Given an affine surface X with rational singularities and minimal resolution X′, the covering of Artin component deformation space where simultaneous resolutions are achieved is Galois group Weyl W associated configuration (−2)-curves on X′. This gives existence actions polynomial rings over Z ring invariants also polynomial. In turn, this leads to a description integral cohomology flag varieti...

Interactions with environment have large impact on the properties of light–harvesting (LH) pigment– protein complexes. Some of these interactions could be modeled by different types of static disorder. Fluctuations of bacteriochlorophyll’s positions in B850 ring from LH2 complex of purple bacteria are investigated in present paper. The nearest neighbour approximation model of the ring is consid...

It is well-known that for the integral group ring of a polycyclic group several decision problems are decidable. In this paper a technique to solve the membership problem for right ideals originating from Baumslag, Cannonito and Miller and studied by Sims is outlined. We want to analyze, how these decision methods are related to Grr obner bases. Therefore, we deene eeective reduction for group ...

For a simply laced and hyperbolic Kac–Moody group G = G(R) over a commutative ring R with 1, we consider a map from a finite presentation of G(R) obtained by Allcock and Carbone to a representation–theoretic construction G(R) corresponding to an integrable representation V λ with dominant integral weight λ. When R = Z, we prove that this map extends to a group homomorphism ρλ,Z : G(Z)→ G(Z). We...