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Non-separable rotation moment invariants
Pattern Recognition, 2022In this paper, we introduce new rotation moment invariants, which are composed of non-separable Appell moments. We prove that Appell polynomials behave under rotation as monomials, which enables easy construction of the invariants. We show by extensive tests that non-separable moments may outperform the separable ones in terms of recognition power and ...
Leonid Bedratyuk +4 more
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Polarization of Separating Invariants
Canadian Journal of Mathematics, 2008AbstractWe prove a characteristic free version of Weyl’s theorem on polarization. Our result is an exact analogue ofWeyl’s theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of cheap polarization, and show that it is ...
Draisma, J., Kemper, G., Wehlau, D.L.
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Rotation Invariant Separable Functions are Gaussian
SIAM Journal on Mathematical Analysis, 1992The following theorem is basic here: ``Let \(f,g: \mathbb{R}\to\mathbb{R}\) satisfy the equation (FE) \(f(x+y)=f(x)f(y)g(xy)\), \(x,y\in\mathbb{R}\), where \(f\) and \(g\) are not identically zero functions. Then the general solution of (FE) is given by \(f(x)=c \exp[A_ 1(x^ 2)/2+A_ 2(x)]\), \(g(x)=c^{- 1}\exp[A_ 1(x)]\), \(x\in\mathbb{R}\), where \(A_
Kannappan, PL., Sahoo, P. K.
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Separation Theorems for Group Invariant Polynomials
The Journal of Geometric Analysis, 2017The present article investigates the existence of separation theorems by polynomials. This is a variation of the complex Hahn-Banach separation theorem, which establishes that if \(K\subset\mathbb C^n\) is a closed convex set and \(z\) is a point in \(\mathbb C^n\setminus K\), then there exists a complex linear form \(f\) with sup\(_{w\in K}\{\mathrm ...
Richard M. Aron +2 more
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Invariant subrings of separable algebras
Israel Journal of Mathematics, 1973This paper gives a necessary and sufficient condition that the ring of invariants of every group of automorphisms of every projective, separable, commutative algebra over a given commutative ring is itself a union of separable, projective subalgebras.
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Spanwise-invariant three-dimensional separated flow
Experimental Thermal and Fluid Science, 1997Abstract Pulsed-wire measurements of mean velocity and Reynolds stesses have been made in a spanwise-invariant, three-dimensional separated flow; the flow is two-dimensional but not coplanar. Three layers have been identified. The effects of three-dimensionality arise mainly in the inner layer (adjacent to the surface), in which the mean flow appears
P.E. Hancock, F.M. McCluskey
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Separable and vector groups whose projectively invariant subgroups are fully invariant
Siberian Mathematical Journal, 2009Summary: We study the Abelian groups all of whose projectively invariant subgroups are fully invariant. We describe the separable and vector groups with this property.
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Invariants and constructions of separable equivalences
Journal of AlgebrazbMATH Open Web Interface contents unavailable due to conflicting licenses.
Juxiang Sun, Guoqiang Zhao
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2008
Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this thesis, we introduce the notion of a geometric separating algebra, a more geometric notion of a separating algebra.
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Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this thesis, we introduce the notion of a geometric separating algebra, a more geometric notion of a separating algebra.
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Invariance for Systems with Separated Motions
IFAC Proceedings Volumes, 2001Abstract The paper presents the methods of synthesis of invariant dynamic systems on the basis of the theory of systems with separated motions with usage of deep feedback and discontinuous controls. Usage of this class of feedback with padding hierarchical structure of synthesized controls allows: to expand the class of invariant systems as ...
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