Complex systems require rigorous analysis using effective method, in order to handle and interpret their information. Spectrum produced from Fourier transform infrared (FTIR) instrument is an example of a complex system, due to their overlapped bands and interactions within the spectrum. Thus, chemometrics techniques are required to further analyze the data, in particular, chemometrics fuzzy autocatalytic set (c-FACS). The c-FACS is initially used to analyze the FTIR spectra of gelatins. However, in this study, the c-FACS is generalized and implemented for analysis of Coronavirus disease 2019 (Covid-19), particularly, the pandemic outbreak in Malaysia. The daily Covid-19 cases in states in Malaysia are modeled and analyzed using c-FACS, to observe the trend and severity of the disease in Malaysia. As a result, the classification of severity of zones in Malaysia are identified. The obtained results offer descriptive insight for strategizing purposes in combating the Covid-19 outbreak in Malaysia.

A generated n-sequence of fuzzy topographic topological mapping, , is a combination of n number of FTTM’s graphs. An assembly graph is a graph whereby its vertices have valency of one or four. A Hamiltonian path is a path that visits every vertex of the graph exactly once. In this paper, we prove that assembly graphs exist in and establish their relations to the Hamiltonian polygonal paths. Finally, the relation between the Hamiltonian polygonal paths induced from to the k-Fibonacci sequence is established and their upper and lower bounds’ number of paths is determined.

This paper explores how electroencephalography (EEG) signals in the Krohn-Rhodes form can be decomposed further using the Jordan-Chevalley decomposition technique. First, the recorded EEG signals of a seizure were transformed into a set of matrices. Each of these matrices was decomposed into its elementary components using the Krohn-Rhodes decomposition method. The components were then further decomposed into semisimple and nilpotent matrices using the Jordan-Chevalley decomposition. These matrices—which are the extended building blocks of elementary EEG signals—provide evidence that the EEG signals recorded during a seizure contain patterns similar to that of prime numbers.

The disabling aspect of epilepsy disease is that it seems to be erratic and random in nature. Electroencephalogram (EEG) serves as an essential non-invasive tool to diagnose and manage epilepsy, allowing the physiological manifestations of irregular cortical excitability to be demonstrated. Certain prior EEG features related to seizure onset may facilitate seizure pattern predictions through mathematical models. A better understanding of these patterns can positively improve epilepsy management and, in turn, improve the quality of life of epilepsy patients. Thus, the goal of the current paper is to show that elementary EEG signals during a seizure can be perceived as prime numbers. First, the recorded EEG signals are written as a product of their elementary components through the Krohn – Rhodes decomposition technique. Following this, every elementary component of EEG signal is expressed in terms of a summation of their simpler parts via the Jordan – Chevalley decomposition process. Conversely, some prime numbers are decomposed similar to Jordan – Chevalley decomposition of elementary EEG signals and presented as Pseudo – Goldbach Theorem. Finally, the results demonstrate substantial evidence that the EEG signals follow a pattern similar to that of the distribution of prime numbers among positive integers.

The objective of this research is to demonstrate a mathematical technique to analyze the Covid-19 outbreak, particularly with respect to Malaysia. The technique is able to accommodate scarcity, quantity, and availability of the data set. The obtained results can offer descriptive insight for reflecting and strategizing actions in combating the pandemic.