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Elements of Monotonic Analysis: Monotonic Functions
2000The theory of IPH functions defined on either the cone ℝ ++ n or the cone ℝ + n can be applied in the study of various classes of monotonic functions. One of possible approaches in this direction is to use the hypographs of decreasing functions and the epigraphs of increasing functions.
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1990
The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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Monotone Classification by Function Decomposition
2005The paper focuses on the problem of classification by function decomposition within the frame of monotone classification. We propose a decomposition method for discrete functions which can be applied to monotone problems in order to generate a monotone classifier based on the extracted concept hierarchy.
Popova, V., Bioch, J.C.
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Weighted Inequalities for Monotone Functions
Mathematische Nachrichten, 1995AbstractWeighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi‐linear operators on monotone functions. Several properties of the classes B(p, n) and C(p, n) introduced by Neugebauer in [13] are given. In particular, we characterize the weight pairs w, v for which \documentclass{article}\pagestyle{empty}
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2010
In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are
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In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are
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Bessel Functions: Monotonicity and Bounds
Journal of the London Mathematical Society, 2000The aim of this paper is the derivation of monotonicity properties of Bessel functions, leading to precise bounds which are uniform in order or argument. Monotonicity with respect to the order \(\nu\) of the magnitude of general Bessel functions. \({\mathcal C}_\nu(x)= aJ_\nu(x)+ bY_\nu(x)\) at positive stationary points of associated functions is ...
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1974
Let H be a bounded, self adjoint transformation on a Hilbert space with spectrum in the open interval (a, b) of the real axis. Suppose that f(x) is a real function defined on the interval (a, b). One then defines the operator f(H) from the spectral decomposition of H as follows: $$ifH = \int {\lambda d{E_\lambda }} thenf\left( H \right) = \int {f ...
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Let H be a bounded, self adjoint transformation on a Hilbert space with spectrum in the open interval (a, b) of the real axis. Suppose that f(x) is a real function defined on the interval (a, b). One then defines the operator f(H) from the spectral decomposition of H as follows: $$ifH = \int {\lambda d{E_\lambda }} thenf\left( H \right) = \int {f ...
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A General Dichotomy of Evolutionary Algorithms on Monotone Functions
IEEE Transactions on Evolutionary Computation, 2020Johannes Lengler
exaly