Fishes of the Eleven Point River Within Arkansas

A survey of the fishes of the Eleven Point River and its tributaries was made between 31 January 1976 and 13 February 1977. Sixty-three collections, literature records and personal communications revealed 90 species distributed among 19 families. This study revealed 31 species previously not reported for this river system. The Eleven Point River is a clear, predominantly springfed Ozark stream which is located in western Randolph County. From the Arkansas-Missouri state line, the Eleven Point River flows south for approximately 64 km before joining the Spring River. Terrain in the Arkansas portion of this river is rugged as the river meanders through the Salem Plateau of the Ozark Mountains

Locating a robber with multiple probes

We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m\geq n$. The present authors showed that, for all but a few small values of $n$, this bound may be improved to $m\geq n/2$, which is best possible. In this paper we consider the natural extension in which the cop probes a set of $k$ vertices, rather than a single vertex, at each turn. We consider the relationship between the value of $k$ required to ensure victory on the original graph and the length of subdivisions required to ensure victory with $k=1$. We give an asymptotically best-possible linear bound in one direction, but show that in the other direction no subexponential bound holds. We also give a bound on the value of $k$ for which the cop has a winning strategy on any (possibly infinite) connected graph of maximum degree $\Delta$, which is best possible up to a factor of $(1-o(1))$.Comment: 16 pages, 2 figures. Updated to show that Theorem 2 also applies to infinite graphs. Accepted for publication in Discrete Mathematic

Subdivisions in the Robber Locating Game

We consider a game in which a cop searches for a moving robber on a graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m \geqslant n$. They conjectured that this bound was best possible for complete graphs, but the present authors showed that in fact the cop wins on $K^{1/m}$ if and only if $m \geqslant n/2$, for all but a few small values of $n$. In this paper we extend this result to general graphs by proving that the cop has a winning strategy on $G^{1/m}$ provided $m \geqslant n/2$ for all but a few small values of $n$; this bound is best possible. We also consider replacing the edges of $G$ with paths of varying lengths.Comment: 13 Page

Rangeland Production Risk Management in Wyoming

Production Economics,

Rangeland Production Risk Management in Montana

Risk and Uncertainty,

Antitrust Immunity and the Economics of Occupational Licensing

[Excerpt] The proposition that the common law tends to evolve in the direction of economic efficiency has been advanced by Posner and others. This proposition implies that, over time, legal precedent which promotes efficiency of exchange in the market, and thus maximizes the wealth of market agents, will displace precedent that is incompatible with this objective. In evaluating market impact, however, it is important to note that legal precedent which is perceived to be compatible with efficient exchange when viewed from the perspective of outmoded economic theory may not be as compatible as it appears