Let G be a graph of order n with minimum degree δ(G)≥n/2+1. Faudree and Li(2012) conjectured that for any pair of vertices x and y in G and any integer 2≤k≤n/2, there exists a Hamiltonian cycle C such that the dis...Let G be a graph of order n with minimum degree δ(G)≥n/2+1. Faudree and Li(2012) conjectured that for any pair of vertices x and y in G and any integer 2≤k≤n/2, there exists a Hamiltonian cycle C such that the distance between x and y on C is k. In this paper, we prove that this conjecture is true for graphs of sufficiently large order. The main tools of our proof are the regularity lemma of Szemer′edi and the blow-up lemma of Koml′os et al.(1997).展开更多
We report the application of multilayered polyelectrolyte-coated gold nanorods(GNRs) as multifunctional optical contrast agents for cancer cell imaging.The surface modification of GNRs improves their chemical stabilit...We report the application of multilayered polyelectrolyte-coated gold nanorods(GNRs) as multifunctional optical contrast agents for cancer cell imaging.The surface modification of GNRs improves their chemical stability and facilitates them to be taken up by cancer cells through electrostatic interaction.The unique longitudinal surface plasmon resonance property of GNRs makes them suitable as both "scattering contrast agents" and "Raman contrast agents".In our experiments,the staining of GNRs in cells was further confirmed by dark field microscopy and Raman microscopy.Our experiment results indicated that GNRs have great potential as multifunctional "optical contrast agents" for future in vivo animal imaging.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11601093 and 11671296)
文摘Let G be a graph of order n with minimum degree δ(G)≥n/2+1. Faudree and Li(2012) conjectured that for any pair of vertices x and y in G and any integer 2≤k≤n/2, there exists a Hamiltonian cycle C such that the distance between x and y on C is k. In this paper, we prove that this conjecture is true for graphs of sufficiently large order. The main tools of our proof are the regularity lemma of Szemer′edi and the blow-up lemma of Koml′os et al.(1997).
基金supported by the Swedish Foundation for Strategic Research (SSF) and the US Air Force Office of Scientific Research (Asia Office)
文摘We report the application of multilayered polyelectrolyte-coated gold nanorods(GNRs) as multifunctional optical contrast agents for cancer cell imaging.The surface modification of GNRs improves their chemical stability and facilitates them to be taken up by cancer cells through electrostatic interaction.The unique longitudinal surface plasmon resonance property of GNRs makes them suitable as both "scattering contrast agents" and "Raman contrast agents".In our experiments,the staining of GNRs in cells was further confirmed by dark field microscopy and Raman microscopy.Our experiment results indicated that GNRs have great potential as multifunctional "optical contrast agents" for future in vivo animal imaging.
