Asian-European Journal of Mathematics

COVID-19 pandemic is one of the worst global disasters in the last century. Its pandemic spread and influence in everyday social life, economics and health is in central interest of concern for all governments in the world. North Macedonia is one of the countries with very high percentage of COVID-19 deaths. The health system in a few periods was before collapse. In this paper, we analyze the COVID-19 epidemic situation in North Macedonia from its beginning. We make analysis and comparisons of the situation in different time epidemic periods. We use regression models and machine learning algorithms in order to make predictions, which can be used as an efficient tool to give directions of the authorities to deal with COVID-19 challenges.

In order to respond to different requirements in banks, airports, hospitals and other organizations, queueing models are used to help in managing and allocating of the resources. Because we live in the pandemic of COVID-19, mass vaccination is necessary for obtaining collective immunity. For mathematical modeling of the vaccination’s process, we use a queueing system as a useful tool for estimating of the capacity requirements and service time. For that purpose, we have made simulation in AnyLogic Simulation Modeling Software. In that simulation, the processes of the vaccination and revaccination are considered. Also, the capacity of queue, the capacity of system, the average waiting time in the queue and in the system are estimated.

This paper is devoted to a description of the modeling of economics and in particular, of business processes. More specifically, it describes the process and the conditions of creating a user-friendly and correct models, as well as the advantages, disadvantages and problems in applying the method of business process simulation. The process of simulation in the field of queueing systems and stock management, which are two of the most basic decision-making areas for all enterprises, is described in more detail. Nowadays, technology offers many solutions for every researcher with hi-end simulation tools, like simulation languages and other software packages. Simple examples are given and commented from computational and economical points of view.

By introducing new variables in the systems of difference equations from the paper [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contrib. Sec. Math. Tech. Sci. 33 (2012) 75–96], new systems of difference equations are obtained. The solutions of these new systems of difference equations depend only on the initial values $a_0,b_0,c_0$ and the coefficients $a_i,i\in N$ . The power series whose coefficients are these solutions present the recurrent solutions for the Lorenz system of differential equations. A comparison between the behavior of the Lorenz system of differential equations and the local behavior of its recurrent solutions for small time steps is examined in examples by computer simulations, as in the papers [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contrib. Sec. Math. Tech. Sci. 33 (2012) 75–96; B. Zlatanovska and D. Dimovski, Systems of difference equations as a model for the Lorentz system, in Proc. Fifth Int. Scientific Conf. FMNS - 2013, Vol. I (Blagoevgrad, Bulgaria, 2013), pp. 102–107 and B. Zlatanovska, Approximation for the solutions of Lorenz system with systems of differential equations, Bull. Math. 41(1) (2017) 51–61].

In this paper, from the expanded class of the second-order linear differential equations, a subclass will be obtained for which a new condition for reductability according to Frobenius will be obtained. Explicit formulas of a particular solution for the subclass of the second-order linear differential equations are obtained. The third-order shortened Lorenz system was obtained from the Modified Lorenz system. In this paper, a particular solution of the third-order shortened Lorenz system via the integrability of the subclass of the second-order linear differential equations under certain conditions is obtained. At the end, via graphical visualization in Mathematica, the theory is supported by examples.

Missing data are encountered in many researches and they are also found in well-conducted and controlled studies. Missing data can reduce the statistical strength of a study and may produce biased estimates, leading to invalid conclusions. This study is focused on the problems and types of missing data, together with the techniques for their approach. The mechanisms by which the missing data are obtained and the methods to study these data are illustrated. We have dealt with the multiple imputations as a very efficient method of imputing the missing data and applying these methods in some simulation cases and in real data time series. We have also prepared and adapted the scripts in the programming language R to conduct the simulations. The proposed mice and Amelia packages for imputing the missing values provide fairly good approximations even in the case of real data.

Maximal regularity is a useful tool for solving abstract parabolic evolution equations. A variant of the one-phase quasistationary Stefan problem can be reduced to a single evolution equation. We approach this problem by maximal regularity and then apply an existence theorem for this type of evolution equation. We use as an assumption that one particular result on the solvability of a degenerate oblique derivative problem extends in an appropriate way.

We give a description of a class of numerical semigroups with embedding dimension equal to 4, defined by four pairwise relatively prime nonnegative integers $n$, $x$, $y_1$ and $y_2$ such that $y_1+y_2=tn$, for $t\ge 2$ and $t\in \mathbb{N}$. Such description provides a mode to determine the characteristics of the corresponding numerical semigroups: the Frobenius number, gaps, genus, etc.

In the aftermath of the COVID-19 pandemic, global financial markets have seen growing uncertainty and volatility and as a consequence, precise prediction of stock price trend has emerged to be extremely challenging. In this background, we propose two time frameworks wherein the Hybrid genetic algorithm (HGA) is used to set up an optimal portfolio included ten stocks traded in Bulgarian stock market during pre and post COVID-19 periods. The fitness function values of constructed HGA during pre- and post-COVID-19 periods were −7.194e${}^{-04}$ and −7.014e${}^{-04}$, respectively. The estimated nonzero portfolio weights during pre-COVID-19 period were ALCM (0.025), HNVK (0.253), HVAR (0.378), MSH (0.204), NEOH (0.038), and SFT (0.102) while during post-COVID-19 period were AGH (0.003), ALCM (0.015), HNVK (0.272), HVAR (0.460), MSH (0.142), NEOH (0.057), SFT (0.031), and SPH (0.021). The corresponding expected portfolio return and portfolio risk during pre-COVID-19 period were 9.825e${}^{-03}$ and 7.163e${}^{-04}$ while during post-COVID-19 period were 9.656e${}^{-03}$ and 6.895e${}^{-04}$, respectively.

