The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1) gauge group. The Chern-Pontryagin index P2n plays a crucial role in both gravity and gauge theories. P2n(gravity) gives the gravitational Lagrangian in 2n dimensions, having the vacuum solution AdS2n. The same but global symmetry is shared with the gauge theories and 0,1-cochains of the Chern-Simon index C2n(gauge) tak...

It is known that to every (1|1)-dimensional supercurve X there is associated a dual supercurve X̂ , and a superdiagonal∆ ⊂ X× X̂ . We establish that the categories ofD-modules on X , X̂ and ∆ are equivalent. This follows from a more general result aboutD-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with conne...

We extend superspace by introducing an antissymetric tensorial coordinate and develop the corresponding extended supersymmetric invariant theory. After integrating over the tensorial coordinate, an effective action describing massive bosons and fermions is explicitely derived for the spacetime dimension D = 2. The adopted procedure is simpler than the Kaluza-Klein one and can suggest an alterna...

We study the gauging of a global U(1) symmetry in gapped system (2+1)d. The procedure has been well-understood for finite group, which leads to new phase with emergent gauge structure and can be described algebraically using mathematical framework modular tensor category (MTC). develop categorical description MTC, taking into account dynamics field absent group case. When ungauged non-zero Hall...

In the title co-crystal, C(2)H(5)NO(2)·C(4)H(6)O(6), the gylcine mol-ecule is present in the zwitterion form. In the tartaric acid mol-ecule there is a short intra-molecular O-H⋯O contact. In the crystal, the tartaric acid mol-ecules are linked via pairs of O-H⋯O hydrogen bonds, forming inversion dimers. These dimers are linked via a number of O-H⋯O and N-H⋯O hydrogen bonds involving the two co...