In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon and then investigate the optimal sets of n -means and the n th quantization errors for all positive integers n . We give an exact formula to determine them, if n is of the form $$n=6k$$ n = 6 k for some positive integer k . We further calculate the quantization dimension, the quantization coefficient, and show that the quantization dimension is equal to the dimension of the object, and the quantization coefficient exists as a finite positive number. Then, we define a mixture of two uniform distributions on the boundary of a semicircular disc and obtain a sequence and an algorithm, with the help of which we determine the optimal sets of n -means and the n th quantization errors for all positive integers n with respect to the mixed distribution. Finally, for a uniform distribution defined on an elliptical curve, we investigate the optimal sets of n -means and the n th quantization errors for all positive integers n .

中文翻译：

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六边形、半圆形和椭圆形曲线上均匀分布的量化

在本文中，首先我们在正六边形的边界上定义了均匀分布，然后研究了所有正整数 n 的最优 n 均值集和第 n 个量化误差。我们给出了一个精确的公式来确定它们，如果 n 对于某个正整数 k 的形式为 $$n=6k$$ n = 6 k 。我们进一步计算量化维数，量化系数，表明量化维数等于物体的维数，量化系数以有限正数的形式存在。然后，我们在半圆盘的边界上定义了两个均匀分布的混合，并获得了一个序列和一个算法，在此帮助下我们确定了所有正整数 n 的最优 n 均值集和第 n 个量化误差。关于混合分布。最后，