Classification of Generalized Multiresolution Analyses

We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions $m$ and matrix-valued filter functions $H$. Given a natural number valued function $m$ and a system of functions encoded in a matrix $H$ satisfying certain conditions, a construction procedure is described that produces an abstract GMRA with multiplicity function $m$ and filter system $H$. An equivalence relation on GMRAs is defined and described in terms of their associated pairs $(m,H)$. This classification system is applied to classical examples in $L^2 (\mathbb R^d)$ as well as to previously studied abstract examples.Comment: 18 pages including bibliograp

The Effect of O-Phenylphenol on the Growth of Some Fungi Occurring in Wood

It is often difficult or impossible to obtain cultures of wood rotting fungi from pieces of decayed wood placed on agar media, because other fungi present in the wood grow out rapidly and hide or suppress the fungus or fungi responsible for the decay. Trichoderma viride Pers. occurs very commonly in decayed wood, grows rapidly on agar media suitable for the isolation of wood-rotting fungi, and makes the isolation of wood decay fungi difficult. Russell (2) reported that Ophenylphenol added to the culture medium at the rate of 0.06 grams per liter would inhibit the growth of Trichoderma but permit wood rotting fungi to grow, although it did inhibit Merulius lacrymans (Wulf.) Fr., a fungus that causes brown rot. Denyer ( 1) tested 20 species of fungi and found that a medium containing O-phenylphenol had little or no inhibitory effect on fungi that cause white rot and on some of those that cause brown rot, but did inhibit some fungi that cause brown cubical rot. Isolations by the authors from decayed wood from buildings, using a medium containing O-phenylphenol, and involving white and brown rots, often failed to yield any wood rotting fungi. For this reason it seemed desirable to determine the effect of O-phenylphenol in the medium upon the growth of some of the common fungi known to cause either white rot or brown rot

Interaction of H_2 and O_2 on platinum (111)

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The Origins of the American Public Trust Doctrine: What Really Happened in Illinois Central

Great cases have the power to shape attitudes about the law in a way that goes far beyond the particular legal propositions for which they stand. Witness the power of Marbury v Madison in supporting an expansive power of judicial review, or of Brown v Board of Education in undermining the legitimacy of invidious racial classifications. Illinois Central Railroad Company v Illinois plays a similar role in the public trust doctrine. The force of Illinois Central, however, derives not so much from its fine phrases or the courage that it took for the Court to reach the decision it did. Rather, Illinois Central is a compelling precedent largely because of its facts, or at least what are presumed to be its facts. The Illinois legislature granted the entire Chicago lake-front, over one thousand acres, to a private railroad corporation! Small wonder that the legislature quickly repented of this deed, or that the Court was compelled to say that this valuable resource is impressed with a public trust that means it can never be sold to a private entity. We have tried to show how the Lake Front Act of 1869 came to be passed, why the railroad's motives were not as pernicious as they are usually portrayed to have been, and how a conscientious legislator might have decided to vote in favor of the Act. We have also concluded that most probably the railroad used corrupt means to procure the legislation. So the reality is more complex than the standard story even begins to intimate. None of this is to suggest that the public trust doctrine is necessarily a bad idea or a good one. But it does suggest that the doctrine should be assessed using arguments more probing than a retelling of the standard narrative of the Illinois Central case. That story is a fable, and can justify the doctrine only if we already believe in it for reasons independent of the lesson the case supposedly teaches

The Great Transformation of Regulated Industries Law

The nation's approach to regulating its transportation, telecommunications, and energy industries has undergone a great transformation in the last quarter-century. The original paradigm of regulation, which was established with the Interstate Commerce Act's regulation of railroads beginning in 1887, was characterized by legislative creation of an administrative agency charged with general regulatory oversight of particular industries. This approach did not depend on weather the regulated industry was naturally competitive or was a natural monopoly, and it was designed to advance accepted goals of reliability and, in particular, non-discrimination. By contrast, under the new paradigm, which is manifested most clearly in the Telecommunications Act of 1996, the goals of regulation have become the promotion of competition and maximization of consumer choice. The role of agencies has been reduced to monitoring access and pricing of "bottleneck" monopolies such as the local telecommunications loop and electricity distribution systems. Having described this transformation in six core common carrier and public utility industries -- railroads, airlines, trucks, telecommunications, electricity, and natural gas -- the Article sets out on a quest to find its causes. No consistent pattern of institutional leadership can be discerned in any of the three types of government actors with the power to compel change: the regulatory agencies, the courts, and the Congress. This suggests that the causes are rooted in deep-seated economic and social forces, such as technological changes, and chain reactions that have emerged as regulatory reform in one industry segment has spread to another segment. The Article concludes that the two most persuasive explanations are that key interest groups have discovered that regulatory change is in their interests, and that an ideological consensus has emerged among economists and other policy elites that the original paradigm entails risks of regulatory failure that exceed the risks of market failure under the new paradigm

Contested Shore: Property Rights in Reclaimed Land and the Battle for Streeterville

Land reclaimed from navigable waters is a resource uniquely susceptible to conflict. The multiple reasons for this include traditional hostility to interference with navigable waterways and the weakness of rights in submerged land. In Illinois, title to land reclaimed from Lake Michigan was further clouded by a shift in judicial understanding in the late nineteenth century about who owned the submerged land, starting with an assumption of private ownership but eventually embracing state ownership. The potential for such legal uncertainty to produce conflict is vividly illustrated by the history of the area of Chicago known as Streeterville, the area of reclaimed land along Lake Michigan north of the Chicago River and east of Michigan Avenue. Beginning in the 1850s, Streeterville was subject to repeated waves of litigation, assertions of squatters’ rights (most notably by George Wellington Streeter, for whom the area is named), conspiracies to obtain federal land grants based on veterans’ rights, schemes in reliance on claims of Native Americans, and a public works project designed to secure the claims of wealthy riparian owners. The riparian owners eventually won the many-sided battle, but only after convincing institutions such as Northwestern University to build substantial structures on the land. The history of Streeterville suggests that when legal title to reclaimed land is highly uncertain, conflict over control of the land is likely to persist until one or more persons succeed in establishing what is perceived to be possession of the land