scholarly journals The Point-Line Collinearity Graph of the Maximal 2-Local Geometry – the First Three Discs

2021 ◽  
Vol 24 (1) ◽  
pp. 53-109
Author(s):  
Peter Rowley ◽  
◽  
Louise Walker ◽  

The disc structure of the point-line collinearity graph for the maximal 2-local geometry associated with the largest simple Fischer group is investigated. For an arbitrary vertex of this graph the first three discs are determined. Additionally a fragment of the fourth disc is uncovered.

2016 ◽  
Vol 19 (1) ◽  
pp. 105-154 ◽  
Author(s):  
Peter Rowley ◽  
Ben Wright

The point-line collinearity graph ${\mathcal{G}}$ of the maximal 2-local geometry for the largest simple Fischer group, $Fi_{24}^{\prime }$, is extensively analysed. For an arbitrary vertex $a$ of ${\mathcal{G}}$, the $i\text{th}$-disc of $a$ is described in detail. As a consequence, it follows that ${\mathcal{G}}$ has diameter $5$. The collapsed adjacency matrix of ${\mathcal{G}}$ is given as well as accompanying computer files which contain a wealth of data about ${\mathcal{G}}$.Supplementary materials are available with this article.


The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.


Author(s):  
Samrit Luoma ◽  
Juha Majaniemi ◽  
Arto Pullinen ◽  
Juha Mursu ◽  
Joonas J. Virtasalo

AbstractThree-dimensional geological and groundwater flow models of a submarine groundwater discharge (SGD) site at Hanko (Finland), in the northern Baltic Sea, have been developed to provide a geological framework and a tool for the estimation of SGD rates into the coastal sea. The dataset used consists of gravimetric, ground-penetrating radar and shallow seismic surveys, drill logs, groundwater level monitoring data, field observations, and a LiDAR digital elevation model. The geological model is constrained by the local geometry of late Pleistocene and Holocene deposits, including till, glacial coarse-grained and fine-grained sediments, post-glacial mud, and coarse-grained littoral and aeolian deposits. The coarse-grained aquifer sediments form a shallow shore platform that extends approximately 100–250 m offshore, where the unit slopes steeply seawards and becomes covered by glacial and post-glacial muds. Groundwater flow preferentially takes place in channel-fill outwash coarse-grained sediments and sand and gravel interbeds that provide conduits of higher hydraulic conductivity, and have led to the formation of pockmarks on the seafloor in areas of thin or absent mud cover. The groundwater flow model estimated the average SGD rate per square meter of the seafloor at 0.22 cm day−1 in autumn 2017. The average SGD rate increased to 0.28 cm day−1 as a response to an approximately 30% increase in recharge in spring 2020. Sensitivity analysis shows that recharge has a larger influence on SGD rate compared with aquifer hydraulic conductivity and the seafloor conductance. An increase in recharge in this region will cause more SGD into the Baltic Sea.


2021 ◽  
Vol 89 (10) ◽  
pp. 2211-2233 ◽  
Author(s):  
Alexander A. Davydov ◽  
Stefano Marcugini ◽  
Fernanda Pambianco

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1196
Author(s):  
Gang Li ◽  
Yawen Zeng ◽  
Huilan Huang ◽  
Shaojian Song ◽  
Bin Liu ◽  
...  

The traditional simultaneous localization and mapping (SLAM) system uses static points of the environment as features for real-time localization and mapping. When there are few available point features, the system is difficult to implement. A feasible solution is to introduce line features. In complex scenarios containing rich line segments, the description of line segments is not strongly differentiated, which can lead to incorrect association of line segment data, thus introducing errors into the system and aggravating the cumulative error of the system. To address this problem, a point-line stereo visual SLAM system incorporating semantic invariants is proposed in this paper. This system improves the accuracy of line feature matching by fusing line features with image semantic invariant information. When defining the error function, the semantic invariant is fused with the reprojection error function, and the semantic constraint is applied to reduce the cumulative error of the poses in the long-term tracking process. Experiments on the Office sequence of the TartanAir dataset and the KITTI dataset show that this system improves the matching accuracy of line features and suppresses the cumulative error of the SLAM system to some extent, and the mean relative pose error (RPE) is 1.38 and 0.0593 m, respectively.


1982 ◽  
Vol 104 (1) ◽  
pp. 41-46
Author(s):  
T. C. Hsu ◽  
I. M. Bidhendi

A superplastic Zn-Al alloy in sheet form is formed into a bulge over a circular hole by pneumatic pressure. The geometry, the stress, the strain, and the strain-rate are determined at various points covering the whole specimen and at various stages of the forming process. The complicated shape, and its complicated changes, are represented by introducing an index for the local geometry, called “prolateness,” which is also related to the local stress ratio in a simple way. The biaxial stress is analyzed into a strain-proportional and a strain-rate-proportional component, which represent, respectively, the quasi-solid and the quasi-liquid behavior of the superplastic material.


1999 ◽  
Vol 271 (1-4) ◽  
pp. 252-255 ◽  
Author(s):  
Wen-Chen Zheng ◽  
Shao-Yi Wu

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.


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