杨绛：人世间最理想的婚姻

百度 建成后的中国散裂中子源成为中国首台、世界第四台脉冲型散裂中子源，填补了国内脉冲中子应用领域的空白，为我国材料科学技术、生命科学、资源环境、新能源等方面的基础研究和高新技术开发提供强有力的研究手段，对满足国家重大战略需求、解决前沿科学问题具有重要意义。

In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory. There are several insights that allow for such a reformulation. The first is that most of the analytic data for describing the class of smooth manifolds can be encoded into certain fibre bundles on manifolds: namely bundles of jets (see also jet bundle). The second insight is that the operation of assigning a bundle of jets to a smooth manifold is functorial in nature. The third insight is that over a certain category, these are representable functors. Furthermore, their representatives are related to the algebras of dual numbers, so that smooth infinitesimal analysis may be used.

Synthetic differential geometry can serve as a platform for formulating certain otherwise obscure or confusing notions from differential geometry. For example, the meaning of what it means to be natural (or invariant) has a particularly simple expression, even though the formulation in classical differential geometry may be quite difficult.

Further reading

• John Lane Bell, Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets (PDF file)
• F.W. Lawvere, Outline of synthetic differential geometry (PDF file)
• Anders Kock, Synthetic Differential Geometry (PDF file), Cambridge University Press, 2nd Edition, 2006.
• R. Lavendhomme, Basic Concepts of Synthetic Differential Geometry, Springer-Verlag, 1996.
• Michael Shulman, Synthetic Differential Geometry
• Ryszard Pawe? Kostecki, Differential Geometry in Toposes