When Should Sellers Use Auctions?

A bidding process can be organized so that offers are submitted simultaneously or sequentially. In the latter case, potential buyers can condition their behavior on previous entrants' decisions. The relative performance of these mechanisms is investigated when entry is costly and selective, meaning that potential buyers with higher values are more likely to participate. A simple sequential mechanism can give both buyers and sellers significantly higher payoffs than the commonly used simultaneous bid auction. The findings are illustrated with parameters estimated from simultaneous entry USFS timber auctions where our estimates predict that the sequential mechanism would increase revenue and efficiency.

Lakshmi Planum: A distinctive highland volcanic province

Lakshmi Planum, a broad smooth plain located in western Ishtar Terra and containing two large oval depressions (Colette and Sacajawea), has been interpreted as a highland plain of volcanic origin. Lakshmi is situated 3 to 5 km above the mean planetary radius and is surrounded on all sides by bands of mountains interpreted to be of compressional tectonic origin. Four primary characteristics distinguish Lakshmi from other volcanic regions known on the planet, such as Beta Regio: (1) high altitude, (2) plateau-like nature, (3) the presence of very large, low volcanic constructs with distinctive central calderas, and (4) its compressional tectonic surroundings. Building on the previous work of Pronin, the objective is to establish the detailed nature of the volcanic deposits on Lakshmi, interpret eruption styles and conditions, sketch out an eruption history, and determine the relationship between volcanism and the tectonic environment of the region

On the size of approximately convex sets in normed spaces

Let X be a normed space. A subset A of X is approximately convex if $d(ta+(1-t)b,A) \le 1$ for all $a,b \in A$ and $t \in [0,1]$ where $d(x,A)$ is the distance of $x$ to $A$. Let \Co(A) be the convex hull and \diam(A) the diameter of $A$. We prove that every $n$-dimensional normed space contains approximately convex sets $A$ with \mathcal{H}(A,\Co(A))\ge \log_2n-1 and \diam(A) \le C\sqrt n(\ln n)^2, where $\mathcal{H}$ denotes the Hausdorff distance. These estimates are reasonably sharp. For every $D>0$, we construct worst possible approximately convex sets in $C[0,1]$ such that \mathcal{H}(A,\Co(A))=\diam(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.Comment: 32 pages. See also http://www.math.sc.edu/~howard

Extremal Approximately Convex Functions and Estimating the Size of Convex Hulls

A real valued function $f$ defined on a convex $K$ is anemconvex function iff it satisfies $$f((x+y)/2) \le (f(x)+f(y))/2 + 1.$$ A thorough study of approximately convex functions is made. The principal results are a sharp universal upper bound for lower semi-continuous approximately convex functions that vanish on the vertices of a simplex and an explicit description of the unique largest bounded approximately convex function~$E$ vanishing on the vertices of a simplex. A set $A$ in a normed space is an approximately convex set iff for all $a,b\in A$ the distance of the midpoint $(a+b)/2$ to $A$ is $\le 1$. The bounds on approximately convex functions are used to show that in $\R^n$ with the Euclidean norm, for any approximately convex set $A$, any point $z$ of the convex hull of $A$ is at a distance of at most $[\log_2(n-1)]+1+(n-1)/2^{[\log_2(n-1)]}$ from $A$. Examples are given to show this is the sharp bound. Bounds for general norms on $R^n$ are also given.Comment: 39 pages. See also http://www.math.sc.edu/~howard

Update of MRST parton distributions.

We discuss the latest update of the MRST parton distributions in response to the most recent data. We discuss the areas where there are hints of difficulties in the global fit, and compare to some other updated sets of parton distributions, particularly CTEQ6. We briefly discuss the issue of uncertainties associated with partons

MRST global fit update.

We discuss the impact of the most recent data on the MRST global analysis - in particular the new high-ET jet data and their implications for the gluon and the new small x structure function data. In the light of these new data we also consider the uncertainty in predictions for physical quantities depending on parton distributions, concentrating on the W cross-section at hadron colliders