In the paper, with the aid of the Čebyšev integral inequality, by virtue of the integral representation of the Riemann zeta function, with the use of two properties of a function and its derivatives involving the exponential function and the Stirling numbers of the second kind, by means of complete monotonicity, the authors establish logarithmic convexity and increasing property of four sequences involving the Bernoulli numbers and their ratios.

中文翻译：

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伯努利数及其比的对数凸性和递增性

文中借助Čebyšev积分不等式，借助黎曼zeta函数的积分表示，利用函数及其导数的两个性质，涉及指数函数和第二类斯特林数，通过完全单调性，作者建立了涉及伯努利数及其比的四个序列的对数凸性和递增性。