The classical HKR-theorem gives an isomorphism of the n-th Hochschild cohomology of a smooth algebra and the n-th exterior power of its module of Kähler differentials. Here we generalize it for simplicial, graded and anticommutative objects in “good pairs of categories”. We apply this generalization to complex spaces and noetherian schemes and deduce two decomposition theorems for their (relati...

We give methods for bounding the higher-order filling functions of a homogeneous nilpotent group and apply them to a family of quadratically presented groups constructed by S. Chen[9]. We find sharp bounds on some higher-order filling invariants of these groups. In particular, we show that groups with arbitrarily large nilpotency class can have euclidean n-dimensional filling volume and give an...

We investigate the computational properties of cellular automata on countable (equivalently, zero entropy) sofic shifts with an emphasis on nilpotency, periodicity, and asymptotic behavior. As a tool for proving decidability results, we prove the Starfleet Lemma, which is of independent interest. We present computational results including the decidability of nilpotency and periodicity, the unde...

Four infinite families of 2-groups are presented, all of whose members possess an outer automorphism that preserves conjugacy classes. The groups in these families are central extensions of their predecessors by a cyclic group of order 2. In particular, for each integer r > 1, there is precisely one 2-group of nilpotency class r in each of the four families. All other known families of 2-groups...

Careful pe r iodon ta l d o c u m e n t a t i o n and su b seq u en t histological examina t ion of 46 h u m a n tee th wi th varying degrees of per iodonta l i nvo lvemen t showed that their pulps r ema ined wi th in normal limits regardless of the severi ty of the pe r iodon ta l disease. Fur the rmore , it was obse rved that ve ry deep caries or extensive corona l res tora t ions were associ...

We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let   $mathcal{B}$   be a Banach  $mathcal{A}-bimodule$. By using some new conditions, we show that $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and $ Z^ell_{mathcal{B}...

A formula is obtained for the dimension a(n; m) of the space of degree m invariants of the regular representation of the n-th order cyclic group. This formula implies in particular that a(n; m) = a(m; n). Moreover, the automorphism group of the multiplicative semigroup generated by invariant monomials of the cyclic group in that representation is determined.

We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n + 1)-th order differential equation and give a simple method for obtaining the differential equation. Also we determine the exponents of the differential equation and derive a bound for the degree of the polynomials, whic...