1, This work organised the known theory of permutation groups and its relationship with Galois Theory.

2, The symmetry group is the permutation group acting to exchange particles of the same type.

3, A permutation group approach to a one dimensional Heisenberg open spin 12 chain with nearest neighbor interactions is studied.

4, There were 3 subluxations in unpermutation group and 5 in permutation group after patellar replacement.

5, With each recursive step, cross products with one additional Permutation Group are formed.

6, To extract additional information from votes, the CBM uses multiple feature matrices, probability feature matrices, vectors and permutation group as basic components.

7, According to the property that all states of a certain cellular automata can build a permutation group, we can design block cipher based on this property.

8, By means of analyzing the equivalence relation of reversible gate logic network to permutation group,[http:///permutation group.html] the reversible gate network cascade was converted into the cycle of symmetric group.

9, In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.

10, The expressions of the chromatic function and the chromatic weight polynomial of a P-graph about a permutation group H are established, de Bruijn s Theorem follows from th.

11, We start by forming an ArrayList containing a set of ArrayLists, in which each of the constituent ArrayLists contains exactly one element of the first Permutation Group.

12, The total antisymmetric basis functions are constructed for irreducible representation of S3 permutation group from nine- dimensional hyperspherical harmonics.