A formula for the Cartier operator on plane algebraic curves.

1987 ◽  
Vol 1987 (377) ◽  
pp. 49-64 ◽  
Keyword(s):  
Algebraic Curves ◽  
Cartier Operator

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

scholarly journals Real plane algebraic curves with prescribed singularities

Topology ◽  
1993 ◽  
Vol 32 (4) ◽  
pp. 845-856 ◽  
Author(s):  
Eugenii Shustin
Keyword(s):  
Algebraic Curves ◽  
Real Plane

Algebraic Curves

Nature ◽  
1951 ◽  
Vol 167 (4259) ◽  
pp. 962-962
Author(s):  
H. T. H. PIAGGIO
Keyword(s):  
Algebraic Curves

scholarly journals Moduli Spaces of Coherent Systems of Small Slope on Algebraic Curves

2009 ◽  
Vol 37 (8) ◽  
pp. 2649-2678 ◽  
Author(s):  
S. B. Bradlow ◽  
O. García-Prada ◽  
V. Mercat ◽  
V. Muñoz ◽  
P. E. Newstead
Keyword(s):  
Moduli Spaces ◽  
Algebraic Curves ◽  
Coherent Systems

scholarly journals On Curve Veering and Flutter of Rotating Blades

1994 ◽  
Vol 116 (3) ◽  
pp. 702-708 ◽  
Author(s):  
D. Afolabi ◽  
O. Mehmed
Keyword(s):  
Algebraic Geometry ◽  
Catastrophe Theory ◽  
Algebraic Curves ◽  
Rotation Speed ◽  
Elastic Stability ◽  
Rotating Blades ◽  
Rotating Blade ◽  
Modes Of Vibration ◽  
Curve Veering ◽  
As If

The eigenvalues of rotating blades usually change with rotation speed according to the Stodola-Southwell criterion. Under certain circumstances, the loci of eigenvalues belonging to two distinct modes of vibration approach each other very closely, and it may appear as if the loci cross each other. However, our study indicates that the observable frequency loci of an undamped rotating blade do not cross, but must either repel each other (leading to “curve veering”), or attract each other (leading to “frequency coalescence”). Our results are reached by using standard arguments from algebraic geometry—the theory of algebraic curves and catastrophe theory. We conclude that it is important to resolve an apparent crossing of eigenvalue loci into either a frequency coalescence or a curve veering, because frequency coalescence is dangerous since it leads to flutter, whereas curve veering does not precipitate flutter and is, therefore, harmless with respect to elastic stability.

Sign in / Sign up

Export Citation Format

Share Document