Results 141 to 150 of about 18,466 (195)

Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization. [PDF]

Philos Trans A Math Phys Eng Sci
Burger M, Kabri S, Korolev Y, Roith T, Weigand L.   +4 more
europepmc   +1 more source

Where octagonal geometry meets chaos: A new S-Box for advanced cryptographic systems. [PDF]

PLoS One
Banga A, Mahmood Y, Mudawi NA, Innab N, Iqbal N, Diab H.   +5 more
europepmc   +1 more source

Uniform Convergence of Deep Neural Networks With Lipschitz Continuous Activation Functions and Variable Widths. [PDF]

IEEE Trans Inf Theory
Xu Y, Zhang H.
europepmc   +1 more source

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Some Trigonometric Inequalities

1989
The paper includes many trigonometric inequalities for the real numbers A, B, C which satisfy the condition \(A+B+C=p,\) where p is a natural number. The first part consists of asymmetric trigonometric inequalities, the second deals with some trigonometric identities which play an important role in proving inequalities.
Mitrinović, Dragoslav S., Pečarić, Josip E., Janous, Walther   +2 more
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Inequalities for Alternating Trigonometric Sums

Results in Mathematics, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, Horst, Liu, Xiuping, Shi, Xiquan
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Sharp inequalities for trigonometric sums

Mathematical Proceedings of the Cambridge Philosophical Society, 2003
Summary: We prove the following two theorems: (I) Let \(n\geq 1\) be a (fixed) integer. Then we have for \(\theta\in(0,\pi)\): \[ \sum^n_{k=1}{\cos(k\theta)\over k}\leq-\log\left(\sin\left({\theta\over 2}\right)\right)+{\pi-\theta\over 2}+\sigma_n, \] with the best possible constant \(\sigma_n=\sum^n_{k=1}(-1)^k/k\).
Alzer, H., Koumandos, S., Alzer, H., Koumandos, S.   +3 more
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Inequalities for Trigonometric Sums

2012
We give a survey of recent results on positive trigonometric sums. Far-reaching extensions and generalizations of classical results are presented. We provide new proofs as well as additional remarks and comments. We also present several other sharp inequalities for trigonometric sums of various types.
Koumandos, S., Koumandos, S.
openaire   +2 more sources

On a Trigonometric Inequality of Szegő

Analysis Mathematica, 2021
Inspired by Fejér's work on univalent functions, \textit{G. Szegő} [Duke Math. J. 8, 559--564 (1941; Zbl 0060.20702)] proved an important trigonometric inequality. The authors extend the domain of validity of that inequality. An application is given as well.
Alzer, H., Kwong, M. K.
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A trigonometrical inequality

Mathematical Proceedings of the Cambridge Philosophical Society, 1951
AbstractThe inequality iswhich is established by an elementary argument and is shown to lead directly to the evaluation of the integraland to the expression of sin x as an infinite product.
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