We analyzed the sunspot-group daily data that were reported by Greenwich Photoheliogrphic Results (GPR) during the period 1874-1976 and Debrecen Photoheliographic Data (DPD) during the period 1977-2017. We determined the equatorial rotation rate [A] and the latitude gradient [B] components of the solar differential rotation by fitting the data in each of the 3-year moving time intervals (3-year MTIs) successively shifted by one year during the period 1874-2017 to the standard law of differential rotation. The values of A and B around the years of maxima and minima of Solar Cycles 12-24 are obtained from the 3-year MTIs series of A and B and studied the long-term cycle-to-cycle modulations in these coefficients. Here we have used the epochs of the maxima and minima of Solar Cycles 12-24 that were recently determined from the revised Version-2 international sunspot-number series. We find that there exits a considerably significant secular decreasing-trend in A around the maxima of solar cycles. There exist no secular trends in both A and B around the minima of solar cycles. The secular trend in B around the maxima of solar cycles is also found to be statistically insignificant. We fitted a cosine function to the values of A, and also to those of B, after removing the corresponding linear trends. The cosine-fits suggest that there exist ~54-year (~94-year) and ~82-year (~79-year) periodicities in A (B) around the maxima and minima of solar cycles, respectively. The amplitude of the cosine-profile of A (B) around the minima of solar cycles is about 41% (65%) larger than that of A (B) around the maxima. In addition, the cosine profiles of A and B suggest a large (up to 180 degree) phase difference between the long-term variations of A, and also between those of B, around maxima and minima of solar cycles.

中文翻译：

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太阳微分自转和太阳黑子活动的长期变化，II：围绕太阳周期最大值和最小值的微分自转 12 – 24

我们分析了 1874-1976 年格林威治日光成像结果 (GPR) 和 1977-2017 年德布勒森日光成像数据 (DPD) 报告的太阳黑子组每日数据。我们通过拟合每个 3 年移动时间间隔 (3 年 MTI) 中的数据来确定赤道自转速率 [A] 和纬度梯度 [B] 分量，该时间间隔在此期间连续移动一年1874-2017年到差速旋转的标准定律。A 和 B 在太阳周期 12-24 的最大值和最小值附近的值是从 A 和 B 的 3 年 MTI 系列中获得的，并研究了这些系数中的长期周期到周期调制。在这里，我们使用了最近从修订后的第 2 版国际太阳黑子数系列确定的太阳活动周期 12-24 的最大值和最小值的历元。我们发现，在太阳活动周期的最大值附近，A 中存在相当显着的长期下降趋势。在太阳周期的最小值附近，A 和 B 都没有长期趋势。还发现 B 围绕太阳周期最大值的长期趋势在统计上是不显着的。在去除相应的线性趋势后，我们为 A 的值以及 B 的值拟合了一个余弦函数。余弦拟合表明在太阳周期的最大值和最小值附近的 A (B) 中分别存在约 54 年（约 94 年）和约 82 年（约 79 年）的周期。A (B) 在太阳活动周期最小值附近的余弦剖面的振幅比 A (B) 在最大值附近的余弦剖面幅度大约 41% (65%)。此外，A 和 B 的余弦分布表明 A 的长期变化之间以及 B 的长期变化之间存在大（高达 180 度）相位差，在太阳周期的最大值和最小值附近。