The COVID-19 global pandemic has likely affected air quality due to extreme changes in human behavior. The aim of this paper is to explore the consequence of the COVID-19 pandemic on the air quality improvement in the Bulgarian city of Stara Zagora using Interrupted Time Series ARMA Model. After adjusting by meteorology and Sunday effect, the results confirm positive and significant effect immediately after the announcement of COVID-19 pandemic in Bulgaria and negative and significant trend in the levels for PM${}_{2.5}$ and O₃. For the remaining CO and NO series of data, the estimate of the time series slope, i.e. the expected change in the concentration associated with a time unit increase is positive and significant. The temporal dynamics for each time series are reported by the ARMA coefficients: an ARMA(2,3) structure is estimated for O₃ and NO, and an ARMA(1,1) is the best choice for CO while AR(5) for PM${}_{2.5}$. Understanding how air pollution is affected during COVID-19 pandemic will contribute to future air quality management policies and human health.

Bootstrap is becoming a useful and very popular tool for obtaining estimations and confidence intervals for coefficients in many researches in different scientific fields without making assumptions about the population. Our goal is to apply bootstrap technique in parameter estimation and confidence intervals for the coefficients in Multiple Logistic Regression model in a study using medical records. We will use R programming language and SPSS software to obtain the coefficients of the model and the estimations using non-parametric bootstrap and we will also make a comparison of the results emphasizing the importance of using resampling methods even in a study with real data.

In addition to the deterministic models, the stochastic models are successfully used for mathematical description of real-world processes and phenomena. They use knowledge from the mathematical theories of probability and statistics to analyze specific properties of complex living systems. This paper considers some stochastic models of various processes and phenomena in genetics. Basic knowledge used in classical stochastic models is considered and applied to real problems from medical genetics with their solutions.

In this paper, we study the periodic boundary value problem for a semilinear fractional-order delayed functional differential inclusion involving Riemann–Liouville derivative in Banach space. The existence of solutions is proved under compactness type conditions on the multivalued term.

In this paper, nonautonomous semilinear evolution inclusions with time lag and nonlocal initial conditions are studied. We define the so-called limit and weak solutions. We prove the existence of solutions when the multivalued part of the right-hand side and the initial functions are Lipschitz under natural conditions on the Lipschitz constants. Afterwards, under the same conditions, a variant of the important in optimal control relaxation theorem is proved.

We consider a power ternary semigroup $P(S)$ associated with a ternary semigroup $S$ and study some properties of $P(S)$ by using the corresponding properties of $S$. After that we study the notion of ordered power ternary semigroup and our main aim is to establish some interconnection between the properties of a ternary semigroup $S$ and the associated ordered ternary semigroup ${𝒫}({𝒮})$.

Some cohomology elements, called $\nu$-classes, as a supergeneralization of universal Chern classes, are introduced for canonical super line bundles over $\nu$-projective spaces, a novel supergeometric generalization of projective spaces. It is shown that these classes may be described by analytic representatives of elements of generalized de Rham cohomology.

Let $G$ be a graph with $n$ vertices and $d_i$ is the degree of its $i$th vertex ($d_i$ is the degree of $v_i$), then the Zagreb matrix of $G$ is the square matrix of order $n$ whose $(i,j)$entry is equal to $d_i+d_j$ if the $i$th and $j$th vertex of $G$ are adjacent, and zero otherwise. The Zagreb energy $ZE(G)$ of a graph $G$ is defined as the sum of the absolute values of the eigenvalues of the Zagreb matrix. In this paper, we compute the Zagreb energy for some of the specific graphs, edge deleted graphs and complements graphs. Moreover, some properties of the eigenvalues and bounds for Zagreb energy are also discussed.

In this paper, several characterizations of quasi-complemented posets in terms of Baer ideals, 0-ideals, and minimal prime ideals are obtained. This extends the results of Jayaram, Cornish and Varlet. Further, we investigate the connections between Baer ideals, 0-ideals, and minimal prime ideals in the class of ${\mathbb{P}}_{MFP}^{\ell }$, which extends the results of Jayaram. Moreover, for a given meet-semilattice $Q$ in the class ${\mathbb{P}}_{MFP}^{\ell }$, we prove that $Q$ is weakly quasi-complemented if and only if each minimal prime ideal in $Id(Q)$ contracts to a minimal prime ideal in $Q$. This extends the result of Cornish to meet-semilattices.

Let ${𝒜}$ and $𝔄$ be two Banach algebras such that ${𝒜}$ is a Banach $𝔄$-bimodule with the left and right compatible actions of $𝔄$ on ${𝒜}$. Let ${𝒜}⋊𝔄$ be a strongly splitting Banach algebra extension of $𝔄$ by ${𝒜}$. In this paper, we investigate some homological aspects such as injectivity, projectivity and flatness of ${𝒜}⋊𝔄$ and give some necessary and sufficient conditions for injectivity, projectivity and flatness of ${𝒜}⋊𝔄$.

The objective of this paper is to construct canonical Orlicz class and study their fundamental properties. Also, we prove that this space contains Henstock–Kurzweil integrable functions.