Gabriel Dimension for Graded Rings

Using techniques of localization for Grothendieck categories with a family of projective generators, we show that for a graded ring R = ⊕ _σ∈G R _σ with finite support if R _e has Gabriel dimension then has Gabriel dimension. Moreover, adding some lattice results, we prove that if has Gabriel dimension then also has Gabriel dimension. This research has been supported by grant MTM2005-3227 from MEC.     

Relative energy and structural differences of axial and equatorial 1-fluoro-1-silacyclohexane

The rotational spectra of the main isotopomer, of the (29)Si and of all (13)C isotopologues of axial and equatorial forms of 1-fluoro-silacyclohexane have been measured by conventional (only main species) and molecular beam Fourier transform microwave spectroscopy. r(0) and partial r(s) structures are given separately for the two forms. The main structural differences are discussed. From dipole moments and relative intensity measurements, a slight preference (E(Eq) - E(Ax) = 42 +/- 24 cm(-1)) for the axial conformer was found. The rotational spectra of some, the most intense, vibrational satellites have also been measured. They belong to the ring-puckering motions.     

Sufficient conditions for the invertibility of adapted perturbations of identity on the Wiener space

Let (W, H, μ) be the classical Wiener space. Assume that U = I _W  + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration of W. We give some sufficient analytic conditions on u which imply the invertibility of the map U. In particular it is shown that if ${u\in {\rm ID}_{p,1}(H)}$ is adapted and if ${\exp(\frac{1}{2}\|\nabla u\|_2^2-\delta u)\in L^q(\mu)}$ , where p ^?1 + q ^?1 = 1, then I _W  + u is almost surely invertible. With the help of this result it is shown that if ${\nabla u\in L^\infty(\mu,H\otimes H)}$ , then the Girsanov exponential of u times the Wiener measure satisfies the logarithmic Sobolev inequality and this implies the invertibility of U = I _W  +  u . As a consequence, if, there exists an integer k ≥  1 such that ${\|\nabla^k u\|_{H^{\otimes(k+1)}}\in L^\infty(\mu)}$ , then I _W  +  u is again almost surely invertible under the almost sure continuity hypothesis of ${t\to\nabla^i \dot{u}_t}$ for i ≤  k ? 1.