DERIVATIVES BY RATIO PRINCIPLE FOR q-SETS ON THE TIME SCALE CALCULUS

被引:4
作者
Cankaya, Mehmet Niyazi [1 ,2 ]
机构
[1] Usak Univ, Fac Appl Sci, Dept Int Trading & Finance, TR-64200 Usak, Turkey
[2] Usak Univ, Fac Art & Sci, Dept Stat, TR-64200 Usak, Turkey
关键词
Entropy; Time Scale Calculus; q-Sets; Coronavirus Disease (COVID-19); GENERALIZED ENTROPIES; ESCORT DISTRIBUTIONS;
D O I
10.1142/S0218348X21400405
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 Double-struck capital 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.
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页数:16
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