Generating Subsets

Recall that the intersection of closed subsets is closed. Therefore (R) is closed for each subset R of S. 

The first section of this chapter is a collection of basic facts about generating sets of closed subsets. We introduce the length function which one obtains from generating subsets, and we establish a connection between generating subsets and commutator subsets. 

In the second section, we introduce the thin residue of a closed subset. The thin residue is a specific commutator subset. We look at the thin residue of a complex product of two closed subsets, at the complex product of the thin residue and the thin radical, and at multiple thin residues of closed subsets. 

In the third section of this chapter, we investigate closed subsets of S generated by elements of valency 2. We start with closed subsets of S which are generated by a single symmetric element of valency 2. After that, we shall look at more general cases. 

Generating sets of elements of S are particularly interesting if they consist of involutions. In fact, a major part of this monograph deals with closed subsets generated by distinguished sets of involutions. Section 3.4 deals with general aspects of closed subsets generated by involutions. 

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Operator 1 ), by (15.56), is proportional to the quasispin operator, and operator W<0kK by (15.59), to double tensor with an odd sum of ranks k + k. These tensors, as shown in Chapter 14, are generators of the Sp4i+2 group, and so the above selection of generator subsets corresponds to the reduction of the Rsi+4 group on the direct product of two subgroups ... 

The following lemma shows in which way generating subsets of S and faithful maps work together. 

PISCES Protein sequence culling server generates subsets of PDB based on users criteria http //dunbrack.fccc.edu/PIS- CES.php/... 

The method generates subset of possible workspace and moves the tip of the gel in the plane. From the viewpoint of problem solving algorithm, it is evaluated that this inverse kinematic model as practical approach efficiency is in high... 

A library is a set of compounds made in parallel fashion that bear a common feature [31]. Their largest common denominator is the scaffold. In extreme cases, the scaffold could be a single functional moiety, such as an amide in a library made from a set of commercial amines and a set of commercial carboxylic acids. The concept of diversity-oriented synthesis usually generates subsets of scaffolds (vide infra). 

The optimal scheduling problem can be reduced to the problem of the optimal selection of one generated subset and assignment. This selection is controlled by the here socalled rating function (fig. 10). Since the rating function det mines the result of the scheduling the rest of this chapter concentrates on it. 

A feature selection process mainly consists of two parts feature subset generation and feature subset evaluation. Feature subset generation is a searching procedure. It generates subsets of features for... 

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