Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications [PDF]
American Control Conference, 2019 We present a new average-based robustness for Signal Temporal Logic (STL) and a framework for optimal control of a dynamical system under STL constraints.
N. Mehdipour, C. Vasile, C. Belta
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The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices [PDF]
International Journal of General Systems, 2017 Complete and incomplete additive/multiplicative pairwise comparison matrices are applied in preference modelling, multi-attribute decision making and ranking. The equivalence of two well known methods is proved in this paper.
Sándor Bozóki, V. Tsyganok
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Calculation of integrals in MathPartner
Discrete and Continuous Models and Applied Computational Science, 2021 We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for ...
Gennadi I. Malaschonok +1 more
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Hyperelliptic integrals and generalized arithmetic–geometric mean [PDF]
The Ramanujan Journal, 2012 Consider \(d=2g+2\) real numbers (there is ultimately no real loss of generality in assuming that \(d\) is even ...
Spandaw, J. (author) +1 more
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Refined Young Inequality and Its Application to Divergences
Entropy, 2021 We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weighted
Shigeru Furuichi, Nicuşor Minculete
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Sharp bounds for Gauss Lemniscate functions and Lemniscatic means
AIMS Mathematics, 2021 For $ a, b > 0 $ with $ a\neq b $, the Gauss lemniscate mean $ \mathcal{LM}(a, b) $ is defined by $ \begin{equation*} \mathcal{LM}(a,b) = \left\{\begin{array}{lll} \frac{\sqrt{a^2-b^2}}{\left[{ {\rm{arcsl}}}\left(\sqrt[4]{1-b^2/a^2}\right)\right]^2}
Wei-Mao Qian, Miao-Kun Wang
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A new generalized refinement of the weighted arithmetic-geometric mean inequality
, 2020 In this paper, we prove that for i = 1,2, . . . ,n , ai 0 and αi > 0 satisfy ∑i=1 αi = 1 , then for m = 1,2,3, . . . , we have ( n ∏ i=1 ai i )m + rm 0 ( n ∑ i=1 ai −n n √ n ∏ i=1 ai ) ( n ∑ i=1 αiai )m where r0 = min{αi : i = 1, . . . ,n} .
M. Ighachane, M. Akkouchi, E. Benabdi
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Arithmetic–Geometric Mean determinantal identity
Linear Algebra and its Applications, 2011 For any \(n\) by \(n\) matrix \(A\), let \(A_{r}\left[ i,j\right] \) denote an \(r\) by \(r\) submatrix consisting of r contiguous rows and columns of \(A\), starting with row \(i\) and column \(j\). Let also the superscript \(t\) stands for transposition of a matrix and \(J_{n}\) be an all-one matrix of order \(n\).
Bayat, M., Teimoori, H.
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On approximating the quasi-arithmetic mean
Journal of Inequalities and Applications, 2019 In this article, we prove that the double inequalities α1[7C(a,b)16+9H(a,b)16]+(1−α1)[3A(a,b)4+G(a,b)4]
Tie-Hong Zhao +3 more
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Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean
Journal of Inequalities and Applications, 2017 In this paper, we find the greatest values α 1 , α 2 $\alpha_{1},\alpha_{2}$ and the smallest values β 1 , β 2 $\beta_{1},\beta_{2}$ such that the double inequalities L α 1 ( a , b ) < AG ( a , b ) < L β 1 ( a , b ) $L_{\alpha_{1}}(a,b)0$ with a ≠ b $a ...
Qing Ding, Tiehong Zhao
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