A universal measure for a pencil of conics and the Great Poncelet Theorem

2014 ◽  
Vol 205 (5) ◽  
pp. 613-632 ◽  
Author(s):  
E. A. Avksentyev
1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.


Omega ◽  
2019 ◽  
Vol 87 ◽  
pp. 191-204 ◽  
Author(s):  
Xin Lu ◽  
Abigail L. Horn ◽  
Jiahao Su ◽  
Jiang Jiang
Keyword(s):  

2018 ◽  
Vol 146 (11) ◽  
pp. 4843-4854
Author(s):  
Evgeny A. Avksentyev ◽  
Vladimir Yu. Protasov
Keyword(s):  

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Li Xiong ◽  
Huiqi Li ◽  
Liang Xu

Cataract is one of the leading causes of blindness in the world’s population. A method to evaluate blurriness for cataract diagnosis in retinal images with vitreous opacity is proposed in this paper. Three types of features are extracted, which include pixel number of visible structures, mean contrast between vessels and background, and local standard deviation. To avoid the wrong detection of vitreous opacity as retinal structures, a morphological method is proposed to detect and remove such lesions from retinal visible structure segmentation. Based on the extracted features, a decision tree is trained to classify retinal images into five grades of blurriness. The proposed approach was tested using 1355 clinical retinal images, and the accuracies of two-class classification and five-grade grading compared with that of manual grading are 92.8% and 81.1%, respectively. The kappa value between automatic grading and manual grading is 0.74 in five-grade grading, in which both variance and P value are less than 0.001. Experimental results show that the grading difference between automatic grading and manual grading is all within 1 grade, which is much improvement compared with that of other available methods. The proposed grading method provides a universal measure of cataract severity and can facilitate the decision of cataract surgery.


2004 ◽  
Vol 61 (15) ◽  
pp. 2675-2695 ◽  
Author(s):  
P. Labbé ◽  
J. Dompierre ◽  
M.-G. Vallet ◽  
F. Guibault ◽  
J.-Y. Trépanier
Keyword(s):  

Author(s):  
Michael Jackson

The subject of this article is suffering – how it is borne and how it is explained – by people in very different circumstances. The author begins by recounting a young Sierra Leonean woman’s story about her wartime suffering and her postwar situation. He then turns to consider the kind of suffering “at a distance” liberal Westerners are wont to experience when confronted by the pain, distress, and misery of others, and finding ourselves at a loss to do anything about it. Finally, the author returns to discuss the way Sierra Leoneans address the suffering of war, offering a critique of the way suffering is commonly construed in the affluent West. The article contemplates how Western reactions to the suffering of others tend to involve a narcissistic focus on one’s inner feelings and thoughts, including one’s feelings for and intellectual reflections on the plight of others. In contrast, the Kuranko in Sierra Leone are less prone to fantasise rescue or salvation, or hope for a world in which there is no pain and rather respond to the suffering with resignation and silence. Such silence may be a way of healing and reconciliation, and not a way of evading or repressing an issue. The anthropology of suffering should therefore evade the Western tendency of excessive verbalising. It can, argues the author, only do justice to suffering by examining each situation as if there were no universal measure against which to judge it, only various points of view that must be taken into account in exploring it.  


Sign in / Sign up

Export Citation Format

Share Document