On Central Gap Numbers of Symmetric Groups

g(G) denotes the central gap number of a group G. We show that for n &#8805; 8, g(Sn) &#8805; n and g(An) &#8805; n-2. We give exact values of g(Sn) and g(An) for small n's. In particular, g(S9) = 9 and g(A9) = 7. Therefore, for any positive integer n &#8800; 1, 3, 5 there is a group G such that n = g(G). G can be finite or infinite.</p

Image processing using miniKanren

An integral image is one of the most efficient optimization technique for image processing. However an integral image is only a special case of delayed stream or memoization. This research discusses generalizing concept of integral image optimization technique, and how to generate an integral image optimized program code automatically from abstracted image processing algorithm. In oder to abstruct algorithms, we forces to miniKanren

Model companions of theories with an automorphism

For a theory $T$ in $L, T_\sigma$ is the theory of the models of $T$ with an automorphism $\sigma$. If $T$ is an unstable model complete theory without the independence property, then $T_\sigma$ has no model companion. If $T$ is an unstable model complete theory and $T_\sigma$ has the amalgamation property, then $T_\sigma$ has no model companion. If $T$ is model complete and has the fcp, then $T_\sigma$ has no model completion