Let $V$ be a vertex operator superalgebra with the natural order 2 automorphism $\sigma$. Under suitable conditions on $V$, $\sigma$-fixed subspace $V_{\bar 0}$ is algebra and category $C_{V_{\bar 0}}$ of 0}$-modules modular tensor category. In this paper, we prove that fermionic M\"uger centralizer 0}}^0$ fermion in generated by irreducible 0}$-submodules $V$-modules. particular, super-modular...

Let $G$ be a countable monoid and let $A$ an Artinian group (resp. module). $\Sigma \subset A^G$ closed subshift which is also subgroup submodule) of $A^G$. Suppose that $\Gamma$ finitely generated consisting pairwise commuting cellular automata \to \Sigma$ are homomorphisms groups modules) with binary operation given by composition maps. We show the valuation action on $\Sigma$ satisfies natur...

I present a new class of topological string theories, and discuss them in two dimensions as candidates for the string description of large-N QCD. The starting point is a new class of topological sigma models, whose path integral is localized to the moduli space of harmonic maps from the worldsheet to the target. The Lagrangian is of fourth order in worldsheet derivatives. After gauging worldshe...

The popularity of six-sigma has given rise to the question: can any company adopt this rigid data driven approach to achieve higher levels of quality? This research suggests that a company must develop a unique combination of resources and competencies to realize the benefits of six-sigma. According to the competency based perspective (CBP), a company first needs to have the assets, skills, and...

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...

Methyl and n-butyl thorium complexes of a rigid 2,6-bis(anilidomethyl)pyridine ligand have been prepared; the n-butyl complex is thermally stable, even at 60 degrees C, while the methyl complexes exhibit a high tendency to eliminate methane via sigma-bond metathesis.

This paper describes the performance of Granular Activated Carbon (GAC) to adsorb and separate glucose and maltose solutes from the industrial effluents by adsorption process. In this study, the capability of Granular Activated Carbon (GAC) to adsorb glucose and maltose were experimentally examined. Commercial GAC (mesh 12-20), supplied by Sigma Aldrich company in...

let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...