In an earlier paper we have shown, how one can successfully use constraint satisfaction techniques for proving and solving formulae in the first-order predicate language over the reals (i.e., real first-order constraints). This approach was restricted to inputs that contain inequality symbols such as ≤, but no equality symbols (=) or disequality symbols ( 6=). In this paper we lay the basis for...

We solve the so-called invariance equation in the class of two-variable Sto-be valid. We recall that, for pq(p − q) = 0 and x = y, the Stolarsky mean S p,q is defined by S p,q (x, y) := q(x p − y p) p(x q − y q) 1 p−q. In the proof first we approximate the Stolarsky mean and we use the computer algebra system Maple V Release 9 to compute the Taylor expansion of the approximation up to 12th orde...

Let O 1 be a (cocompact) Fuchsian group, given as the group of units of norm one in a maximal order O in an indeenite quaternion division algebra over Q. Using the (classical) Selberg trace formula, we show that the eigenvalues of the automorphic Laplacian for O 1 and their multiplicities coincide with the eigenvalues and multiplicities of the Laplacian deened on the Maaa newforms for the Hecke...

We introduce a generalization of the Hermite normal form for matrices over a principal ideal ring R which may contain zero divisors. That normal form allows us to solve the following basic linear algebra problems. Equality decision, containment test and element test for submodules of R k , k 2 IN. The determination of images, kernels, and inverse images of homomorphisms ' : R l ! R k , l; k 2 I...

Let A, B be two regular commutative unital Banach algebras such that B is integral over A. In 2003, Dawson and Feinstein showed that the topological stable rank tsr(B) = 1 whenever tsr(A) = 1. In this note, we investigate whether we will have tsr(A) = tsr(B) in general. For instance, when A is a commutative unital C∗-algebra, we show that tsr(A) ≤ tsr(B), and the equality holds at least when th...

We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative Z2-graded algebras tending in a suitable limit to a dense subalgebra of the Z2-graded algebra of H∞-functions on the (2|2)-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the superde...

We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommu-tative Z 2-graded algebras tending in a suitable limit to a dense subalgebra of the Z 2-graded algebra of H ∞-functions on the (2|2)-dimensional supersphere. Noncom-mutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the su...

Eggert’s Conjecture says that if R is a finite-dimensional nilpotent commutative algebra over a perfect field F of characteristic p, and R(p) is the image of the p-th power map on R, then dimF R ≥ p dimF R(p). Whether this very elementary statement is true is not known. We examine heuristic evidence for this conjecture, versions of the conjecture that are not limited to positive characteristic ...

We introduce forest straight-line programs (FSLPs) as a compressed representation of unranked ordered node-labelled trees. FSLPs are based on the operations of forest algebra and generalize tree straight-line programs. We compare the succinctness of FSLPs with two other compression schemes for unranked trees: top dags and tree straight-line programs of first-child/next sibling encodings. Effici...

We introduce the fuzzy supersphere as sequence of nite-dimensional, noncommu-tative Z 2-graded algebras tending in a suitable limit to a dense subalgebra of the Z 2-graded algebra of H 1-functions on the (2j2)-dimensional supersphere. Noncom-mutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the supe...