On the Geometry of Hypersurfaces of Low Degrees in the Projective Space

2017 ◽  
pp. 55-90 ◽  
Author(s):  
Olivier Debarre
Keyword(s):  
Projective Space ◽  
Low Degrees

FULL WEIGHT BEARING KINEMATIC MRI STUDY OF TT-TG DISTANCE: COMPARING PATIENTS WITH PATELLOFEMORAL PAIN TO HEALTHY INDIVIDUALS

2015 ◽  
Vol 21 (4.1) ◽  
pp. 638-642
Author(s):  
Andrius Brazaitis ◽  
Algirdas Tamosiunas ◽  
Janina Tutkuviene
Keyword(s):  
Patellar Instability ◽  
Weight Bearing ◽  
Patellofemoral Pain ◽  
Full Weight Bearing ◽  
Trochlear Groove ◽  
Patellar Tilt ◽  
Full Extension ◽  
Low Degrees ◽  
Mri Study ◽  
Kinematic Magnetic Resonance Imaging

Purpose. The aim of the present study was to investigate tibial tuberosity-trochlear groove (TT-TG) distance dynamics in patients with patellofemoral pain (PFP) and pain free individuals by using full weight bearing kinematic magnetic resonance imaging (MRI) And correlation with patellar instability. Materials and methods. 51 female individuals with PFP and 26 pain free female individuals participated in the study. The kinematic MRI was performed with 1,5 T MRI unit and full-weight bearing. TT-TG distance, bissect offset (BSO) and patellar tilt angle (PTA) were measured in steps of 10° between 50° of flexion to full extension. Results. The TT–TG was higher in PFP patients compared to volunteers’ from 40° to full extension. This difference was statistically significant (p<0.01). PFP patients demonstrated statistically significantly greater TT-TG distance increase from 30° to full extension. BSO and PTA were moderately correlated to TT-TG from 20° of flexion to full extension. Conclusion. TT-TG distance is dynamic and increases significantly during extension in patients with PFP and pain free individuals, depending on knee flexion angle. It shows different pattern of dynamics in PFP group. TT-TG distance is associated with patellar instability (BSO and PTA) at low degrees of flexion.

Non-Compact Complex Projective Space as a Phase Space

2020 ◽  
Vol 17 (5) ◽  
pp. 744-747
Author(s):  
E. Khastyan ◽  
H. Shmavonyan
Keyword(s):  
Phase Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Complex Projective

scholarly journals Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jacob L. Bourjaily ◽  
Andrew J. McLeod ◽  
Cristian Vergu ◽  
Matthias Volk ◽  
Matt von Hippel ◽  
...  
Keyword(s):  
Projective Space ◽  
Feynman Integral ◽  
Weighted Projective Space

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

scholarly journals Urban organic aerosol composition in Eastern China differs from North to South: Molecular insight from a liquid chromatography-Orbitrap mass spectrometry study

2019 ◽  
Author(s):  
Kai Wang ◽  
Ru-Jin Huang ◽  
Martin Brüggemann ◽  
Yun Zhang ◽  
Lu Yang ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Liquid Chromatography ◽  
Eastern China ◽  
Organic Aerosol ◽  
Photochemical Oxidation ◽  
Lower Latitude ◽  
Molecular Formula ◽  
Aerosol Composition ◽  
Orbitrap Mass Spectrometry ◽  
Low Degrees

Abstract. Particulate air pollution in China is influencing human health, ecosystem and climate. However, the chemical composition of particulate aerosol, especially of the organic fraction, is still not well understood. In this study, particulate aerosol samples with a diameter &amp;leq; 2.5 μm (PM2.5) were collected in January 2014 in three cities located in Northeast, East and Southeast China, i.e., Changchun, Shanghai and Guangzhou, respectively. Organic aerosol (OA) in the PM2.5 samples was analyzed by ultrahigh performance liquid chromatography (UHPLC) coupled to high-resolution Orbitrap mass spectrometry in both negative mode (ESI−) and positive mode electrospray ionization (ESI+). After a non-target screening including molecular formula assignments, compounds were classified into five groups based on their elemental composition, i.e., CHO, CHON, CHN, CHOS and CHONS. The CHO, CHON and CHN compounds present the dominant signal abundances of 81–99.7 % in the mass spectra and the majority of these compounds were assigned to mono- and polyaromatics, suggesting that anthropogenic emissions are a large source of urban OA in all three cities. However, the chemical characteristics of these compounds varied among different cities. The degree of aromaticity and the number of polyaromatic compounds were significantly higher in samples from Changchun, which could be attributed to the large emissions from residential heating (i.e., coal combustion) during winter time in Northeast China. Moreover, the ESI− analysis showed higher H / C and O / C ratios for organic compounds in Shanghai and Guangzhou compared to samples from Changchun, indicating that OA in lower latitude regions of China experiences more intense photochemical oxidation processes. The majority of sulfur-containing compounds (CHOS and CHONS) in all cities were assigned to aliphatic compounds with low degrees of unsaturation and aromaticity. Again, samples from Shanghai and Guangzhou exhibit a larger chemical similarity but largely differ from those from Changchun.

scholarly journals Varieties of minimal rational tangents on double covers of projective space

2012 ◽  
Vol 275 (1-2) ◽  
pp. 109-125 ◽  
Author(s):  
Jun-Muk Hwang ◽  
Hosung Kim
Keyword(s):  
Projective Space ◽  
Double Covers

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

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