Curves of Low Degrees on Fano Varieties

2013 ◽  
pp. 133-145
Author(s):  
Olivier Debarre
Keyword(s):  
Fano Varieties ◽  
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.

scholarly journals Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type

2021 ◽  
Author(s):  
Lie Fu ◽  
Robert Laterveer ◽  
Charles Vial
Keyword(s):  
Projective Variety ◽  
Arbitrary Dimension ◽  
Smooth Projective Variety ◽  
The Other ◽  
Fano Variety ◽  
Fano Varieties ◽  
Intersection Product ◽  
Canonical Class ◽  
Main Input

AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Küchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow–Künneth decomposition, by establishing this for two families of Todorov surfaces.

scholarly journals On properness of K-moduli spaces and optimal degenerations of Fano varieties

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Harold Blum ◽  
Daniel Halpern-Leistner ◽  
Yuchen Liu ◽  
Chenyang Xu
Keyword(s):  
Moduli Spaces ◽  
Fano Varieties

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 Betti numbers and pseudoeffective cones in 2-Fano varieties

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giosuè Emanuele Muratore
Keyword(s):  
Large Class ◽  
Betti Numbers ◽  
Fano Varieties ◽  
Higher Dimensional ◽  
Special Case ◽  
Answering Questions

Abstract The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher-dimensional analogous properties of Fano varieties. We consider (weak) k-Fano varieties and conjecture the polyhedrality of the cone of pseudoeffective k-cycles for those varieties, in analogy with the case k = 1. Then we calculate some Betti numbers of a large class of k-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index at least n − 2, and we complete the classification of weak 2-Fano varieties answering Questions 39 and 41 in [2].

The Influence of the Degree of Crystallinity on the Glass Transition Temperature of Polymers

2013 ◽  
Vol 864-867 ◽  
pp. 751-754 ◽  
Author(s):  
Andrey Askadskii ◽  
Marina Popova ◽  
Tatyana Matseevich ◽  
Elena Kurskaya
Keyword(s):  
Glass Transition ◽  
Transition Temperature ◽  
Glass Transition Temperature ◽  
Degree Of Crystallinity ◽  
Low Degrees ◽  
The Degree Of Crystallinity

The influence of the degree of crystallinity of polymers on the glass transition temperature Tg of their amorphous domains is quantitatively analyzed. The analysis is made based on the Mandelkerns ideas [ concerning the restrictive effect of crystallization on the mobility of macromolecules within the amorphous domains. At low degrees of crystallinity, Tg of amorphous domains slowly increases, and then increases much faster at high degrees of crystallinity.

scholarly journals Geometry and topology of the space of Kähler metrics on singular varieties

2018 ◽  
Vol 154 (8) ◽  
pp. 1593-1632 ◽  
Author(s):  
Eleonora Di Nezza ◽  
Vincent Guedj
Keyword(s):  
Einstein Metrics ◽  
Normal Space ◽  
Fano Varieties ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Metric Properties ◽  
Singular Varieties ◽  
Underlying Space ◽  
And Topology ◽  
Kähler Einstein Metrics

Let $Y$ be a compact Kähler normal space and let $\unicode[STIX]{x1D6FC}\in H_{\mathit{BC}}^{1,1}(Y)$ be a Kähler class. We study metric properties of the space ${\mathcal{H}}_{\unicode[STIX]{x1D6FC}}$ of Kähler metrics in $\unicode[STIX]{x1D6FC}$ using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.

scholarly journals An Overview of the Carbonatites from the Indian Subcontinent

2020 ◽  
Vol 12 (1) ◽  
pp. 85-116 ◽  
Author(s):  
Kirtikumar Randive ◽  
Tushar Meshram
Keyword(s):  
Sri Lanka ◽  
Indian Subcontinent ◽  
Source Rocks ◽  
Time Range ◽  
Alkaline Complex ◽  
Comprehensive Information ◽  
Igneous Origin ◽  
Continental Rifts ◽  
Low Degrees ◽  
Orogenic Belts

AbstractCarbonatites are carbonate-rich rocks of igneous origin. They form the magmas of their own that are generated in the deep mantle by low degrees of partial melting of carbonated peridotite or eclogite source rocks. They are known to occur since the Archaean times till recent, the activity showing gradual increase from older to younger times. They are commonly associated with alkaline rocks and be genetically related with them. They often induce metasomatic alteration in the country rocks forming an aureole of fenitization around them. They are host for economically important mineral deposits including rare metals and REE. They are commonly associated with the continental rifts, but are also common in the orogenic belts; but not known to occur in the intra-plate regions. The carbonatites are known to occur all over the globe, majority of the occurrences located in Africa, Fenno-Scandinavia, Karelian-Kola, Mongolia, China, Australia, South America and India. In the Indian Subcontinent carbonatites occur in India, Pakistan, Afghanistan and Sri Lanka; but so far not known to occur in Nepal, Bhutan, Bangladesh and Myanmar. This paper takes an overview of the carbonatite occurrences in the Indian Subcontinent in the light of recent data. The localities being discussed in detail cover a considerable time range (>2400 Ma to <0.6 Ma) from India (Hogenakal, Newania, Sevathur, Sung Valley, Sarnu-Dandali and Mundwara, and Amba Dongar), Pakistan (Permian Koga and Tertiary Pehsawar Plain Alkaline Complex which includes Loe Shilman, Sillai Patti, Jambil and Jawar), Afghanistan (Khanneshin) and Sri Lanka (Eppawala). This review provide the comprehensive information about geochemical characteristics and evolution of carbonatites in Indian Subcontinent with respect to space and time.

Sign in / Sign up

Export Citation Format

Share Document