On some connections between the Gompertz function and special numbers

Rza̧dkowski, Grzegorz; Rzadkowski, Wojciech; Wójcicki, Paweł M.

doi:10.1080/14029251.2015.1079419

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…In our further work, we intend to use, in a similar way, the logistic wavelets of higher order (see Section 2.3). Moreover, using appropriate special numbers we are going to define analogous wavelets for the Gompertz function (see some initial calculations [29,30]) or for some generalizations of the logistic function (for preliminary theorems see [31]).…”

Section: Discussionmentioning

confidence: 99%

Logistic Wavelets and Their Application to Model the Spread of COVID-19 Pandemic

Rza̧dkowski

Figlia²

2021

Applied Sciences

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In the present paper, we model the cumulative number of persons, reported to be infected with COVID-19 virus, by a sum of several logistic functions (the so-called multilogistic function). We introduce logistic wavelets and describe their properties in terms of Eulerian numbers. Moreover, we implement the logistic wavelets into Matlab’s Wavelet Toolbox and then we use the continuous wavelet transform (CWT) to estimate the parameters of the approximating multilogistic function. Using the examples of several countries, we show that this method is effective as a method of fitting a curve to existing data. However, it also has a predictive value, and, in particular, allows for an early assessment of the size of the emerging new wave of the epidemic, thus it can be used as an early warning method.

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Section: Discussionmentioning

confidence: 99%

Logistic Wavelets and Their Application to Model the Spread of COVID-19 Pandemic

Rza̧dkowski

Figlia²

2021

Applied Sciences

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“…4). Using some appropriate special numbers we are going to define analogous wavelets for the Gompertz function (see some initial calculations [13], [14]) or for the fractional logistic functions (some preliminary theorems see [15]).…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Logistic wavelets and logistic function: An application to model the spread of SARS-CoV-2 virus infections

Rzadkowski

2020

Preprint

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In the present paper, we model the cumulative number of persons reported to be infected by the SARS-CoV-2 virus, in a country or a region, by a sum of logistic functions. For a given logistic function, using Eulerian numbers, we find the zeros of its successive derivatives and their relationship with the saturation level of this function. In a given time series, having potentially the logistic trend, we use its second differences to determine points corresponding to these zeros. To estimate the parameters of the approximating logistic function, we define and use logistic wavelets. Then we apply the theory to the cases of SARS-CoV-2 infections in the United States and the United Kingdom.

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Study on the cohesive shear characteristics and intrinsic modelling of the root–tailing soil interface of Amorpha fruticosa

Yang

Hao

Cheng

et al. 2022

Sci Rep

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To study the soil consolidation effect of shrub plant roots on tailings soil and to explore the frictional characteristics of plant roots on tailings soil, three experimental conditions of the root–soil interface were established by using a modified indoor direct shear instrument with binders such as liquid sodium silicate and cyanoacrylate to conduct direct shear frictional tests at the root–soil interface using the roots of the typical slope protection plant Amorpha fruticosa. The Gompertz improved curve model was established by using the relationship between shear stress and shear displacement and the trend of the root–soil interface parameter index. The results were compared between the improved Gompertz curve model and the Clough–Duncan hyperbolic model, and a two-factor coupled improved Gompertz interfacial intrinsic structure model with normal stress and cohesive strength factor was established. The results showed that the interface shear stress and shear displacement showed strain hardening characteristics at different normal pressures for cohesive strength ratios of 1.5 and 1.7 at the root–tailing soil interface. At a cohesive strength ratio of 1.6, strain-softening was observed from 100 to 300 kPa and strain hardening was observed at 400 kPa. The improved Gompertz curve model predicts the shear stress and shear displacement curves at the root–soil interface with different cohesive strengths more reasonably than the Clough–Duncan hyperbolic model, and the maximum accuracy can be improved by nearly 40%. The two-factor coupled improved Gompertz curve model can fit the shear stress versus shear displacement relationship at the A. fruticosa root–tailing soil interface.

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On some connections between the Gompertz function and special numbers

Cited by 4 publications

References 14 publications

Logistic Wavelets and Their Application to Model the Spread of COVID-19 Pandemic

Logistic Wavelets and Their Application to Model the Spread of COVID-19 Pandemic

Logistic wavelets and logistic function: An application to model the spread of SARS-CoV-2 virus infections

Study on the cohesive shear characteristics and intrinsic modelling of the root–tailing soil interface of Amorpha fruticosa

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