Systems Ay ≥ 0 with a degenerate cone of solutions are considered ill-posed since finite-precision algorithms are not expected to find points in the cone of solutions. Consequently, common condition numbers for these systems, such as C(A) [15] and C (A) [2], which are based on the notion of distance to the nearest ill-posed problem, become infinite on such ill-posed instances. In this paper we ...

Relief wells are used extensively to relieve excess hydrostatic pressure in pervious foundation strata overlain by impervious top strata, conditions which often exist landward of levees and downstream of dams and hydraulic structures. Placing well outlets in below-surface trenches or collector pipes helps dry up seepage areas downstream of levees and dams. Relief wells are often used in combina...

The topic of this paper arises naturally in the context of affine Springer fibers, which we now take a moment to discuss. Let G be a semisimple complex algebraic group, and let g denote its Lie algebra. We then have the affine Grassmannian X = G(F )/G(O), where O is the ring C[[ǫ]] of formal power series, and F is its fraction field C((ǫ)). For any u ∈ g(F ) = g ⊗C F the closed subset X = {g ∈ ...

The μ-invariant μ = (μ1, μ2, μ3) of a rational space curve gives important information about the curve. In this paper, we describe the structure of all parameterizations that have the same μ-type, what we call a μ-stratum, and as well the closure of strata. Many of our results are based on papers by the second author that appeared in the commutative algebra literature. We also present new resul...

In order to determine the pattern and timing of exhumation and uplift in the Teton Range, fission-track analysis of apatites has been applied to three sections encompassing ~ 2 km of vertical relief along the Teton escarpment. The resulting data provide new insights on the doming of the Precambrian-Cambrian unconformity and on the Teton exhumation/uplift history prior to the Miocene initiation ...

One hundred fifty-one patients with primary biliary cirrhosis (PBC) grouped into four strata based on entry serum bilirubin ( < 2 mg/dL vs. 2 md/dL or greater) and liver histology (stages I, II vs. stages III, IV-Ludwig criteria) were randomized within each stratum to ursodiol or placebo given in a single dose of 10 to 12 mg/kg at bedtime for 2 years. Placebo- (n = 74) and ursodiol- treated (n ...