Vol. 11, No. 1 (2022): Regular Issue

A digraph $D=(V,A)$ is called a bipartite digraph if there exists a partition $(X,Y)$ of $V(D)$ into two partite sets such that every arc of $D$ has its end-vertices in different partite sets. It is called balanced if $|X| = |Y|$. If a digraph $D$ has a directed cycle $C$ which covers all of its vertices, then $D$ is Hamiltonian. This paper mainly introduces some sufficient conditions for Hamiltonian cycles in balanced bipartite digraph.

In designing a leader-follower system, the main challenge is how to distinguish the leader among other moving robots. In this paper, a multi robot system will be designed in which the robots are attracting to a spotlight as their leader. This behavior is inspired from the collective motion of the Artemia aggregations. Two dynamical models will be designed based on the newton equation and its parameters can be estimated by two methods: first, depending on the physical feature of the robots, second, the using the least square estimation method. The performance of the proposed systems will be tested by: tracking the spotlight path, achieving formation and avoiding obstacles depending on the virtual circle method. For this purpose, several experiment will be implemented, which may be divided into two scenarios: without and with obstacles. Each scenario has three type of experiments, depending on the spotlight path, such as the straight, circle and zigzag path experiment. These tests will be implemented within the V-REP simulator and the results of the tests show perfect behavior of the robots during the path tracking and the obstacles avoiding.

In this paper, we study the fractional order CHIKV infection model with latency. First, we establish the existence and uniqueness solutions of CHIKV model with latency. Next, we present the local and global stability of fractional order CHIKV model with latency. Finally, we produce some numerical solutions by using MATLAB software that supports the analytical results.

Let $G$ be a simple graph of order $n$. The resolvent Estrada index of $G$ is defined as $REE(G)=\sum_{i=1}^n {\frac{n-1}{n-1-\lambda _i }} $, where $\lambda _1 , \lambda _2 , \cdots , \lambda _n $ are the eigenvalues of the adjacency matrix $A(G)$. In this paper, we present several lower bounds of the resolvent Estrada indices for line graphs of any regular graphs and their complementary graphs.

A model addressing the phagocytosing process of macrophage ingesting oxidised LDL in atherosclerotic plaque formation is presented in this research manuscript. The biological phenomenon of plaque formation has been exposed here in terms of a reaction-diffusion model system in one spatial dimension (1D) by means of no-flux boundary conditions. The present article is mainly focused with the existence and stability of equilibrium solutions as obtained by the model parameters and interpretation of those results in terms of their potential bio-medical implications. Bifurcation analysis of the model system provides six relevant parameters of significance which are clinically sensible. A careful analysis of the model under submission provides an insight to the inflammatory route involved in the atherosclerotic plaque formation.

The impulsive differential equations with unpredictable perturbations are under investigation. The definition of the discontinuous unpredictable function with the discrete unpredictable set of discontinuity moments is introduced. The existence and uniqueness of asymptotically stable discontinuous unpredictable solutions for quasi linear systems are proved. Examples with simulations are given to illustrate the results.

Social distancing is a leading concern to the infectious COVID-19 outbreak or any other epidemic diseases which are spreading through the close contact or droplet transmission between a susceptible and infected person. An SIR model is introduced to describe the disease dynamics of the closed cases of Iran as of 31 March 2020. As the pandemic is going on, it is difficult to discuss more insights. We have tried to show the effect of social distancing on the spreading of COVID-19. The study reveals that the well maintains of social or physical distancing reduces the number of infections and deaths due to COVID-19.

In this paper, we establish some new conditions for the existence and uniqueness of solutions for a class of nonlinear $\psi$-Caputo fractional Volterra-Fredholm integro-differential equations with boundary conditions. The desired results are proved by using Banach and Schaefer's fixed point theorems in Banach spaces. Furthermore, Ulam's type stability of the proposed problem is studied.

Platform-vibrator with shock is widely used in the construction industry for compacting and molding large concrete products. Its mathematical model corresponds to a two-body 2-DOF vibro-impact system with a soft impact. A soft impact is simulated with nonlinear Hertzian contact force. When the control parameter (technological mass of mold with concrete) changes, the model exhibits interesting phenomena inherent in a nonlinear non-smooth vibro-impact system, namely: boundary and interior crises, crisis-induced intermittency, transient chaos, and a hysteresis zone. Phase trajectories with Poincaré maps, graphs of time series and contact forces, Fourier spectra, and wavelet characteristics are used in numerical investigations to determine the realized oscillatory modes. We hope this analysis can help to avoid undesirable platform-vibrator behaviour during design and operation due to inappropriate system parameters.

In this paper, we propose a method for solving quasiconvex nonsmooth multiobjective optimization problems. The proposed method extends the conditional subgradient method, from mono-objective to multiobjective optimization problems. We show that the sequence generated using this method converge to Pareto optimal points of the problem.

The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our suggestions are for more neat comprehension of chaos in the domain. The novelties can serve for revisited models as well as motivate new ones.

In this work, we are concerned with a problem for a nonlinear viscoelastic wave equation with strong damping, source and delay terms, we proved a blow up result for the solution with negative initial energy under suitable conditions.

This work deals with the qualitative behavior of a delay differential equation arising from an SIS epidemiological model. The population is assumed to be of exponential demographic structure and delay corresponds to the infectious period. A death rate caused by infection is considered. The study is based on the exponential ordering properties in the context of monotone systems. A new sufficient condition of the asymptotic stability of the endemic disease equilibrium is derived. Then we provide a new sufficient condition of global asymptotic stability of the disease free equilibrium. Moreover, the author proves that the established condition of global stability is different from that obtained in 1995 by H.W. Hethecote and P. van den Driessche. The obtained results are then illustrated by numerical simulations.

Optimization for all disciplines is very important and relevant. Optimization has played a key role in the design and operation of industrial reactors, separation processes, heat exchangers and complete plants in Chemical Engineering. In this paper, a novel hybrid meta-heuristic optimization algorithm which is based on Differential Evolution (DE), Gradient Evolution (GE) and Jumping Technique (+) named as Differential Gradient Evolution Plus (DGE+) is presented. The main concept of this hybrid algorithm is to enhance its exploration and exploitation ability. The proposed algorithm hybridizes the above-mentioned algorithms with the help of an improvised dynamic probability distribution, additionally provides a new shake off method to avoid premature convergence towards local minima. The performance of DGE+ is investigated in thirteen benchmark unconstraint functions and the results are compared to the other state-of-the-art meta-heuristics. The comparison shows that the proposed algorithm is able to outperform the other state-of-the-art meta-heuristics in almost all benchmark functions. To evaluate the efficiency of the DGE+ it has also been applied to complex constrained non-linear chemical design problems such as optimal operation of alkylation unit, reactor network design, optimal design of heat exchanger network, optimization of an isothermal continuous stirred tank reactor, the results of comparison revealed that the proposed algorithm is able to provide very compact, competitive and promising performance.

In this paper, we generalize the mathematical model of the human liver by recently introduced hybrid fractional derivative. We achieve the existence and uniqueness results via Schauder's and Banach fixed point theorems, respectively. We use the Laplace transformation technique to attain the series type solution of the human liver model. In the end, we give the conclusion of the manuscript and future research direction.