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"Geometry, Analytic"
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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in ℝⁿ
The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable
conformal minimal surfaces in
All our new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice
of a conformal structure. This enables us to obtain significant new applications to the global theory of non-orientable minimal
surfaces. In particular, we construct proper non-orientable conformal minimal surfaces in
eBook
Sir Cumference and the Viking's map : a math adventure
\"Xaxon Yellowbearyd was the fiercest Viking warrior of his time. Now a map to his hidden treasure lies in the hands of Radius and Per. Together the cousins must decode the strange numbered grid on the map-- and figure out the secret of the Viking's X and Y axes\"--P. [4] of cover
Book
Effective faithful tropicalizations associated to linear systems on curves
For a connected smooth projective curve
Let
As an application, when
eBook
Micro-milling force modeling with tool wear and runout effect by spatial analytic geometry
One of the major limitations of micro-milling applications in industries is its fast tool wear, which leads to low machining precision and efficiency. An accurate force model is fundamental for optimization micro-milling processes and minimize the tool wear. However, a generic model with tool runout and wear effect has not yet been established, which limits its practical application under varied working conditions. In this paper, a new idea is introduced by applying the spatial analytic geometry (SAG) method, under this framework the micro-milling force model is established based on the analysis of the geometrical relationship among the cutting edge positions, pre-processed workpiece morphology, and cutting force directions considering tool runout and wear effect. In this model, the tool runout is identified exclusively by only one parameter, namely the distance away from the center that perpendicular to the feed direction, so that it could be calibrated conveniently by calculating the ratio of resultant forces corresponding to different cutting edges. The tool wear–induced force is then modeled as increment of force coefficients to the original model. Therefore, the new force model with considering tool wear has the same form as the fresh tool. Finally, the accuracy and efficiency of the model are validated by experiments under varied working conditions.
Journal Article
Analytic geometry and Hodge--Frobenius structure
We study Frobenius structures in higher dimensional p-adic analytic geometry and the corresponding p-adic functional analysis. This will build up foundations for further study on some generalized cohomology of Frobenius modules and the corresponding generalized Iwasawa theory and generalized noncommutative Tamagawa number conjectures in the spirit of Burns--Flach--Fukaya--Kato and Nakamura (as well as certainly the original noncommutative Tamagawa number conjectures as observed by Pal--Zábrádi). We will work in the program proposed by Carter-Kedlaya--Zábrádi and after Pal--Zábrádi, and we will follow closely the approach from Kedlaya--Pottharst--Xiao to investigate the corresponding deformation of the generalized p-adic Hodge structures.
Journal Article
