In the "lost notebook", Ramanujan recorded infinite product expansions for where r -= r(q) is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan's function k ...
In this paper, we prove the following result. Let ξ be a saturated formation and ∑ a Hall system of a soluble group G. Let X be a w-solid set of maximal subgroups of G such that ∑ reduces into each element of X. Co...
The work is partially supported by NNSF of China(10471078)RSDP of China
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f betwo integer-valued functions defined on V(G) such that 2k - 2 ≤ g(x) ≤ f(x) for all x ∈ V(G).Let H be a subgraph of G with mk edges. In this...