Let m be a positive integer and let ? finite set. The m-closure of G?Sym(?) is the largest permutation group on having same orbits as G in its induced action Cartesian product ?m. 1-closure 2-closure solvable need not solvable. We prove that always for m?3.

Let G be a permutation group of set ? and k positive integer. The k-closure is the greatest (w.r.t. inclusion) subgroup G(k) in Sym(?) which has same orbits as under componentwise action on ?k. It proved that finite nilpotent coincides with direct product k-closures all its Sylow subgroups.

It is proved that if G = G1 ∗G3 G2 is free product of probability measure preserving s-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid G3, then the sofic dimension s(G) satisfies the equality s(G) = h(G01)s(G1) + h(G 0 2)s(G2) − h(G 0 3)s(G3) where h is the normalized Haar measure on G. Let G be a group. The sofic dimension of G is an asymptotic invariant that accoun...

The ring-shift isomerization of sym-octahydrophenanthrene (sym-OHP) to sym-octahydroanthracene (sym-OHA) catalyzed by acidic zeolites (Mordenite (MOR) and Faujasite (FAU)) was investigated by the ONIOM(DFT:UFF) and DFT approaches. A "five-membered ring" mechanism through carbocation rearrangement via 1-2 migration was proved to be kinetically favored over a "six-membered ring" mechanism through...

We describe an infinite-dimensional algebra of hidden symmetries of N = 4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the N = 4 SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solvi...

Software product evaluation is a tool to choose among alternative software products for an intended application, but can also assist the developers of the software in judging the relevance of their product and in identifying missing functionalities. The suitability of software products is dependent on the intended application scenario and environment, which is why quantitative, objective metric...