Search

The coronavirus was discovered in Wuhan, China, in December 2019. Scientists and medical practitioners have warned that this fatal virus could spread quickly from person to person in its early stages and its impact will be far more vigorous than the previously discovered viruses. The World Health Organization has given warning propaganda to all nations about this harmful virus. However, the diffusion speed of COVID‐19 was so rapid that it spread to all countries much faster than the researchers predicted, causing the widespread human disaster. The genetic variations of COVID‐19 have also astounded researchers today, as it modifies its mutation with very large genetic strains. The virus is regarded as a human version of the disease, resulting in the common cold, dry cough, and respiratory problems in severe cases. According to health organisations, the coronavirus directly affects the lungs, causing main problems such as difficulty breathing. It is also tough for physicians to diagnose the disease level properly by using the regular process. Even though the virus can be detected in regular testing methods, even computed tomography (CT) and X‐ray images are widely used in the medical field to identify the respiratory problems caused by the COVID‐19 virus. Like COVID‐19, some other types of pneumonia respiratory diseases also affect the human lungs. The fractal dimension (FD) is an interesting non‐linear measure to describe the complexity of visual images. In this context, the complexity of X‐ray images is analysed by using the fractal dimension. The fractal dimension is an excellent non‐linear measurement for describing the complexity of realistic images. The difference between the complexity of the X‐ray images of COVID‐19‐infected patients and the X‐ray images of other types of pneumonia respiratory diseases is well explained by using the fractal dimension. It is also concluded that the fractal dimension discriminates the lung diseases due to COVID‐19 from various pneumonia respiratory diseases. [ABSTRACT FROM AUTHOR]

M. Das proved that the relative multifractal measures are mutually singular for the self-similar measures satisfying the significantly weaker open set condition. The aim of this paper is to show that these measures are mutually singular in a more general framework. As examples, we apply our main results to quasi-Bernoulli measures.

We compute a lower bound of Billingsley–Hausdorff dimension, defined by Gibbs measure, of the level set related to Birkhoff average in the countable symbolic space $\mathbb{N}^{\mathbb{N}}$.

This study provides a general multifractal formalism that overcomes the limitations of the traditional one. The generic Hewitt-Stromberg measures are used to introduce and study a multifractal formalism. The generic Hewitt-Stromberg dimensions' upper and lower bounds are estimated, producing results even at places q where the upper and lower multifractal Hewitt-Stromberg dimension functions diverge. [ABSTRACT FROM AUTHOR]

This appendix gives a lower bound of the Billingsley-Hausdorff dimension of a level set related to Birkhoff average in the “non-compact” symbolic space $\mathbb{N}^{\mathbb{N}}$, defined by Gibbs measure.

The properties of various fractal and multifractal measures and dimensions have been under extensive study in the real-line and higher-dimensional Euclidean spaces. In non-Euclidean spaces, it is often impossible to construct non-trivial self-similar or self-conformal sets, etc. We consider in the present paper the proper way to phrase the definitions for use in general metric spaces. We investigate the relative Hausdorff measures and the relative packing measures defined in a separable metric space. We give some product inequalities which are a consequence of a new version of density theorems for these measures. Moreover, we prove that and can be expressed as Henstock-Thomson variation measures. The question of the weak-Vitali property arises in this context. [ABSTRACT FROM AUTHOR]

In this paper. we intend to estimate the multifractal Hausdorff and the packing dimensions of product measures. The results in this paper establish the connections with various multifractal dimensions of measures on Rn. and generalize many known results about Hausdorff and packing dimensions of measures. [ABSTRACT FROM AUTHOR]

Thanks to the efforts of our reviewers in 2022, the median time to first decision was 17 days and the median time to publication was 37 days. Regardless of whether the articles they examined were ultimately published, the editors would like to express their appreciation and thank the following reviewers for the time and dedication that they have shown I Mathematics i : those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). I Mathematics i was able to uphold its high standards for published papers due to the outstanding efforts of our reviewers. [Extracted from the article]

I Axioms i was able to uphold its high standards for published papers due to the outstanding efforts of our reviewers. [Extracted from the article]

Thanks to the efforts of our reviewers in 2022, the median time to first decision was 18 days and the median time to publication was 41 days. I Fractal and Fractional i was able to uphold its high standards for published papers due to the outstanding efforts of our reviewers. [Extracted from the article]