LAWS, DECISIONS, AND RULINGS

Invariant representation for rectilinear rulings

Ruling gap ratios are an affine-invariant characterization of parallel ruling configurations in scanned documents. This report quantifies the advantage of simultaneous extraction of horizontal and vertical rulings. It demonstrates that every ruling gap ratio can be derived from a minimal set of basis ratios. The effect on the basis ratios of noise on the radial coordinates of individual rulings...

Rulings of Legendrian knots as spanning surfaces

Each ruling of a Legendrian link can be naturally treated as a surface. For knots, the ruling is 2–graded if and only if the surface is orientable. For 2–graded rulings of homogeneous (in particular, alternating) knots, we prove that the genus of this surface is at most the genus of the knot. While this is not true in general, we do prove that the canonical genus (a.k.a. diagram genus) of any k...

Allowance Trading Activity and State Regulatory Rulings :

The U.S. Acid Rain Program is one of the first, and by far the most extensive, applications of a market based approach to pollution control. From the beginning, there has been concern whether utilities would participate in allowance trading, and whether regulatory activity at the state level would further complicate utilities' decision to trade allowances. This paper finds that public utility c...

ADE-bundle over rational surfaces, configuration of lines and rulings

To each del Pezzo surface Xn (resp. ruled surface, ruled surface with a section), we describe a natural Lie algebra bundle of type En (resp. Dn−1, An−2) over it . Using lines and rulings on any such surface, we describe various representation bundles corresponding to fundamental representations of the corresponding Lie algebra. When we specify a geometric structure on the surface to reduce the ...

ADE-bundle over rational surfaces, configuration of lines and rulings