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Full-Text Articles in Physical Sciences and Mathematics
An Improved Oscillation Criteria For First Order Dynamic Equations, Özkan Öcalan
An Improved Oscillation Criteria For First Order Dynamic Equations, Özkan Öcalan
Turkish Journal of Mathematics
In this work, we consider the first-order dynamic equations \begin{equation*} x^{\Delta }(t)+p(t)x\left( \tau (t)\right) =0,\text{ }t\in \lbrack t_{0},\infty )_{\mathbb{T}} \end{equation*} where $p\in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{R}^{+}\right) , $ $\tau \in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{T}\right) $ and $\tau (t)\leq t,\ \lim_{t\rightarrow \infty }\tau (t)=\infty $. When the delay term $\tau (t)$ is not necessarily monotone, we present a new sufficient condition for the oscillation of first-order delay dynamic equations on time scales.
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
Turkish Journal of Mathematics
We investigate a family of probability distributions, with three parameters associated with the dynamic Gompertz function. We prove its existence for various parameter sets and discuss the existence of its time scale moments. Afterwards, we investigate the special case of discrete time scales, where it is shown that the discrete Gompertz distribution is a $q$-geometric distribution of the second kind. Further, we find their $q$-binomial moments, we bound their expected value, and we show how a classical Gompertz distribution is obtained from them.