scholarly journals The Funk–Radon transform for hyperplane sections through a common point

2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Michael Quellmalz
Keyword(s):  
Radon Transform ◽  
Higher Dimensions ◽  
Common Point ◽  
Mean Values ◽  
Generalized Radon Transform ◽  
Spherical Radon Transform ◽  
Range Characterization ◽  
Hyperplane Sections

Abstract The Funk–Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk in 1911, the Funk–Radon transform has been generalized to other families of circles as well as to higher dimensions. We are particularly interested in the following generalization: we consider the intersections of the sphere with hyperplanes containing a common point inside the sphere. If this point is the origin, this is the same as the aforementioned Funk–Radon transform. We give an injectivity result and a range characterization of this generalized Radon transform by finding a relation with the classical Funk–Radon transform.

scholarly journals Surface and Underground Geomechanical Characterization of an Area Affected by Instability Phenomena in Zaruma Mining Zone (Ecuador)

2021 ◽  
Vol 13 (6) ◽  
pp. 3272
Author(s):  
Paúl Carrión-Mero ◽  
Maribel Aguilar-Aguilar ◽  
Fernando Morante-Carballo ◽  
María José Domínguez-Cuesta ◽  
Cristhian Sánchez-Padilla ◽  
...  
Keyword(s):  
Mass Movement ◽  
Mining Activity ◽  
Mining District ◽  
Mean Values ◽  
Surface Areas ◽  
Definition Of ◽  
Action Measures ◽  
Geomechanical Characterization ◽  
The City

In the last decade, in the mining district of Zaruma-Portovelo, there has been significant land subsidence related to uncontrolled mining activity. The purpose of this work was to carry out a surface and underground geomechanical characterization of a mining sector north of the city of Zaruma that allows the definition of potentially unstable areas susceptible to the mass movement. The methodology used consists of the following stages: (i) compilation of previous studies; (ii) surface and underground characterization of rocky material to establish its susceptibility to mass movement; (iii) interpretation of results; and (iv) proposal of action measures. Among the most relevant results, it stands out that 26.1% of the 23 stations characterized on the surface present conditions that vary from potentially unstable to unstable. In underground galleries, the studied mean values of the 17 stations indicate that the rock has a medium to good quality, representing a medium susceptibility to gallery destabilization. The results obtained for the surface areas (depths up to 50 m, where altered materials predominate) and the underground areas (depths > 50 m, where the alterations are specific) can be used to identify the areas with a more significant potential for instability. For both cases, it has been possible to define specific monitoring, control, and planning actions for sensitive areas.

scholarly journals Controllability of Continuous Bimodal Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Josep Ferrer ◽  
Juan R. Pacha ◽  
Marta Peña
Keyword(s):  
Linear Systems ◽  
Higher Dimensions ◽  
Linear Dynamics ◽  
Explicit Characterization ◽  
Separating Hyperplane

We consider bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. We prove that the study of controllability can be reduced to the unobservable case, and for these ones we obtain a simple explicit characterization of controllability for dimensions 2 and 3, as well as some partial criteria for higher dimensions.

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

scholarly journals Automatic measurement and characterization of the dynamic properties of tethered membrane wings

2019 ◽  
Vol 4 (1) ◽  
pp. 41-55 ◽  
Author(s):  
Jan Hummel ◽  
Dietmar Göhlich ◽  
Roland Schmehl
Keyword(s):  
Dynamic Properties ◽  
Test Procedure ◽  
Control Unit ◽  
Automatic Measurement ◽  
Simulation Models ◽  
Test Method ◽  
Subsequent Work ◽  
Aerodynamic Parameter ◽  
Mean Values

Abstract. We have developed a tow test setup for the reproducible measurement of the dynamic properties of different types of tethered membrane wings. The test procedure is based on repeatable automated maneuvers with the entire kite system under realistic conditions. By measuring line forces and line angles, we determine the aerodynamic coefficients and lift-to-drag ratio as functions of the length ratio between power and steering lines. This nondimensional parameter characterizes the angle of attack of the wing and is varied automatically by the control unit on the towed test bench. During each towing run, several test cycles are executed such that mean values can be determined and errors can be minimized. We can conclude from this study that an objective measurement of specific dynamic properties of highly flexible membrane wings is feasible. The presented tow test method is suitable for quantitatively assessing and comparing different wing designs. The method represents an essential milestone for the development and characterization of tethered membrane wings as well as for the validation and improvement of simulation models. On the basis of this work, more complex maneuvers and a full degree of automation can be implemented in subsequent work. It can also be used for aerodynamic parameter identification.

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