1 Tensor Categories 4 Extending ̋ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Invertible objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Internal Hom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Rigid tensor categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Tensor functors . . . . ...

mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. in theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. the wiener polarity index ...

The field theory dual to the Freedman-Townsend model of a non-Abelian anti-symmetric tensor field is a nonlinear sigma model on the group manifold G. This can be extended to the duality between the Freedman-Townsend model coupled to Yang-Mills fields and a nonlinear sigma model on a coset space G/H. We present the supersymmetric extension of this duality and find that the target space of this n...

1 K and K0 of schemes Let X be a quasi-projective variety. We define K(X) as follows. Let Fvb(X) be the free abelian group on all isomorphism classes of vector bundles (of finite rank) over X and consider the equivalence relation Rvb(X) generated by the following. If 0 → E1 → E2 → E3 → 0 is an exact sequence of vector bundles, then [E2] = [E1] + [E3]. The quotient Fvb(X)/Rvb(X) is called K(X). ...

A role of reducible connections in Non-Abelian Seiberg-Witten invariants is analyzed with massless Topological QCD where monopole is extended to non-Abelian groups version. By giving small external fields, we found that vacuum expectation value can be separated into a part from Donaldson theory , a part from Abelian Monopole theory and a part from non-Abelian monopole theory. As a by-product, w...

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms toge...

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.