Related Experiment Video
Updated: Mar 7, 2026

Optimization of Processing of Tiebangchui with Highland Barley Wine Based on the Box-Behnken Design Combined with the Entropy Method
Published on: May 19, 2023
Optimal inequalities for bounding Toader mean by arithmetic and quadratic means
Tie-Hong Zhao1, Yu-Ming Chu1, Wen Zhang2
1School of Mathematics and Computation Sciences, Hunan City University, Yiyang, 413000 China.
Abstract:
In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text], and we provide new bounds for the complete elliptic integral [Formula: see text] [Formula: see text] of the second kind, where [Formula: see text], [Formula: see text] and [Formula: see text] are the Toader, arithmetic, and quadratic means of a and b, respectively.
Related Concept Videos
Trimmed Mean
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the...
Arithmetic Mean
When all the values in a data set are not unique, the sum in the numerator can be calculated by multiplying each distinct value by its frequency.
Sometimes, the arithmetic mean of a sample can be affected by a few data points...
Root Mean Square
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...
Harmonic Mean
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...
Geometric Mean
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
Weighted Mean
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...

