Application of Generalized Cauchy Process on Modeling the Long-Range Dependence and Self-Similarity of Sea Surface Chlorophyll Using 23 years of Remote Sensing Data

Understanding the temporal characteristics of sea surface chlorophyll (SSC) is helpful for marine environmental management. This study chose 10 time series of remote daily sea surface chlorophyll products from the European Space Agency during the period from July 29, 1998 to December 31, 2020. A generalized Cauchy model was employed to capture the local and global behaviors of sea surface chlorophyll from a fractal perspective; the fractal dimension D measures the local similarity while the Hurst parameter H measures the global long-range dependence. The generalized Cauchy model was fitted to the empirical autocorrelation function values of each SSC series. The results showed that the sea surface chlorophyll was multi-fractal in both space and time with the D values ranging from 1.0000 to 1.7964 and H values ranging from 0.6757 to 0.8431. Specifically, regarding the local behavior, 9 of the 10 series had low D values (<1.5), representing weak self-similarity; on the other hand, regarding the global behavior, high H values represent strong long-range dependence that may be a general phenomenon of daily sea surface chlorophyll.

Characterizations of the Cauchy distribution associated with integral transforms

We give two new simple characterizations of the Cauchy distribution by using the Möbius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.

An Asymmetric Bimodal Distribution with Application to Quantile Regression

In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data.

Research Progress and Prospects of the Constitutive Model of Green Ecological Concrete

Green ecological concrete is a new type of building material. It is important to study the relationship of the green ecological concrete between stresses and strains. In the paper, some constitutive models which are suitable to the green ecological concrete are introduced. These models include the linear elastic constitutive model, cauchy model, kuper-gerstle model, constitutive model based on the rheological theory, constitutive model based on plastic fracture theory etc. The constitutive model based on the rheological theory well describes the mechanical properties of the green ecological concrete.