‎A set of vertices $S$ of a graph $G$ is called a fixing set of $G$‎, ‎if only the trivial automorphism of $G$ fixes every vertex in $S$‎. ‎The fixing number of a graph is the smallest cardinality of a fixing‎ ‎set‎. ‎The fixed number of a graph $G$ is the minimum $k$‎, ‎such that ‎every $k$-set of vertices of $G$ is a fixing set of $G$‎. ‎A graph $G$‎ ‎is called a $k$-fixed graph‎, ‎if its fix...

We give the full set of S matrices for extensions of D(n)1 permutation orbifolds, extending our previous work to the yet unknown case of integer spin spinor currents. The main tool is triality of SO(8). We also provide fixed point resolution matrices for spinor currents of D(n)1 permutation orbifolds with n even and not multiple of four, where the spinor currents have half-integer spin.

We define a fixed point topological charge for the two–dimensional O(3) lattice σ–model which is free of topological defects. We use this operator in combination with the fixed point action to measure the topological susceptibility for a wide range of correlation lengths. The results strongly suggest that it is not a physical quantity in this model. The procedure, however, can be applied to oth...

We note that the recent direct measurement of the top quark mass at 173.3±5.6 (stat)±6.2 (syst) by DØ collaboration severely constrains the theoretically attractive infra-red fixed point scenario of the top quark Yukawa coupling in supersymmetric GUTs. For one-step unified models the above mentioned measurement bounds the arbitrary but experimentally determinable parameter tanβ to the range 1.3...