Spherical functions on a finite affine space with a series of Zelevinsky subgroups

1995 ◽  
Vol 57 (3) ◽  
pp. 300-306
Author(s):  
E. E. Petrov
Keyword(s):  
Affine Space ◽  
Spherical Functions ◽  
Finite Affine

Minimal 2-coverings of a finite affine space based on GF(2)

1983 ◽  
Vol 8 (3) ◽  
pp. 375-388 ◽  
Author(s):  
Gyula Katona ◽  
Jaya Srivastava
Keyword(s):  
Affine Space ◽  
Finite Affine

The Polytope ofm-Subspaces of a Finite Affine Space

2007 ◽  
Vol 41 (3) ◽  
pp. 317-344
Author(s):  
Julie Christophe ◽  
Jean-Paul Doignon
Keyword(s):  
Affine Space ◽  
Finite Affine

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

scholarly journals Generative Models for Relief Perspective Architectures

2021 ◽  
Author(s):  
Leonardo Baglioni ◽  
Federico Fallavollita
Keyword(s):  
Research Methodology ◽  
Affine Space ◽  
Three Dimensional ◽  
Generative Models ◽  
Linear Perspective ◽  
Dimensional Structure ◽  
Three Dimensional Structure ◽  
Present Essay ◽  
Santa Maria

AbstractThe present essay investigates the potential of generative representation applied to the study of relief perspective architectures realized in Italy between the sixteenth and seventeenth centuries. In arts, and architecture in particular, relief perspective is a three-dimensional structure able to create the illusion of great depths in small spaces. A method of investigation applied to the case study of the Avila Chapel in Santa Maria in Trastevere in Rome (Antonio Gherardi 1678) is proposed. The research methodology can be extended to other cases and is based on the use of a Relief Perspective Camera, which can create both a linear perspective and a relief perspective. Experimenting mechanically and automatically the perspective transformations from the affine space to the illusory space and vice versa has allowed us to see the case study in a different light.

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