Results 81 to 90 of about 119 (101)
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On Brauer's theorem and Cassini's ovals
Russian Mathematical Surveys, 1998Let \(A=[a_{ij}]\) be a square complex matrix and \(\text{spr}(A)\) its spectral radius (largest of the absolute values of eigenvalues) and \(\text{spa}(A)\) its spectral abscissa (largest of the real parts of the eigenvalues). It is a classical result that the eigenvalues of \(A\) are in the union of Gerschgorin and Ostrowski circles, whose centers ...
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A single oval of Cassini for the zeros of a polynomial
Linear and Multilinear Algebra, 2012We derive two ovals of Cassini, each containing all the zeros of a polynomial. The computational cost to obtain these ovals is similar to that of the Brauer set for the companion matrix of a polynomial, although they are frequently smaller. Their derivation is based on the Gershgorin set for an appropriate polynomial of the companion matrix.
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Cassini ovals for robust mitosis detection in cellular imaging
Journal of MicroscopyAbstractAccurate detection of mitosis is crucial in automated cell analysis, yet many existing methods depend heavily on deep learning models or complex detection techniques, which can be computationally intensive and error‐prone, particularly when segmentation is incomplete.
Reza Yazdi, Hassan Khotanlou
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About the geometry of the Cassini oval, its non-convexity degree and $\varepsilon$-offset layer
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2022The paper studies the geometry of a closed nonconvex smooth simply connected curve on a plane — of the Cassini oval, as well as the geometry of the $\varepsilon$-layer around the set whose boundary is the Cassini oval. Various analytical representations of the $\varepsilon$-layer boundary are formed, and special points of this boundary are described ...
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Cassini Oval to Limacon: An Analytic Conversion
2021This paper illustrates how a Cassini Oval can be converted to a Limacon using analytic Geometry.
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Journal of Optics A: Pure and Applied Optics, 2005
In this paper the nullfield method with discrete sources (NFM-DS) is applied to analysis of light scattering by biconcave Cassini-like particles, which can be described as oblate discspheres with central concavities on their top and bottom. As far as we know this is a first attempt to apply a modification of the T-matrix method to model such a ...
Jens Hellmers +2 more
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In this paper the nullfield method with discrete sources (NFM-DS) is applied to analysis of light scattering by biconcave Cassini-like particles, which can be described as oblate discspheres with central concavities on their top and bottom. As far as we know this is a first attempt to apply a modification of the T-matrix method to model such a ...
Jens Hellmers +2 more
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Russian Universities Reports. Mathematics
In this article, we introduce and study a class P_n (φ_λ) of functions φ(z)=1+c_n z^n+c_(n+1) z^(n+1)+⋯, n≥1, analytic in the open unit disk E, subordinate to the function φ_λ (z)=1+(1-λ)z/(1-λz^2), 0≤λ<1. From a geometric point of view, this means that the set of values of the function φ(z) is contained within the region φ_λ (E) bounded by the ...
Fedor F. Maiyer +3 more
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In this article, we introduce and study a class P_n (φ_λ) of functions φ(z)=1+c_n z^n+c_(n+1) z^(n+1)+⋯, n≥1, analytic in the open unit disk E, subordinate to the function φ_λ (z)=1+(1-λ)z/(1-λz^2), 0≤λ<1. From a geometric point of view, this means that the set of values of the function φ(z) is contained within the region φ_λ (E) bounded by the ...
Fedor F. Maiyer +3 more
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Appendix D: Area within a Maximum Range Oval of Cassini
2004The area within a maximum range oval of Cassini is developed in this appendix. The development is in two parts: (1) the area within a single oval, where the baseline, L < 2√κ and κ = bistatic maximum range constant, and (2) the area within two identical ovals, surrounding the transmitter and receiver, where L ≥ 2√κ.
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Automated Construction of Airfoils Lattice Based on Cassini Oval
Chemical and Petroleum Engineering (English Translation of Khimicheskoe I Neftyanoe Mashinostroenie), 2023P R Vallejo Maldonado
exaly