The definitions of derivatives as delta and nabla in time scale theory are kept to follow the notion of the classical derivative. The jump operators are used to transfer the notion from the classical derivative to the derivatives in the time scale theory. The jump operators can be determined by analyst to model phenomena. In this study, the definitions of derivatives in the time scale theory are transferred to ratio of function which has jump operators from q-deformation. If we use q-deformation as a subset of real line ℝ, we can have a chance to define a derivative via consulting ratio of two expressions on q-sets. The applications are performed to produce the new entropy functions by use of the partition function and the derivatives proposed. The concavity and convexity of the proposed entropy functions are examined by use of Taylor expansion with first-order derivative. The entropy functions can catch the rare events in an image. It can be observed that rare events or minor changes in regular pattern of an image can be detected efficiently for different values of q when compared with the proposed entropies based on q-sense.

中文翻译：

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时间尺度演算上 q 集的比率原理的导数

时间尺度理论中将导数定义为 delta 和 nabla 的定义保持遵循经典导数的概念。跳跃算子用于将概念从经典导数转移到时间尺度理论中的导数。分析人员可以确定跳转算子以对现象建模。在这项研究中，时间尺度理论中导数的定义被转换为具有跳跃算子的函数的比率q-形变。如果我们使用q-作为实线子集的变形ℝ，我们可以通过参考两个表达式的比率来定义导数q-套。通过使用配分函数和所提出的导数来执行应用以产生新的熵函数。通过使用具有一阶导数的泰勒展开来检查所提出的熵函数的凹凸性。熵函数可以捕捉图像中的罕见事件。可以观察到，对于不同的q与基于提议的熵相比q-感觉。