Optimal bounds of exponential type for arithmetic mean by Seiffert-like mean and centroidal mean

Author(s):  
Ling Zhu
2021 ◽  
Vol 6 (12) ◽  
pp. 13024-13040
Author(s):  
Ling Zhu ◽  
◽  
Branko Malešević ◽  

<abstract><p>In this paper, optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type are established using the monotone form of L'Hospital's rule and the criterion for the monotonicity of the quotient of power series.</p></abstract>


Author(s):  
Hui-Zuo Xu ◽  
Wei-Mao Qian

We provide the optimal bounds for the arithmetic mean in terms of harmonic, contra-harmonic and new Seiffert-like means.


2012 ◽  
Vol E95-B (2) ◽  
pp. 647-650
Author(s):  
Ning WANG ◽  
Julian CHENG ◽  
Chintha TELLAMBURA

2019 ◽  
Vol 484 (1) ◽  
pp. 7-11
Author(s):  
N. F. Abuzyarova

We consider the problem of obtaining the restrictions on the zero set of an entire function of exponential type under which this function belongs to the Schwartz algebra and invertible in the sense of Ehrenpreis.


2011 ◽  
Vol 26 (4) ◽  
pp. 579-585 ◽  
Author(s):  
Charles R. Sampson ◽  
John Kaplan ◽  
John A. Knaff ◽  
Mark DeMaria ◽  
Chris A. Sisko

Abstract Rapid intensification (RI) is difficult to forecast, but some progress has been made in developing probabilistic guidance for predicting these events. One such method is the RI index. The RI index is a probabilistic text product available to National Hurricane Center (NHC) forecasters in real time. The RI index gives the probabilities of three intensification rates [25, 30, and 35 kt (24 h)−1; or 12.9, 15.4, and 18.0 m s−1 (24 h)−1] for the 24-h period commencing at the initial forecast time. In this study the authors attempt to develop a deterministic intensity forecast aid from the RI index and, then, implement it as part of a consensus intensity forecast (arithmetic mean of several deterministic intensity forecasts used in operations) that has been shown to generally have lower mean forecast errors than any of its members. The RI aid is constructed using the highest available RI index intensification rate available for probabilities at or above a given probability (i.e., a probability threshold). Results indicate that the higher the probability threshold is, the better the RI aid performs. The RI aid appears to outperform the consensus aids at about the 50% probability threshold. The RI aid also improves forecast errors of operational consensus aids starting with a probability threshold of 30% and reduces negative biases in the forecasts. The authors suggest a 40% threshold for producing the RI aid initially. The 40% threshold is available for approximately 8% of all verifying forecasts, produces approximately 4% reduction in mean forecast errors for the intensity consensus aids, and corrects the negative biases by approximately 15%–20%. In operations, the threshold could be moved up to maximize gains in skill (reducing availability) or moved down to maximize availability (reducing gains in skill).


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