When a bright astronomical object (source) is gravitationally lensed by a foreground mass (lens), its image appears to be located at different positions. The lens equation describes the relations between the locations of the lens, source, and images. The lens equation used for the description of the lensing behavior caused by a lens system composed of multiple masses has a form with a linear combination of the individual single lens equations. In this paper, we examine the validity of the linear nature of the multi-lens equation based on the general relativistic point of view.

To examine the effect of neighboring galaxies on the gravitational lensing statistics, we performed numerical simulations of lensing by many galaxies. The models consist of a galaxy in the rich cluster like Coma, or a galaxy surrounded by field galaxies in Ω0 = 1 universe with Ωgal = 0.1, Ωgal = 0.3 or Ωgal=1.0, Ωgal is the total mass in galaxies. Field galaxies either have the same mass or follow Schechter luminosity function and luminosity-velocity relation. Each lensing galaxy is assumed to be singular isothermal sphere (SIS) with finite cutoff radius. In most simulations, the lensing is mainly due to the single galaxy. But in Ωgal = 0.3 universe, one out of five simulations have 'collective lensing' event in which more than two galaxies collectively produce multiple images. These cases cannot be incorporated into the simple 'standard' lensing statistics calculations. In cases where 'collective lensing' does not occur, distribution of image separation changes from delta function to bimodal distribution due to shear induced by the surrounding galaxies. The amount of spread in the distribution is from a few % up to ~50% of the mean image separation in case when the galaxy is in the Coma-like cluster or when the galaxy is in the field with Ωgal = 0.1 or Ωgal=0.3. The mean of the image separation changes less than 5% compared with a single lens case. Cross section for multiple image lensing turns out to be relatively insensitive to the presence of the neighboring galaxies, changing less than 5% for Coma-like cluster and Ωgal=0.1, 0.3 universe cases. So we conclude that Coma-like cluster or field galaxies whose total mass density Ωgal < 0.3 do not significantly affect the probability of multiple image lensing if we exclude the 'collective lensing' cases. However, the distribution of the image separations can be significantly affected especially if the 'collective lensing' cases are included. Therefore, the effects of surrounding galaxies may not be negligible when statistics of lensing is used to deduce the cosmological informations.

In this paper we propose a new perspective for explaining galaxy rotation curves. We conjecture that there is a gravitational moment of inertia which, together with gravitational mass, contributes to the gravitational potential. We substantiate a formula for the potential created by the moment of inertia. We validate our model by computing orbital rotation velocities for several galaxies and showing that computed rotation velocities correspond to the observed ones. Our proposed approach is capable of accounting for constant gas velocities outside of a galactic disc without relying on the dark matter hypothesis. Furthermore, it addresses several problems faced by the application of the dark matter hypothesis, e.g., the absence of inward collapse of dark matter into a galaxy, the spherical distribution of dark matter around galaxies, and absence of traces of the effect of dark matter in two ultra-diffuse galaxies, NGC 1052-DF2, and NGC 1052-DF4.

중첩에너지(FGFE)가 방사선조사식품의 판별 특성에 미치는 영향을 연구하고자, 밀과 대두를 시료로 0-5 kGy의 감마선을 조사한 다음 FGFE 처리된 시료의 발광특성(광자극발광, 열발광)과 발아율의 변화를 처리직후와 6개월 저장 후 비교하였다. 조사식품의 스크리닝 방법으로서 두 시료에 대한 광자극발광(PSL) 분석 결과, 비 조사 시료(0 kGy)는 모두 700 photon counts/min 이하의 음성(negative)을 나타내었고, 1 k