Abstract. Using Maz’ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in R. For n ≥ 8, combined with a result in [S2], these estimates lead to the solvability of the L Dirichlet problem for the biharmonic equation on Lipschitz domains for a new range of p. In the case of convex domains, the estimates allow u...

Th erien and Wilke characterized the Until hierarchy of linear temporal logic in terms of aperiodic monoids. Here, a temporal operator able to count modulo q is introduced. Temporal logic augmented with such operators is found decidable as it is shown to express precisely the solvable regular languages. Natural hierarchies are shown to arise when modular and conventional operators are interleav...

It is shown how the arithmetic structure of algebraic curves encoded in the HasseWeil L-function can be related to affine Kac-Moody algebras. This result is useful in relating the arithmetic geometry of Calabi-Yau varieties to the underlying exactly solvable theory. In the case of the genus three Fermat curve we identify the Hasse-Weil L-function with the Mellin transform of the twist of a numb...

Noncommutative U (1) gauge theory in 4−dimensions is shown to be equivalent in some scaling limit to an ordinary non-linear sigma model in 2−dimensions. The model in this regime is solvable and the corresponding exact beta function is found. We also show that classical U (n) gauge theory on R d−2 ×R 2 θ can be approximated by a sequence of ordinary (d − 2)−dimensional Georgi-Glashow models with...

The first aim of this note is to fill a gap in the literature by giving proof following refinement Shafarevich's theorem on solvable Galois groups: Given global field $k$, finite set $\mathcal{S}$ primes and group $G$, there extension $k$ $G$ which all are totally split. To that end, we prove that, given every split embedding problem $G \rightarrow {\rm{Gal}}(L/k)$ over with nilpotent kernel ha...

The main result of this paper states that for any group G with an automatic structure L with unique representatives one can construct a uniform partial algorithm which detects L-rational subgroups and gives their preimages in L. This provides a practical, not just theoretical, procedure for solving the occurrence problem for such subgroups. 1. Generalized word problem and rational structures on...

smooth coefficients aα(x), L+ be a formally adjoint differential operation. Let L0, L0 be minimal operators (i.e., for example, D(L0) is the clozure of C∞ 0 (Ω) in the norm of the graph ‖u‖L = ‖u‖L2(Ω)+‖Lu‖L2(Ω)), and L, L+ be maximal expansions of L,L+ in the space L2(Ω) respectively (i.e. L = (L0 ) ∗, L+ = (L0)∗), L̃ = L|D(L̃) where D(L̃) is the clozure of C∞(Ω̄) in the norm of the graph ‖u‖L and...

Let G be a solvable block transitive automorphism group of a 2− (v; 5; 1) design and suppose that G is not 0ag transitive. We will prove that (1) if G is point imprimitive, then v = 21, and G6 Z21 : Z6; (2) if G is point primitive, then G6A L(1; v) and v = p, where p is a prime number with p ≡ 21 (mod 40), and a an odd integer. c © 2002 Elsevier Science B.V. All rights reserved.

We prove that N( f )= |L( f )| for any continuous map f of a given infranilmanifold with Abelian holonomy group of odd order. This theorem is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We will also show that although their fundamental groups are solvable, the infranilmanifolds we consider are in general not solvmanifolds, and hence they cannot be treated using the ...