In this paper, we determine completely the initial Fitting ideal of the minus part of the ideal class group of an abelian number field over Q up to the 2-component.This answers an open question of Mazur and Wiles (Invent Math 76:179-330, 1984) up to the 2-component, and proves Conjecture 0.

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Suppose that L/k is a finite and abelian extension such that k is a totally real base field and L is a CM-field. We regard the ideal class group Cl L of L as a Gal(L/k)-module. As a sequel of the paper [8] by the first author, we study a problem whether the Stickelberger element for L/k times the annihilator ideal of the roots of unity in L is in the Fitting ideal of Cl L , and also a problem whether it is in the Fitting ideal of the Pontrjagin dual (Cl L ) ∨ . We systematically construct extensions L/k for which these properties do not hold, and also give numerical examples.

Wireless network technology has been well developed and used for various applications in the world. Particularly in resident area, most people use Wi-Fi system such as IEEE802.11a.b.g.n system as access lines to Internet. However, since most of the residents leak their electromagnetic waves to neighbor without any security keys, the network security problems have become serious in resident areas. On the other hand, large scale disasters in metropolitan areas as well as country side area in Japan are anticipated. In those cases of natural disasters information infrastructure must be preserved to keep the safe life for residents.In this paper, we propose a disaster communication network method based on leaked wave from resident wireless LANs system. The leaked waves outdoor from each resident can be used as urgent information infrastructure on which not only residents but public officers can also use to transmit the disaster information, resident safety information, evacuation information each other through Internet. We investigated practical feasibility of the disaster communication network by the leaked wave by evaluating the throughput, round trio time in actual resident area in Japan. Throughput this performance evaluation, we could verify the feasibility of our suggested disaster network method.

In this paper, the influence of our proposed Urban Disaster Information System by moving object is experimented and discussed. It is widely known that the network conditions between wireless node and the setup wireless LAN (Access point) is influenced by moving objects like cars, animals, and bullet train. Therefore, Disaster Information System in urban area is necessary to consider with the influences by such moving objects in order to main QoS like audio and video transmission. The field experiment is held by using moving cars and trains, and the observed electromagnetic wave is discussed for the influence for our proposed Disaster Information Networks.