We determine the upper central series of the maximal normal p–subgroup of the automorphism group of a bounded abelian p–group.

The coefficients c(n, k) defined by (1− kx) = X n≥0 c(n, k)x reduce to the central binomial coefficients `

and Applied Analysis 3 −λ (0, 0, rp) = − N 󵄨󵄨󵄨󵄨󵄨1 + r2 p󵄨󵄨󵄨󵄨󵄨3/2 (0, 0, rp) − (0, 0, 1 r2 p)M0 − ∑ 1≤i<p ( 1 󵄨󵄨󵄨󵄨󵄨ri − rp󵄨󵄨󵄨󵄨󵄨2 + 1 󵄨󵄨󵄨󵄨󵄨ri + rp󵄨󵄨󵄨󵄨󵄨2)Mi (0, 0, 1) − 1 󵄨󵄨󵄨󵄨󵄨2rp󵄨󵄨󵄨󵄨󵄨2Mp (0, 0, 1) . (11) In order to simplify the equations, we defined a0,j = −2/|1+r2 j |3/2, aj,j = −1/4r3 j , where j = 1, . . . , p; ai,j = (1/|ri − rj|2ri − 1/|ri + rj|2ri), when i < j; ai,j = −(1/|ri − rj|2ri + 1/...

Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...

Purpt~sc: To design :l rcproduciblc in vitro model to study central island (Cl) formation following PRK. To investignte technical parameters offccting tbc rate and chwxtcristics ofccntrrll islrmd alicr PICK. Methods: We wed PMMA contact lenses to nwdcl the convex quasispherical surface of the cornea. A total of 60 lenses were ablated using 3 different cxcimcr lasers. Lenses were nblated for n t...

We present an improved solution for the Firing Squad Synchronization Problem (FSSP) for digraph-based P systems. We improve our previous FSSP algorithm by allowing the general to delegate a more central cell in the P system to send the final command to synchronize. With e being the eccentricity of the general and r denoting the radius of the underlying digraph, our new algorithm guarantees to s...