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A set a1 …, ak of different residues mod v is called a difference set (v, k, λ) (v>k > λ) if the congruence ai — aj ≡ d (mod v) has exactly λ solutions for d ≢ 0 (mod v). Singer  has demonstrated the existence of a difference set (v, k, 1) if k — 1 is a prime power, and difference sets for λ > 1 have been constructed by various authors; but necessary and sufficient conditions for the existence of a (v, k, λ) are not known. It has not been possible so far to find a difference set with λ = 1 if k — 1 is not a prime power and it has therefore been conjectured that no such difference set exists.
Molecular studies have shown the type collection of Omphalina oreades to be conspecific with a small brown basidiolichen from the Appalachian range in Newfoundland, both with 4-spored basidia. Two sequences deposited in GenBank, originally identified as O. grisella, fell in the same clade. Sequences of the type collection of Omphalia grisella, with 2-spored basidia, formed a sister clade together with two GenBank deposits, one identified as O. grisella and the other as Omphalina velutina. Omphalina oreades is recombined here as Lichenomphalia oreades comb. nov., and the species redescribed and illustrated. Sequences of the internal transcribed spacer regions of nuclear ribosomal DNA (ITS rDNA) from the algae associated with two collections of L. oreades fell within a highly supported clade with members of an undetermined species of Coccomyxa. The most abundant algal ribosomal large subunit sequence from granules at the base of a different collection matched GenBank sequences identified as Chloroidium ellipsoideum, which is probably either a free-living algal species or a partner to a species of Trapeliopsis. The second most abundant sequence matched Coccomyxa subellipsoidea and is the most likely photobiont of L. oreades. Further studies are required to elucidate the relationship of L. velutina to these taxa.
The conventional approach to a merger problem takes corporations merely as decision-making units or firms within the classical market framework. This approach dictates a ban on many horizontal mergers almost by definition. The basic proposition advanced in this paper is that the control of corporations may constitute a valuable asset, that this asset exists independent of any interest in either economies of scale or monopoly profits, that an active market for corporate control exists, and that a great many mergers are probably the result of the successful workings of this special market.
Basically this paper will constitute an introduction to a study of the market for corporation control. The emphasis will be placed on the antitrust implications of this market, but the analysis to follow has important implications for a variety of economic questions. Perhaps the most important implications are those for the alleged separation of ownership and control in large corporations. So long as we are unable to discern any control relationship between small shareholders and corporate management, the thrust of Berle and Means's famous phrase remains strong. But, as will be explained below, the market for corporate control gives to these shareholders both power and protection commensurate with their interest in corporate affairs.
A fundamental premise underlying the market for corporate control is the existence of a high positive correlation between corporate managerial efficiency and the market price of shares of that company.
Many small communities use septic tanks as a method of partial sewage treatment in situations where effluents may be satisfactorily discharged into the soil. These systems are also suitable for use in many situations where intermittent occupation occurs. Where effluents are discharged into streams in which serious pollution is likely, further treatment by secondary processes is necessary, and in many situations tertiary treatment processes are added as a final safeguard. Prefabricated or package-plant systems using variants of the activated-sludge process or special types of percolating filter, have become available and can be designed by the manufacturers to satisfy all of the purposes of primary and secondary treatment in specific situations. Maintenance requirements of most of these processes are small, but no system may be operated for long periods without a minimum of maintenance.
Some of the simplest systems of sewage treatment can provide excellent sanitary conditions and a high level of protection from health hazards and environmental deterioration if properly designed and operated. Package plants are compact and convenient but not necessarily more effective. They are usually dependent on a reliable power-supply, but have many advantages on restricted sites or sites requiring rapid development or expansion.
Applications have been received from Dr. Peter Wheatley (proposed by UK), Prof. Harald Schuh (proposed by Austria), and Dr. Busaba Kramer (proposed by Thailand). All applications were endorsed, with the caveat that Dr. Kramer's application needs to be endorsed by at least one of the other commissions since she has not a publication record in our field.
Commission 21, one of IAU's smallest commissions, consists of some hundred members and consultants working to understand and describe the light of the night sky with emphasis on the diffuse components. Many more work on these topics without being members of the commission. Light is here defined in its broader sense of electromagnetic radiation of any frequency. The diffuse components of the light of the night sky encompass a variety of physical phenomena over the full range of cosmic distance scales and include scattered light, thermal emission, line emission, and any other emission phenomena producing a diffuse light source. These attract interest not only as scientific topics of study in their own right but also as an unwanted foreground or background against which all other sky phenomena are observed. Commission 21 has for mandate to promote research and availability of results on issues related to the diffuse light of the night sky. This document is a report on activities in this field and is not confined to the activities of its members, no distinction is made between work carried out by commission members and non commission members. The report is organized starting with a summary of the state of broad surveys that provide most of the observations. The report on developments in the various disciplines start with the sources closest to the observer known as airglow and progresses by way of the interplanetary and interstellar mediums to the increasingly distant integrated starlight, diffuse galactic light and diffuse emission in other galaxies ending with the extragalactic background radiation.
Although the three-dimensional structure of the
dimeric class 3 rat aldehyde dehydrogenase has recently
been published (Liu ZJ et al., 1997, Nature Struct
Biol 4:317–326), few mechanistic studies have
been conducted on this isoenzyme. We have characterized
the enzymatic properties of recombinant class 3 human stomach
aldehyde dehydrogenase, which is very similar in amino
acid sequence to the class 3 rat aldehyde dehydrogenase.
We have determined that the rate-limiting step for the
human class 3 isozyme is hydride transfer rather than deacylation
as observed for the human liver class 2 mitochondrial enzyme.
No enhancement of NADH fluorescence was observed upon binding
to the class 3 enzyme, while fluorescence enhancement of
NADH has been previously observed upon binding to the class
2 isoenzyme. It was also observed that binding of the NAD
cofactor inhibited the esterase activity of the class 3
enzyme while activating the esterase activity of the class
2 enzyme. Site-directed mutagenesis of two conserved glutamic
acid residues (209 and 333) to glutamine residues indicated
that, unlike in the class 2 enzyme, Glu333 served as the
general base in the catalytic reaction and E209Q had only
marginal effects on enzyme activity, thus confirming the
proposed mechanism (Hempel J et al., 1999, Adv Exp
Med Biol 436:53–59). Together, these data suggest
that even though the subunit structures and active site
residues of the isozymes are similar, the enzymes have
very distinct properties besides their oligomeric state
(dimer vs. tetramer) and substrate specificity.
In a recent paper I. J. Schoenberg  considered relations
where the av are rational integers and the ζv are roots of unity. We may in (1) replace all negative coefficients av by −av replacing at the same time ζv by −ζv so that we may, if it is convenient, assume that all av are positive. If we do this and arrange the ζr so that their arguments do not decrease with v then (1) can, as suggested by Schoenberg (oral communication) be interpreted as a convex polygon with integral sides whose angles are rational when measured in degrees. Accordingly we shall call a relation (1) a polygon if all av are non-negative. We shall call a polygon (1) k-sided if all av are positive. The polygon is called degenerate if two of the ζv are equal. Schoenberg calls these polygons polar rational polygons (abbreviated prp) because the vectors composing them have rational coordinates in their polar representations. Schoenberg showed that every prp can be obtained as a linear combination with integral positive or negative coefficients of regular p-gons where p is a prime.
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