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11.
Oliver Lorscheid 《Archiv der Mathematik》2007,88(4):344-348
This paper shows that for a local field K, a subfield k ⊂ K and a variety X over k, X is complete if and only if for every finite field extension Kʹ | K, the set X(Kʹ) is compact in its strong topology.
The author likes to thank Florian Pop, Jakob Stix, Stefan Wewers, Gunther Cornelissen and his own parents for their support.
Received: 13 April 2006 相似文献
12.
Chris Rasmussen Michelle Zandieh Karen King Anne Teppo 《Mathematical Thinking and Learning》2005,7(1):51-73
The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing. 相似文献
13.
14.
Shyam K. Singh Oliver S. Fetzer John B. Hynes Thomas C. Williams 《Journal of heterocyclic chemistry》1991,28(5):1459-1461
Nitration of 2-amino-4-oxo-(3H)-5-trifluoromethylquinazoline is shown to occur exclusively at C6 as determined from an analysis of long range 1H and 19F scalar couplings to ring carbons. Nitration of 2-amino-4-oxo-(3H)-5-fluoroquinazoline is found to occur both at C6 and C8 as evident from an analysis of the 19F and 1H couplings of the ring protons. 相似文献
15.
16.
Julie Clutterbuck Oliver C. Schnürer Felix Schulze 《Calculus of Variations and Partial Differential Equations》2007,29(3):281-293
We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge
spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay
rates.
The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions
of Non-linear Evolution Equations”. 相似文献
17.
Rational approximation of vertical segments 总被引:1,自引:0,他引:1
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive. 相似文献
18.
Ohne Zusammenfassung 相似文献
19.
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over large categories, preprint, 2005]. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for a classification of polynomial and homogeneous functors. In the n-homogeneous model structure, the nth derivative is a Quillen functor to the category of spectra with Σn-action. After taking into account only finitary functors—which may be done in two different ways—the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T.G. Goodwillie [T.G. Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003) 645-711 (electronic)]. 相似文献