Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

Hidden in the expansion of the Kontsevich integral, graded by loops rather than by degree, is a new notion of finite type invariants of knots, closely related to S-equivalence, and with respect to which the Kontsevich integral is the universal finite type invariant, modulo S-equivalence. In addition, the 2-loop part Q of the Kontsevich integral behaves like an equivariant version of Casson’s in...

Cohomology classes defined by polylogarithms have been one of the main tools to study special values of L-functions. Most notably, they play a decisive role in the study of the Tamagawa number conjecture for abelian number fields ([Be2], [Del], [HuW] [Hu-Ki]), CM elliptic curves ([Den], [Ki2]) and modular forms ([Be1], [Ka]). Polylogarithms have been defined for relative curves by Beilinson and...

This paper is a follow-up work of the previous study generalized abelian gauge field theory under rotor model order $n$ higher derivatives. We will quantization this using path integral approach and find out Feynman propagator (2-point correlation function) theory. also investigate Proca action derive for massive case.

Exact conserved quantities on the cylinder I: conformal case. Abstract The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a twisted " spin −1/2 " chain. A very useful mapping to the more common nonlin-ear integral...