Influence of New Sleeve Composite on Fracture Behavior of Anterior Teeth with Flared Root Canals

We evaluated the fracture strength and failure mode of non-ferrule teeth with flared root canals that were restored using new experimental sleeve composites. Fifty endodontically treated anterior teeth with flared root canals were restored with direct restorations utilizing different techniques. Group A had teeth (non-ferrule) restored using commercialized MI glass fiber post + Gradia Core as core build-up. Group B had teeth (non-ferrule) restored with commercialized i-TFC glass fiber post + sleeve system. In Group C, the teeth (non-ferrule) were restored with an experimental sleeve composite with commercialized MI glass fiber post and Gradia Core. Group D, teeth (non-ferrule), were restored using custom-made tapered E-glass filling post and Gradia Core. Group E, teeth (with ferrule), were restored with commercialized MI glass fiber post + Gradia Core. After core construction, all specimens underwent direct composite crown restoration and were loaded until fracture using a universal testing machine. Average fracture loads were compared, and the failure modes were observed. Group C exhibited significantly greater fracture strength than other groups (p </p

Determinant Bundles, Quillen Metrics, and Mumford Isomorphisms Over the Universal Commensurability Teichm\"uller Space

There exists on each Teichm\"uller space $T_g$ (comprising compact Riemann surfaces of genus $g$), a natural sequence of determinant (of cohomology) line bundles, $DET_n$, related to each other via certain ``Mumford isomorphisms''. There is a remarkable connection, (Belavin-Knizhnik), between the Mumford isomorphisms and the existence of the Polyakov string measure on the Teichm\"uller space. This suggests the question of finding a genus-independent formulation of these bundles and their isomorphisms. In this paper we combine a Grothendieck-Riemann-Roch lemma with a new concept of $C^{*} \otimes Q$ bundles to construct such an universal version. Our universal objects exist over the universal space, $T_\infty$, which is the direct limit of the $T_g$ as the genus varies over the tower of all unbranched coverings of any base surface. The bundles and the connecting isomorphisms are equivariant with respect to the natural action of the universal commensurability modular group.Comment: ACTA MATHEMATICA (to appear); finalised version with a note of clarification regarding the connection of the commensurability modular group with the virtual automorphism group of the fundamental group of a closed Riemann surface; 25 pages. LATE

Fundamentals of direct limit Lie theory

We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on locally convex spaces. This enables us to push all basic constructions of finite-dimensional Lie theory to the case of direct limit groups. In particular, we obtain an analogue of Lie's third theorem: Every countable-dimensional real or complex locally finite Lie algebra is enlargible, i.e., it is the Lie algebra of some regular Lie group (a suitable direct limit group).Comment: 33 pages (v2: Lemma 7.12 and Proposition 7.13 corrected, clearer distinction between analyticity and convenient analyticity