scholarly journals On the Projective Geometry of the Supercircle: A Unified Construction of the Super Cross-Ratio and Schwarzian Derivative

2008 ◽  
Vol 2008 ◽  
Author(s):  
Jean-Philippe Michel ◽  
Christian Duval
Keyword(s):  
Projective Geometry ◽  
Schwarzian Derivative ◽  
Cross Ratio

scholarly journals Non-Euclidean Biosymmetries and Algebraic Harmony in Genomes of Higher and Lower Organisms

2021 ◽  
Vol 248 ◽  
pp. 01010
Author(s):  
Sergey Petoukhov ◽  
Elena Petukhova ◽  
Vitaly Svirin
Keyword(s):  
Projective Geometry ◽  
Double Helix ◽  
Nucleotide Sequences ◽  
Cross Ratio ◽  
Harmonic Progression ◽  
The Cross ◽  
Dna Double Helix ◽  
Cooperative Organization ◽  
Relationship Of ◽  
The Relationship

The article is devoted to the study of the relationship of non-Euclidean symmetries in inherited biostructures with algebraic features of information nucleotide sequences in DNA molecules in the genomes of eukaryotes and prokaryotes. These genomic sequences obey the universal hyperbolic rules of the oligomer cooperative organization, which are associated with the harmonic progression 1/1, 1/2, 1/3,.., 1/n. The progression has long been known and studied in various branches of mathematics and physics. Now it has manifested itself in genetic informatics. The performed analysis of the harmonic progression revealed its connection with the cross-ratio, which is the main invariant of projective geometry. This connection consists in the fact that the magnitude of the cross-ratio is the same and is equal to 4/3 for any four adjacent members of this progression. The long DNA nucleotide sequences have fractal-like structure with so called epi-chains, whose structures are also related to the harmonic progression and the projective-geometrical symmetries. The received results are related additionally to a consideration of DNA double helix as helical antenna. This fact of the connection of genetic informatics with the main invariant of projective geometry can be used to explain the implementation of some non-Euclidean symmetries in genetically inherited structures of living bodies.

RECALCULATION OF THE LOADS CURRENT OF ACTIVE MULTI-PORT NETWORKS ON THE BASIS OF PROJECTIVE GEOMETRY

2013 ◽  
Vol 22 (05) ◽  
pp. 1350031 ◽  
Author(s):  
A. A. PENIN
Keyword(s):  
Projective Geometry ◽  
Direct Current ◽  
Power Supply ◽  
Power Supply System ◽  
Traditional Approach ◽  
Cross Ratio ◽  
Supply System ◽  
The Cross ◽  
The Given

For an active multi-port network of a direct current, as a model of a power supply system, the problem of recalculation of the changeable loads currents is considered. The approach on the basis of projective geometry is used for interpretation of changes or "kinematics" of regime parameters of a circuit. The changes of the regime parameters are introduced otherwise, through the cross ratio of four points with use of projective coordinates. Easy-to-use formulas of the recalculation of the currents, which possess the group properties at change of conductivity of the loads, are obtained. It allows expressing the final values of the currents through the intermediate changes of the currents and conductivities. Disadvantages of the traditional approach, which uses the changes of resistance in the form of increments, are shown. The given approach is applicable to the analysis of "flowed" form processes of the various physical natures.

Projector calibration based on cross ratio invariance

2020 ◽  
Vol 13 (6) ◽  
pp. 1-9
Author(s):  
YANG Jian-bai ◽  
◽  
ZHAO Jian ◽  
SUN Qiang ◽  
Keyword(s):  
Cross Ratio ◽  
Projector Calibration

Projective Geometry

1988 ◽  
Author(s):  
Pierre Samuel
Keyword(s):  
Projective Geometry
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