A note on discrete wave packet frames in ℂN

We show that for every nonzero vector [Formula: see text] in [Formula: see text], the discrete wave packet system [Formula: see text] constitutes a frame for the unitary space [Formula: see text]. An application of this result is given, where frame conditions cannot be derived from discrete wavelet systems in [Formula: see text]. The canonical dual of discrete wave packet frame is also discussed.

PROTECTION OF THE SEA REGION FROM OIL POLLUTION BY TANKER SHIP

In the context of national law, Law Number 32 Year 2009 concerning Environmental Protection and Management (UUPPLH) provides an understanding of the environment as a unitary space with all objects, forces, and living things, including humans and their behavior, which affect nature itself, continuity of life, and the welfare of humans and other living things. Environmental protection has general principles, namely: Sovereignty over natural resources and the responsibility not to cause damage to the environment of other states or areas beyond national jurisdiction; Principle of preventive action; Cooperation; Sustainable development. Specifically the mandate of the 1945 Constitution is spelled out in the weighing section of Law Number 32 of 2009 concerning Protection of Environmental Management (UUPPLH) which states that a good and healthy environment is the human right of every Indonesian citizen as mandated in Article 28H of the Law 1945 Constitution of the Republic of Indonesia. This law states that environmental protection and management are systematic and integrated efforts undertaken to preserve environmental functions and prevent environmental pollution and / or damage which includes planning, utilization, control, maintenance, supervision and law enforcement.

Bezirke als neue Räume der Verwaltung

This article deals with the introduction of state administrative institutions at the district level in the Habsburg Monarchy and their several reforms in the period from 1848 to 1868. It analyzes these processes in a spatial perspective and with a focus on implementation. First, it shows that new spaces of administration were constructed on several levels, especially the districts themselves and the district offices. This was done not by unilaterally expunging earlier forms of spatial organization, but rather in complex interplay with them. Numerous groups of actors were involved in negotiating this, including not only politicians and bureaucrats, but also members of the general population in various roles. In this sense there was a substantial component of ›state-building from below‹ in the creation of the district administrations. Finally, some consequences arising from the new organization of space are outlined, from the quantitative increase in state administrative activity via improved possibilities for production and use of spatial knowledge to advances in the construction of the territory as a unitary space of the state.