Let Z denote a finite collection of reduced points in projective n-space and let I denote the homogeneous ideal of Z . The points in Z are said to be in (i, j)-uniform position if every cardinality i subset of Z imposes the same number of conditions on forms of degree j . The points are in uniform position if they are in (i, j)-uniform position for all values of i and j . We present a symbolic ...

II. STUDY DESIGN AND METHODOLOGY ..........................................430 A. Content Analysis.......................................................................431 B. Primer on the Doctrine of Equivalents.....................................432 C. Database Construction ............................................................435 D. Measurement Criteria..................................

In the first part, we introduce randomized algorithms as a new notion of efficient algorithms for decision problems. We classify randomized algorithms according to their error probabilities, and define appropriate complexity classes. (RP, coRP, ZPP, BPP, PP). We discuss which classes are realistic proposals for design of probabilistic algorithms. We cover the implementation of randomized algori...

1. Uniformity and correlation 1 1.

Introduction. The purpose of this report is to draw attention to some nontrivial connections between the ("continuous") theory of irregularities of distribution and discrete mathematics. The object of the theory of irregularities of distribution is to measure the uniformity (or nonuniformity) of sequences and point sets. For instance: how uniformly can an arbitrary set of N points in the unit c...

Let Z denote a finite collection of points in projective n-space and let I denote the homogeneous ideal of Z. The points in Z are said to be in (i, j)-uniform position if every cardinality i subset of Z imposes the same number of conditions on forms of degree j. The points are in uniform position if they are in (i, j)-uniform position for all values of i and j. We present a symbolic algorithm t...

The accurate production of a rainfall environment similar to natural rainfall by a rainfall simulator (RS) is a crucial and challenging task in rainfall instrument testing or calibration. Although the spatial uniformity of rainfall accumulation is a key parameter of an RS, the spatial uniformity comparison between simulated rainfall and natural rainfall, and the spatial uniformity improvements ...