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The affine index polynomial invariant of flat virtual knots
Journal of Knot Theory and Its Ramifications, 2014We define the affine index polynomial of a flat virtual knot in a similar way as the case of a virtual knot, and show that it is described by the affine index polynomial of any overlying virtual knot. Let K be a virtual knot, and F the underlying flat virtual knot of K.
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An affine index polynomial invariant and the forbidden move of virtual knots
Journal of Knot Theory and Its Ramifications, 2016Kauffman defines an affine index polynomial invariant for virtual knots. The invariant is induced from a numerical invariant called an [Formula: see text]-writhe. In this paper, we provide the difference of the values obtained from invariants between two virtual knots which can be transformed into each other by a single forbidden move. As a result, we
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Coninvolutory matrices, multi-affine polynomials, and invariant circles
Linear and Multilinear Algebra, 2022Hristo Sendov, Junquan Xiao
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2019
Summary: In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic \(f(x,y) = 0\) and a Darboux invariant of the form \(f(x,y)^\lambda e^{st}\) with \(\lambda, s \in \mathbb R\) and \(s \neq 0\).
Schlomiuk, Dana, Vulpe, Nicolae
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Summary: In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic \(f(x,y) = 0\) and a Darboux invariant of the form \(f(x,y)^\lambda e^{st}\) with \(\lambda, s \in \mathbb R\) and \(s \neq 0\).
Schlomiuk, Dana, Vulpe, Nicolae
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Infinite families of 2-designs derived from affine-invariant codes
Journal of Combinatorial Designs, 2021Yan Liu, Xiwang Cao
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ASIFT: A New Framework for Fully Affine Invariant Image Comparison
SIAM Journal on Imaging Sciences, 2009Jean-Michel Morel
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Affine invariant classification and retrieval of texture images
Pattern Recognition, 2003Jianguo Zhang, Tieniu Tan
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Affine Invariant Geometry for Non-rigid Shapes
International Journal of Computer Vision, 2014Ron Kimmel, Dan Raviv
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Affine Invariant Detection: Edge Maps, Anisotropic Diffusion, and Active Contours
Acta Applicandae Mathematicae, 1999Peter Olver +2 more
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