scholarly journals Derived geometry of the first formal neighbourhood of a smooth analytic cycle

2020 ◽  
Vol 361 ◽  
pp. 106924
Author(s):  
Julien Grivaux
Keyword(s):  
Derived Geometry

scholarly journals Predicting the overall response of an orthogonal 3D woven composite using simulated and tomography-derived geometry

2020 ◽  
Vol 243 ◽  
pp. 112169 ◽  
Author(s):  
Adam Ewert ◽  
Borys Drach ◽  
Kostiantyn Vasylevskyi ◽  
Igor Tsukrov
Keyword(s):  
Woven Composite ◽  
Overall Response ◽  
Derived Geometry

scholarly journals Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

2013 ◽  
Vol 77 (3) ◽  
pp. 109-138 ◽  
Author(s):  
Mario Micheli ◽  
Mario Micheli ◽  
П Михор ◽  
Peter W Michor ◽  
Давид Мамфорд ◽  
...  
Keyword(s):  
Diffeomorphism Groups ◽  
Derived Geometry

BMD AND DXA-derived geometry parameters differ according to type of hip osteoarthritis

Bone ◽  
2010 ◽  
Vol 47 ◽  
pp. S37
Author(s):  
M.C. Castano Betancourt⁎ ◽  
F. Rivadeneira ◽  
H. Kerkhof ◽  
A. Hofman ◽  
S. Bierma Zeinstra ◽  
...  
Keyword(s):  
Hip Osteoarthritis ◽  
Derived Geometry

scholarly journals LIE ALGEBROIDS AS SPACES

2018 ◽  
Vol 19 (2) ◽  
pp. 487-535 ◽  
Author(s):  
Ryan Grady ◽  
Owen Gwilliam
Keyword(s):  
Tangent Bundle ◽  
Symplectic Structure ◽  
Vector Bundles ◽  
Natural Generalization ◽  
Lie Algebroids ◽  
Lie Algebroid ◽  
Faithful Functor ◽  
Derived Geometry

In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) $L_{\infty }$ space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of $L_{\infty }$ spaces. Then we show that for each Lie algebroid $L$, there is a fully faithful functor from the category of representations up to homotopy of $L$ to the category of vector bundles over the associated $L_{\infty }$ space. Indeed, this functor sends the adjoint complex of $L$ to the tangent bundle of the $L_{\infty }$ space. Finally, we show that a shifted symplectic structure on a dg Lie algebroid produces a shifted symplectic structure on the associated $L_{\infty }$ space.

scholarly journals Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

2013 ◽  
Vol 77 (3) ◽  
pp. 541-570 ◽  
Author(s):  
Mario Micheli ◽  
Peter W Michor ◽  
David Mumford
Keyword(s):  
Diffeomorphism Groups ◽  
Derived Geometry

scholarly journals Can we detect the stellar differential rotation of WASP-7 through the Rossiter–McLaughlin observations?

2020 ◽  
Vol 493 (4) ◽  
pp. 5928-5943
Author(s):  
L M Serrano ◽  
M Oshagh ◽  
H M Cegla ◽  
S C C Barros ◽  
N C Santos ◽  
...  
Keyword(s):  
White Noise ◽  
Radial Velocity ◽  
Differential Rotation ◽  
Precise Determination ◽  
Next Generation ◽  
Velocity Signal ◽  
Rotating Star ◽  
Derived Geometry ◽  
Hot Jupiter

ABSTRACT The Rossiter–McLaughlin (RM) effect is the radial velocity signal generated when an object transits a rotating star. Stars rotate differentially and this affects the shape and amplitude of this signal, on a level that can no longer be ignored with precise spectrographs. Highly misaligned planets provide a unique opportunity to probe stellar differential rotation via the RM effect, as they cross several stellar latitudes. In this sense, WASP-7, and its hot Jupiter with a projected misalignment of ∼90°, is one of the most promising targets. The aim of this work is to understand if the stellar differential rotation is measurable through the RM signal for systems with a geometry similar to WASP-7. In this sense, we use a modified version of soap3.0 to explore the main hurdles that prevented the precise determination of the differential rotation of WASP-7. We also investigate whether the adoption of the next generation spectrographs, like ESPRESSO, would solve these issues. Additionally, we assess how instrumental and stellar noise influence this effect and the derived geometry of the system. We found that, for WASP-7, the white noise represents an important hurdle in the detection of the stellar differential rotation, and that a precision of at least 2 m s−1 or better is essential.

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