Projective geometry on the bundle of volume forms

1998 ◽  
Vol 62 (1-2) ◽  
pp. 66-83 ◽  
Author(s):  
Paul F. Dhooghe ◽  
Annouk Van Vlierden
Keyword(s):  
Projective Geometry ◽  
Volume Forms

Fuzzy plane projective geometry

1993 ◽  
Vol 54 (2) ◽  
pp. 191-206 ◽  
Author(s):  
K.C. Gupta ◽  
Suryansu Ray
Keyword(s):  
Projective Geometry

scholarly journals Einstein on involutions in projective geometry

2021 ◽  
Author(s):  
Tilman Sauer ◽  
Tobias Schütz
Keyword(s):  
Projective Geometry ◽  
Common Theme ◽  
Infinite Point

AbstractWe discuss Einstein’s knowledge of projective geometry. We show that two pages of Einstein’s Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting with particular emphasis on the infinite point. We offer a conjecture as to the probable purpose of these geometric considerations.

scholarly journals Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage

2019 ◽  
Vol 23 (3) ◽  
pp. 1281-1304 ◽  
Author(s):  
Ben R. Hodges
Keyword(s):  
Free Surface ◽  
Finite Volume ◽  
Source Term ◽  
Weighting Function ◽  
Bottom Topography ◽  
Urban Drainage ◽  
Venant Equation ◽  
Saint Venant Equations ◽  
Volume Forms ◽  
Conservative Flux

Abstract. New integral, finite-volume forms of the Saint-Venant equations for one-dimensional (1-D) open-channel flow are derived. The new equations are in the flux-gradient conservation form and transfer portions of both the hydrostatic pressure force and the gravitational force from the source term to the conservative flux term. This approach prevents irregular channel topography from creating an inherently non-smooth source term for momentum. The derivation introduces an analytical approximation of the free surface across a finite-volume element (e.g., linear, parabolic) with a weighting function for quadrature with bottom topography. This new free-surface/topography approach provides a single term that approximates the integrated piezometric pressure over a control volume that can be split between the source and the conservative flux terms without introducing new variables within the discretization. The resulting conservative finite-volume equations are written entirely in terms of flow rates, cross-sectional areas, and water surface elevations – without using the bottom slope (S0). The new Saint-Venant equation form is (1) inherently conservative, as compared to non-conservative finite-difference forms, and (2) inherently well-balanced for irregular topography, as compared to conservative finite-volume forms using the Cunge–Liggett approach that rely on two integrations of topography. It is likely that this new equation form will be more tractable for large-scale simulations of river networks and urban drainage systems with highly variable topography as it ensures the inhomogeneous source term of the momentum conservation equation is Lipschitz smooth as long as the solution variables are smooth.

Modern Projective Geometry.

1969 ◽  
Vol 76 (10) ◽  
pp. 1168
Author(s):  
Josephine H. Chanler ◽  
Robert J. Bumcrot
Keyword(s):  
Projective Geometry

Classical projective geometry and arithmetic groups

1991 ◽  
Vol 290 (1) ◽  
pp. 441-462 ◽  
Author(s):  
Mark McConnell
Keyword(s):  
Projective Geometry ◽  
Arithmetic Groups

Cartesian and Projective Geometry

1953 ◽  
Vol 37 (321) ◽  
pp. 224
Author(s):  
W. J. Hodgetts ◽  
R. Walker
Keyword(s):  
Projective Geometry
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