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In 6, the authors construct a cochain complex C\!H^* (Z₊) on the cohomology of a moment-angle complex Z₊ and call the resulting cohomology the double cohomology, H\!H^* (Z₊). In this paper, we study the change of rank in double cohomology after gluing an n-simplex to a simplicial complex K in certain conditions. As an application, we give a positive answer to an open problem in 6: For any even integer r, there always exists a simlicial complex K such that rank H\!H^* (Z₊) =r.
Zhilei Zhang (Wed,) studied this question.