Crystallization temperatures of primitive olivine crystals have been widely used as both a proxy for, or an intermediate step in calculating, mantle temperatures. The olivine-spinel aluminum-exchange thermometer has applied to samples from mid-ocean ridges and large igneous provinces, yielding considerable variability crystallization We supplement the existing data with new temperature estimate...

Let Xbe an irreducible algebraic variety defined over a field k. let ¡X be a sheaf of (noncommutative) noetherian A-algebras on X containing the sheaf of regular functions 0 and let R be the ring of global sections. We show that under quite reasonable abstract hypotheses (concerning the existence of a faithfully flat overring of R obtained from the local sections of ifî) there is an equivalence...

After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois extensions) can be given geometric meaning extending their geometric interpretations in the commutative case. On the other hand, we show that some constructions...

The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over the Robba ring (the ring of germs of rigid analytic functions on an unspecified open annulus of outer radius 1) over a discretely valued field. In this paper, we give a third-generation proof of this theorem, which...

the aim of this study is investigation of the relation between theoretical and practical knowledge of teachers in curriculum implementation paradigms. in this article, three relationships between theoretical knowledge and practical knowledge were presented. these were formed with regard to three paradigms in curriculum studies field which based on relationship between theory and practice. three...

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...

We quantize the generators of the little subgroup of the asymptotic Poincaré group of Lorentzian four-dimensional canonical quantum gravity in the continuum. In particular, the resulting ADM energy operator is densely defined on an appropriate Hilbert space, symmetric and essentially self-adjoint. Moreover, we prove a quantum analogue of the classical positivity of energy theorem due to Schoen ...

Whereas formal verification of timed systems has become a very active field of research, the idealized mathematical semantics of timed automata cannot be faithfully implemented. Recently, several works have studied a parametric semantics of timed automata related to implementability: if the specification is met for some positive value of the parameter, then there exists a correct implementation...