Graph partitioning, or the dividing of a graph into two more parts based on certain conditions, arises naturally throughout discrete mathematics, and problems this kind have been studied extensively. In 1990s, Ando conjectured that vertices every cubic can be partitioned induce isomorphic subgraphs. Using probabilistic methods together with delicate recolouring arguments, we prove Ando's conjec...

synovial mesenchymal stem cells and hydroxyapatite-based artificial bone +Shimomura K; Moriguchi Y; Ando W; Nansai R; Susa T; Imade K; Mochiduki S; Fujie H; Kita K; Mae T; Nakata K; Shino K; Yoshikawa H; Nakamura N +Osaka University Graduate School of Medicine, Osaka, Japan, Kansai Rosai Hospital, Hyogo, Japan, Kogakuin University, Tokyo, Japan, Tokyo Metropolitan University, Tokyo, Japan, Osak...

Let $$H$$ be a Hilbert space. We investigate the properties of weak limit points iterates random projections onto $$K\geq 2$$ closed convex sets in and parallel residuals greedy approximation with respect to $$K$$ dictionaries. In case these imply convergence all cases known so far. particular, we give short proof theorem Amemiya Ando on when are subspaces. The question general remains open.