On Equivalence of Known Families of APN Functions in Small Dimensions

In this extended abstract, we computationally check and list the CCZ-inequivalent APN functions from infinite families on $\mathbb{F}_2^n$ for n from 6 to 11. These functions are selected with simplest coefficients from CCZ-inequivalent classes. This work can simplify checking CCZ-equivalence between any APN function and infinite APN families.Comment: This paper is already in "PROCEEDING OF THE 20TH CONFERENCE OF FRUCT ASSOCIATION

Note on DBI dynamics of Dbrane Near NS5-branes

In this note, we investigate the homogeneous radial dynamics of (Dp, NS5)-systems without and with one compactified transverse direction, in the framework of DBI effective action. During the homogeneous evolution, the electric field on the D-brane is always conserved and the radial motion could be reduced to an one-dimension dynamical system with an effective potential. When the Dp-brane energy is not high, the brane moves in a restricted region, with the orbits depending on the conserved energy, angular momentum through the form of the effective potential. When the Dp-brane energy is high enough, it can escape to the infinity. It turns out that the conserved angular momentum plays an interesting role in the dynamics. Moreover, we discuss the gauge dynamics around the tachyon vacuum and find that the dynamics is very reminiscent of the string fluid in the rolling tachyon case.Comment: 13 pages, 2 figures; typos corrected, discussions improved; gauge dynamics has been include