Heat kernels are used in this paper to express the analytic index of projectively invariant Dirac type operators on Γ covering spaces of compact manifolds, as elements in the K-theory of certain unconditional completions of the twisted group algebra of Γ. This is combined with V. Lafforgue’s results in the untwisted case, to compute the range of the trace on the K-theory of these algebras, unde...

Let Γ be a group together with a sequence of normal subgroups Γ ⊃ Γ1 ⊃ Γ2 ⊃ . . . of finite index [Γ : Γk] such that T k Γk = {1}. Let (X,Y ) be a (compact) 4n-dimensional Poincaré pair and p : (X,Y )→ (X,Y ) be a Γ-covering, i.e. normal covering with Γ as deck transformation group. We get associated Γ/Γk-coverings (Xk, Yk)→ (X,Y ). We prove that sign(X,Y ) = lim k→∞ sign(Xk, Yk) [Γ : Γk] , whe...

Milk was co-fermented with Bacillus subtilis HA and Lactiplantibacillus plantarum EJ2014 to produce a dairy ingredient enriched poly-γ-glutamic acid (γ-PGA) γ-aminobutyric (GABA). The first fermentation of milk B. resulted in viscous broth pH 6.56, 0.26% acidity, 1.40 mg/g tyrosine equivalent, 17.21 U/g protease activity. viable cell counts indicated 8.74 log CFU/mL, the consistency index alkal...

Let Γ be a nonelementary Kleinian group and H<Γ finitely generated, proper subgroup. We prove that if has finite covolume, then the profinite completions of H are not isomorphic. If index in Γ, there is onto which maps but does not. These results streamline existing proofs exist full-sized groups profinitely rigid absolute sense. They build on circle ideas can used to distinguish among subgroup...

A new method of solving the Einstein–Friedmann dynamical equations of a spatially homogeneous and isotropic universe is presented. The method is applicable when the equation of state of the material content assumes the form P = (γ − 1) ρ, γ = constant. The solution for the expansion factor is commonly given only for γ = 0, 1 and 4/3 when the curvature index is K = ±1. The proposed procedure is ...

A conjecture of Moore claims that if Γ is a group and H a finite index subgroup of Γ such that Γ −H has no elements of prime order (e.g. Γ is torsion free), then a Γ-module which is projective over H is projective over Γ. The conjecture is known for finite groups. In that case, it is a direct consequence of Chouinard’s theorem which is based on a fundamental result of Serre on the vanishing of ...

An important property of strongly regular graphs is that the second subconstituent of any primitive strongly regular graph is always connected. Brouwer asked to what extent this statement can be generalized to distanceregular graphs. In this paper, we show that if γ is any vertex of a distanceregular graph Γ and t is the index where the standard sequence corresponding to the second largest eige...

Let G be a connected non-compact Q-simple real algebraic group defined over Q, that is, the identity component of the group of the real points of a connected Q-simple algebraic group which is R-isotropic. Let Γ ⊂ G(Q) be an arithmetic subgroup of G. As is well known, Γ has finite co-volume in G [BH]. Denote by μG the G-invariant Borel probability measure on Γ\G. Two subgroups Γ1 and Γ2 of G are...

We consider a smooth groupoid of the form Σ ⋊ Γ where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local conformal diffeomorphisms. After defining a K-cycle on the crossed product C0(Σ) ⋊ Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem of Connes and Moscovici. This involves in particular a general...

We consider Cayley graphs Γ over dihedral groups, dihedrants for short, which admit an automorphism group G acting regularly on the arc set of Γ . We prove that, if D2n ≤G≤ Aut(Γ ) is a regular dihedral subgroup of G of order 2n such that any of its index 2 cyclic subgroups is core-free in G, then Γ belongs to the family of graphs of the form (Kn1 ⊗ · · · ⊗Kn )[Kc m], where 2n= n1 · · ·n m, and...