In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime numbe...In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.展开更多
In this short review we elaborate the significance of resummation in kτ factorization theorem,and summarize the recent progresses in the calculations of the next-to-leading order contributions to B meson decays from ...In this short review we elaborate the significance of resummation in kτ factorization theorem,and summarize the recent progresses in the calculations of the next-to-leading order contributions to B meson decays from the perturbative QCD(PQCD)approach.We also comment on the current sta-tus of the PQCD approach and highlight some key issues to develop it in the near future for more phenomenological applications.展开更多
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...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 paper, it is proved that every (mg + m - 1, mf - m +l)-graph G has (g, f)-factorizations randomly k-orthogonal to H under some special conditions.展开更多
文摘In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.
基金This work was sup-ported by the National Natural Science Foundation of China(NSFC)under Grant Nos.11805060,11975112,and 11775117.
文摘In this short review we elaborate the significance of resummation in kτ factorization theorem,and summarize the recent progresses in the calculations of the next-to-leading order contributions to B meson decays from the perturbative QCD(PQCD)approach.We also comment on the current sta-tus of the PQCD approach and highlight some key issues to develop it in the near future for more phenomenological applications.
基金The work is partially supported by NNSF of China(10471078)RSDP of China
文摘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 paper, it is proved that every (mg + m - 1, mf - m +l)-graph G has (g, f)-factorizations randomly k-orthogonal to H under some special conditions.
