scholarly journals Special geometry, cubic polynomials and homogeneous quaternionic spaces

1992 ◽  
Vol 149 (2) ◽  
pp. 307-333 ◽  
Author(s):  
B. de Wit ◽  
A. Van Proeyen
2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Matteo Petrera ◽  
Yuri B. Suris ◽  
Kangning Wei ◽  
René Zander

AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.


Rheumatology ◽  
2021 ◽  
Vol 60 (Supplement_1) ◽  
Author(s):  
Stephanie J W Shoop-Worrall ◽  
Suzanne M M Verstappen ◽  
Wendy Costello ◽  
Saskya P Angevare ◽  
Yosef Uziel ◽  
...  

Abstract Background/Aims  Younger and older people with rheumatic diseases may experience increased anxiety during the COVID-19 pandemic, due to the uncertainty regarding their likelihood of contracting the virus, its complications alongside their existing condition and whether their immunosuppressive treatments pose additional risks. This study explored trajectories of anxiety in parents of children and young people (CYP) with rheumatic diseases and adults with rheumatic diseases in the six months following March 2020 during the COVID-19 pandemic. Methods  CYP and adults recruited to the international COVID-19 European Patient Registry, a parent-led, online, self-referred prospective cohort recruiting participants globally, were selected if enrolled within 20th March to 17th April 2020. Anxiety scores (0-10, 10=Highest anxiety) were collected weekly for up to 28 weeks and denoted parent anxiety in the CYP cohort and self-reported anxiety in the adult cohort. Group-based trajectory models explored anxiety clusters using censored-normal models in the CYP and adult populations, separately. Linear, quadratic and cubic polynomials were tested within 1 to 10 clusters and optimal models selected based on a combination of model fit (BIC), parsimony and clinical plausibility. Demographic (country, age, gender) and clinical (diagnosis, disease control, respiratory comorbidity, immunosuppressive therapy) information and COVID-19 mitigation behaviours (isolation, distancing, none) were collected at initial enrolment and compared between clusters using Chi-squared, Fisher’s exact and Kruskal-Wallis tests. Results  Among 498 CYP and 2640 adults, most were female (65%, 89%) and from the UK (50%, 84%), respectively. The most common diagnoses were polyarticular JIA (37%) and oligoarticular JIA (29%) among CYP and RA among the adults (63%). Respiratory comorbidities were uncommon in the CYP (10%) and adult (17%) cohorts, and most were taking any immunosuppressive therapies (85%, 87%), respectively. As of March 2020, 88% and 79% were self-isolating, respectively. In both the parents of CYP and adult cohorts, four trajectory clusters were identified with similar patterns: Persistent extremely high anxiety (32%, 17%), persistent high anxiety (43%, 41%), high anxiety that marginally improved (25%, 32%) and moderate anxiety that improved (11%, 10%). Among CYP, few characteristics distinguished the clusters. However, in the adult cohort, clusters with greater and more persistent anxiety were associated with higher levels of respiratory comorbidities, higher use of immunosuppressive therapies, higher initial levels of self-isolation and slightly older age than those with lower or improving anxiety over time. Conclusion  This study reports four trajectories of anxiety during the COVID-19 pandemic that are consistent across parents of CYP with rheumatic diseases and among adults with these conditions. Despite relatively lower risks for CYP, parental anxiety regarding COVID-19 was high and not associated with characteristics of their child or of their child's disease. Among adults with rheumatic diseases, greater anxiety was associated with risk factors potentially associated with COVID-19 morbidity and mortality. Disclosure  S.J.W. Shoop-Worrall: None. S.M.M. Verstappen: None. W. Costello: None. S.P. Angevare: None. Y. Uziel: None. C. Wouters: None. N. Wulffraat: Honoraria; Sobi. Grants/research support; Abbvie. R. Beesley: None.


2000 ◽  
Vol 78 (4) ◽  
pp. 650-662 ◽  
Author(s):  
Jean-Marc Rousseaux ◽  
Hervé Muhr ◽  
Edouard Plasari

2009 ◽  
Vol 193 ◽  
pp. 95-110 ◽  
Author(s):  
Giorgio Ottaviani

AbstractWe compute the equation of the 7-secant variety to the Veronese variety (P4,O(3)), its degree is 15. This is the last missing invariant in the Alexander-Hirschowitz classification. It gives the condition to express a homogeneous cubic polynomial in 5 variables as the sum of 7 cubes (Waring problem). The interesting side in the construction is that it comes from the determinant of a matrix of order 45 with linear entries, which is a cube. The same technique allows to express the classical Aronhold invariant of plane cubics as a pfaffian.


2000 ◽  
Vol 33 (2) ◽  
pp. 13-18 ◽  
Author(s):  
Peter Crouch ◽  
Fátima Silva Leite ◽  
Margarida Camarinha

2011 ◽  
Vol 701 (5) ◽  
pp. 640-645 ◽  
Author(s):  
Sergio Ferrara ◽  
Alessio Marrani ◽  
Armen Yeranyan
Keyword(s):  

2018 ◽  
Vol 6 (4) ◽  
pp. T1067-T1080 ◽  
Author(s):  
Ursula Iturrarán-Viveros ◽  
Andrés M. Muñoz-García ◽  
Jorge O. Parra ◽  
Josué Tago

We have applied instantaneous seismic attributes to a stacked P-wave reflected seismic section in the Tenerife field located in the Middle Magdalena Valley Basin in Colombia to estimate the volume of clay [Formula: see text] and the density [Formula: see text] at seismic scale. The well logs and the seismic attributes associated to the seismic trace closer to one of the available wells (Tenerife-2) is the information used to train some multilayered artificial neural networks (ANN). We perform data analysis via the gamma test, a mathematically nonparametric nonlinear smooth modeling tool, to choose the best input combination of seismic attributes to train ANNs to estimate [Formula: see text] and [Formula: see text]. Once the ANNs are trained, they are applied to predict these parameters along the seismic line. From the continuous estimations of [Formula: see text], we distinguish two facies: sands for [Formula: see text] and shales when [Formula: see text]. These estimations confirm the production of the Mugrosa C-Sands zone, and we draw the brown shale that correlates with the high-amplitude attributes and the yellow sand that correlates with the low-amplitude attributes. Using the well-log information for [Formula: see text] and the facies classification (also in the well log), two cubic polynomials that depend on time (or depth) are obtained, one for sands and the other for shales, to fit the [Formula: see text]. These two cubic polynomials and the facies classification obtained from the [Formula: see text] at the seismic scale enable us to estimate [Formula: see text] at the seismic scale. To validate the 2D [Formula: see text] and [Formula: see text] predicted data, a forward-modeling software (the Kennett reflectivity algorithm) is used. This model calculates synthetic seismograms that are compared with the real seismograms. This comparison indicates a small misfit that suggests that the [Formula: see text] and [Formula: see text] images are representing the reservoir description characteristics and the ANN method is accurate to map these parameters.


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