Let A be a unital maximal full algebra of operator fields with base space [0, 1] and fibre algebras {At}t∈[0,1]k . We show that the stable rank of A is bounded above by the quantity supt∈[0,1]ksr(C([0, 1] )⊗ At). Here the symbol “sr” means stable rank. Using the above estimate, we compute the stable ranks of the C-algebras of the (possibly higher rank) discrete Heisenberg groups.

Consider stationary ergodic measures for which the difference between the expected length of a uniquely decodable code and the block entropy is asymptotically bounded by a constant. Using ergodic decomposition, it is shown that the number of such measures is less than the base of the logarithm raised to the power of that constant. In consequence, an analogous statement is derived for excess len...

A criterion for the approximability of all solutions heat equation in a bounded cylindrical domain that belong to Lebesgue class by more regular (e.g., Sobolev) same with larger base is obtained. Namely, complement smaller one must have no (nonempty connected) compact components. As an important corollary, we prove theorem on existence doubly orthogonal basis corresponding pair Hilbert spaces.

We study the complexity of rewrite systems shown terminating via the dependency pair framework using processors for reduction pairs, dependency graphs, or the subterm criterion. The complexity of such systems is bounded by a multiple recursive function, provided the complexity induced by the employed base techniques is at most multiple recursive. Moreover this upper bound is tight. 1998 ACM Sub...

Given a compact p-adic Lie group over an arbitrary base field we prove that its distribution algebra is Fréchet-Stein with Auslander regular Banach algebras whose global dimensions are bounded above by the dimension of the group. As an application, we show that nonzero coadmissible modules coming from smooth or, more generally, U(g)-finite representations have a maximal grade number (codimensio...