We develop a rigid-analytic theory of relative ampleness for line bundles and record some applications to faithfully flat descent for morphisms and proper geometric objects. The basic definition is fibral, but pointwise arguments from the algebraic and complex-analytic cases do not apply, so we use cohomological properties of formal schemes over completions of local rings on rigid spaces. An an...

Let Λ be a preprojective algebra of type A, D, E, and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ-module, and we introduce a mutation operation between complete rigid modules in Sub Q. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to G. R...

A formal expression is obtained for the energy loss per . . _ turn, of a rigid bunch of electrons, to a closed cy lindrical cavity with quality factor Q. -The expression is valid provided the diameter of the entrance and exit ports for the beam are small ._.. .'compared to the bunch length. The effect of the ports is studied in an independent computational method. The energy loss is numerically...

In this paper, we introduce a general theory of corner rings in noncommutative rings that generalizes the classical notion of Peirce decompositions with respect to idempotents. Two basic types of corners are the Peirce corners eRe (e2 = e) and the unital corners (corners containing the identity of R). A general corner is both a unital corner of a Peirce corner, and a Peirce corner of a unital c...

We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-CalabiYau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite globa...

tooth/implant supported fixed prostheses may present biomechanical design problems, as the implant is rigidly anchored within the alveolus, whereas the tooth is attached by the periodontal ligament to the bone allowing movement. many clinicians prefer tooth/implant supported fixed prosthesis designs with rigid connectors. however, there are some doubts about the effect of attachment placement i...

The molecular structure of AI(tBu)3(NH2CH2CHzPh) is determined by the crystal packing of the phenyl rings and the pseudo spherical Al(tBu)3 units, and may be viewed as a layered structure consisting of double sheets of the phenyl rings and the Al(tBu)3 units. The A1-N-C-C linkage shows severe disorder as a result of its flexibility. The structure of Al(tBu)3 (NH2CH2CH2Ph) can be likened to a mo...

INTRODUCTION Intrastromal corneal rings or segments are approved for the treatment of myopia and astigmatism associated with keratoconus. We describe a clinicopathological case of intrastromal corneal rings. For the first time, the molecular pathological findings of intrastromal corneal rings in the cornea are illustrated. CASE PRESENTATION A 47-year-old African-American man with a history of...

Skutterudites based on CoSb3 have high thermoelectric efficiency, but the low fracture strength is a serious consideration for commercial applications. To understand the origin of the brittleness in CoSb3, we examine the response along various shear and tensile deformations using density functional theory. We find that the Co−Sb bond dominates the ideal strength. Among all the shear and tensile...