arXiv subjects

Jun Ge

Publications and source records attributed to Jun Ge.

40 records · Page 3Linked to original sources

arXiv2014

When will the crossing number of an alternating link decrease by two via a crossing change?

Let $D$ be a reduced alternating diagram of a non-split link $L$ and $\tilde{L}$ be the link whose diagram is obtained from $D$ by a crossing change. If $\tilde{L}$ is alternating, then $c(\tilde{L})\leq c(L)-2$. In this paper we explore when $c(\tilde{L})=c(L)-2$ holds and obtain a simple sufficient and necessary condition in terms of plane graphs corresponding to $L$. This result is obtained via analyzing the behavior of the Tutte polynomial of the signed plane graph corresponding to $\tilde{L}$.

math.GT↗

arXiv2014

Equivalence Classes of Colorings

For any link and for any modulus $m$ we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of the link, the equivalence class of a non-trivial m-coloring is formed by each assignment of colors to the arcs of the diagram that is obtained from the former coloring by a permutation of the colors in the arcs which preserves the coloring condition at each crossing. This requirement implies topological invariance of the equivalence classes. We show that for a prime modulus the number of equivalence classes depends on the modulus and on the rank of the coloring matrix (with respect to this modulus).

math.GT↗

arXiv2013

Rainbow C_4's and Directed C_4's: the Bipartite Case Study

In this paper we obtain a new sufficient condition for the existence of directed cycles of length 4 in oriented bipartite graphs. As a corollary, a conjecture of H. Li is confirmed. As an application, a sufficient condition for the existence of rainbow cycles of length 4 in bipartite edge-colored graphs is obtained.

math.CO↗

arXiv2010

Low energy cluster beam deposited BN films as the cascade for Field Emission

The atomic deposited BN films with the thickness of nanometers (ABN) were prepared by radio frequency magnetron sputtering method and the nanostructured BN films (CBN) were prepared by Low Energy Cluster Beam Deposition. UV-Vis Absorption measurement proves the band gap of 4.27eV and field emission of the BN films were carried out. F-N plots of all the samples give a good fitting and demonstrate the F-N tunneling of the emission process. The emission of ABN begins at the electric field of 14.6 V/μm while that of CBN starts at 5.10V/μm. Emission current density of 1mA/cm2 for ABN needs the field of 20V/μm while that of CBN needs only 12.1V/μm. The cluster-deposited BN on n-type Silicon substrate proves a good performance in terms of the lower gauge voltage, more emission sites and higher electron intensity and seems a promising substitute for the cascade of Field Emission.

cond-mat.mes-hall↗