Results 51 to 60 of about 61,133 (171)

Sharpening and generalizations of Carlson's double inequality for the arc cosine function [PDF]

open access: yesJiao-Lian Zhao, Chun-Fu Wei, Bai-Ni Guo, and Feng Qi, Sharpening and generalizations of Carlson's double inequality for the arc cosine function, Hacettepe Journal of Mathematics and Statistics 41 (2012), no. 2, 201--209, 2009
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
arxiv  

Sharpening and generalizations of Carlson's inequality for the arc cosine function [PDF]

open access: yesBai-Ni Guo and Feng Qi, Sharpening and generalizations of Carlson's inequality for the arc cosine function, Hacettepe Journal of Mathematics and Statistics 39 (2010), no. 3, 403--409, 2009
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
arxiv  

Derivatives of the Lp-cosine transform

open access: yesAdvances in Mathematics, 2003
The $L^p$-cosine transform of an even, continuous function $f\in C_e(\Sn)$ is defined by: $$H(x)=\int_{\Sn}|\ip{x} |^pf( ) d ,\quad x\in {\R}^n.$$ It is shown that if $p$ is not an even integer then all partial derivatives of even order of $H(x)$ up to order $p+1$ (including $p+1$ if $p$ is an odd integer) exist and are continuous everywhere in ${\R}
openaire   +3 more sources

Riemann-Liouville Fractional Cosine Functions [PDF]

open access: yesarXiv, 2015
In this paper, a new notion, named Riemann-Liouville fractional cosine function is presented. It is proved that a Riemann-Liouville $\alpha$-order fractional cosine function is equivalent to Riemann-Liouville $\alpha$-order fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math. Nachr. 288, No. 7, 784-797 (2015)].
arxiv  

The cosine measure relative to a subspace [PDF]

open access: yesarXiv
The cosine measure was introduced in 2003 to quantify the richness of a finite positive spanning sets of directions in the context of derivative-free directional methods. A positive spanning set is a set of vectors whose nonnegative linear combinations span the whole space. The present work extends the definition of cosine measure.
arxiv  

Statistical Advantages of Perturbing Cosine Router in Mixture of Experts [PDF]

open access: yesarXiv
The cosine router in Mixture of Experts (MoE) has recently emerged as an attractive alternative to the conventional linear router. Indeed, the cosine router demonstrates favorable performance in image and language tasks and exhibits better ability to mitigate the representation collapse issue, which often leads to parameter redundancy and limited ...
arxiv  

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