Blow up analysis for Boltzmann-Poisson equation in Onsager's theory for point vortices with multi-intensities

In this paper we consider the minimizing sequence for some energy functional of an elliptic equation associated with the mean field limit of the point vortex distribution one-sided Borel probability measure. If such a sequence blows up, we derive some estimate which is related to the behavior of solution near the blow-up point. Moreover, we study the two intensities case to consider the sufficient condition for this estimate. Our main results are new for the standard mean field equation as well.Comment: arXiv admin note: text overlap with arXiv:1412.490

Uniqueness of Nash equilibria in quantum Cournot duopoly game

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.Comment: 7 pages, 2 figure

Overview of the Nishinoshima comprehensive scientific research project, in 2021

小笠原諸島の西之島は2013年から2021年までに5度の噴火で元の陸地は全域が溶岩に覆われ、火山灰が堆積して大地がリセットされた。この島は太平洋上に孤立し、最寄の陸地から130kmも隔離された無人島であることから、海洋島における生態系の一次遷移を人為的影響のない状態で観察できる世界に例のない場所と言える。生物、地質及び火山活動における網羅的な分野の調査を噴火直後から実施することで、火山島の形成過程、噴火による生物相への影響、新たな遷移の開始時点の状況等を把握することができる。そこで、西之島の自然環境の最新情報を記録して科学的価値を評価するための総合学術調査が企画され、2019年調査に続き、2021年7月、9月の2度にわたり、モニタリング調査を実施した。新規に海域調査を実施したほか、UAVやAUVを活用した新規の調査も取り入れた。本調査は環境省とともに、東京大学及び日本放送協会との連携により行われている。調査の実施に当たっては、火山活動が活発な島における安全管理には十分配慮したほか、調査による人為的な影響を最小限に抑えるため、外来生物の侵入を防止するための検疫を徹底した。Nishinoshima Island in the Ogasawara Islands has erupted five times between 2013 and 2021. The entire original land area was covered by lava, as well as by thick deposits of volcanic ash that have reset the land surface. As an uninhabited island isolated in the Pacific Ocean and 130 km apart from the nearest land, it offers an unique opportunity to observe primary succession on an oceanic island without human impacts. Thus, it is important to conduct comprehensive field surveys on its biota, geology and volcanic activities immediately after the eruption in order to understand the formation process of the volcanic island, the impact of the eruption on the biota, and the situations at the start of primary succession. Therefore, a comprehensive scientific survey was planned to record the latest information on the nature of Nishinoshima Island and assess its scientific value. It was conducted twice, in July and September 2021, following the 2019 survey. This is the first survey of marine biota around Nishinoshima Island, and UAVs and AUVs were also actively used to conduct the survey safely during volcanic activity. The survey was carried out in collaboration with the Ministry of the Environment, the University of Tokyo and the Japan Broadcasting Corporation (NHK). In carrying out the survey, sufficient attention was paid to safety management on the volcanically active island, and quarantine was also strictly enforced as a measure to prevent the invasion of alien species in order to eliminate any human impact of the survey.departmental bulletin pape