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For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rationalq-difference equation.
      
We also describe the multiplication rules of the above basos elements ofY.
      
These are analogous to "fusion rules" in tensor product decomposition and their derivation obtains from an analysis of theR-matrix.
      
The result generalizes and implies the classical "branching rules" that describe the restriction of an irreducible representation of the symmetric groupSn toSn-1.
      
By constructing an interval extension of adjustable entropy function and some region deletion test rules, a new interval algorithm is presented.
      
Parallel mining and application of fuzzy association rules
      
Then, we improve the search technology of apriori algorithm and present the algorithm for mining fuzzy association rules.
      
As the database size becomes larger and larger, a better way is to mine fuzzy association rules in parallel.
      
Boolean parallel algorithm is improved to discover frequent fuzzy attribute set, and the fuzzy association rules with at least a minimum confidence are generated on all processors.
      
Last, we discuss the application of fuzzy association rules in the classification.
      
The example shows that the accuracy of classification systems of the fuzzy association rules is better than that of the two popular classification methods: C4.5 and CBA.
      
Based on analyzing force distribution rules of the distance potential force field, a standard is introduced here to distinguish the false one from contour points.
      
The influence of the exciting current and armature reaction on the DC voltage ripple of the generator is discussed in detail, and the nonlinear rules are gained that DC voltage ripple changes accordingly.
      
In the mean time, some guidelines or "design rules" are summarized by the results of this study.
      
These differences were analyzed and discussed, and some basic rules of spatial distribution of landscape elements were proposed.
      
The EB test rules are constructed by the kernel estimation method.
      
The asymptotical optimality and convergence rates of the EB test rules are obtained.
      
A reduction algorithm based on rough set theory is designed to find minimum reducts from all discrete variables in the preparation set to represent diagnosis rules succinctly.
      
The diagnosis rules mining from SCADA systems' database are expressed directly by variables in the database, making it easy for engineers to understand and use in industry applications.
      
To recover the vehicle's kinetic energy maximally, braking shift rules for a mild hybrid electric vehicle (HEV) equipped with automatic manual transmission (AMT) are brought forward and effects of transmission ratios are considered.
      
 

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