify operations of the satellite in space, the space environment tests such as the vibration, shock and thermal-vacuum test were performed. The accurate calibration data were obtained in our test facilities. Here, we report the test results of the flight model of the NISS.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.49.1-49.1
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• 2014

The NISS (Near-infrared Imaging Spectrometer for Star formation history) onboard NEXTSat-1 is the near-infrared instrument onboard NEXTSat-1 which is being developed by KASI. The imaging low-resolution spectroscopic observation in the near-infrared range for nearby galaxies, low background regions, star-forming regions and so on will be performed on orbit. After the System Requirement Review, the optical design is changed from on-axis to the off-axis telescope which has a wide field of view (2 deg. ${\times}$ 2 deg.) as well as the wide wavelength range from 0.95 to $3.8{\mu}m$. The mechanical structure is considered to endure the launching condition as well as the space environment. The design of relay optics is optimized to maintain the uniform optical performance in the required wavelength range. The stray light analysis is being made to evade a light outside a field of view. The dewar is designed to operate the infrared detector at 80K stage. From the thermal analysis, we confirmed that the telescope can be cooled down to around 200K in order to reduce the large amount of thermal noise. Here, we report the current status of the NISS development.