مجله بین المللی محاسبات و مدل سازی ریاضی
سال یازدهم شماره 1 (Winter 2021)

‎Banana Xanthomonas Wilt (BXW) is an infectious disease caused by Xanthomonas campestris pv‎. ‎musacearum‎. ‎The model incorporates a new class of protected banana plants into banana plant population‎. ‎This new class are the susceptible banana plant that are treated with fertilizers‎. ‎The basic reproduction number‎, Ro , ‎is obtained using next generation matrix‎. ‎The model analysis is done and equilibrium points are analysed to establish the local and global stability of disease-free and endemic equilibrium solution‎. ‎It is shown that if the basic reproduction number‎, ‎Ro‎≤1, ‎then banana xanthomonas wilt is cleared from banana plantation and is globally asymptotically stable and if Ro>1‎, ‎the endemic equilibrium point is globally asymptotically stable and the disease persists in banana plant population‎. ‎The impact of parameters in BXW model is investigated using sensitivity analysis‎. ‎Numerical simulations are performed to justify the analytical findings‎.

In this paper, we propose a fractional order model of leukemia in terms of a system of ordinary differential equations with the Caputo derivative that provides convenience for initial conditions of the differential equations. Firstly, we prove the global existence, positivity, and boundedness of solutions. The local stability properties of the equilibrium are obtained by using fractional Routh-Hurwitz stability criterion. Furthermore, a suitable Lyapunov functions are constructed to prove the global stability of equilibrium. Finally, numerical simulation of the model are presented to illustrate our theoretical results for different choices of fractional order of derivative α. Then, we can observe the impact of fractional derivative α on the evolution of the model states.

‎A new continuous distribution called Lindley-Lindley distribution is defined‎ ‎and studied‎. ‎Relevant mathematical properties are derived‎. ‎We‎ ‎present three characterizations of the new distribution based on the truncated moments of certain functions of the random variable;‎ ‎the hazard function and in terms of the conditional expectation of a‎ ‎function of the random variable‎. ‎Some new bivariate type distributions using‎ ‎Farlie Gumbel Morgenstern copula‎, ‎modified Farlie Gumbel Morgenstern‎ ‎copula and Clayton copula are introduced‎. ‎The main‎ ‎justification of this paper is to show how different frequentist estimators‎ ‎of the new model perform for different sample sizes and different parameter‎ ‎values and to provide a guideline for choosing the best estimation method‎ ‎for the parameters of the proposed model‎. ‎The unknown parameters of the new‎ ‎distribution are estimated using the maximum likelihood‎, ‎ordinary‎ ‎least squares‎, ‎Cramer-Von-Mises‎, ‎weighted least squares and Bayesian methods‎. ‎The obtained estimators are compared using‎ ‎Markov Chain Monte Carlo simulations and observed that Bayesian estimators‎ ‎are generally more efficient than the other estimators.

Heat equation is a partial differential equation that describes the distribution of temperature (heat) in a given body over time. In this study, a finite volume based method is used to solve three-dimensional heat equation. A MATLAB code is developed to implement the numerical method in a unit cube. The stability of the numerical scheme is analysed using the Von Neumann method. An example is provided in order to demonstrate the method. The numerical solution by the method is in an excellent agreement with the exact solution for the example considered. The computational procedures used in this study can provide good insights to solve a three dimensional diffusion equation arising in many physical phenomena.

Complex systems and information flow such as command, control, communication, computer intelligence, inference, and expert systems exhibit an increasing dependence on the system's nature and information flow. For this reason, it is both the flow exchange of information in the system and the emergent information properties of the system, which are central to the definition, design and analysis of such systems. Besides, the achievement of human-level machine intelligence has long been one of the principal objectives of Artificial Intelligence (AI). Machine intelligence methods have gained many orders of magnitude in computational capability in the last decade, especially in cognitive science and cognitive informatics. This research discussed the difference between Human IQ and Machine Intelligence Quotient (MIQ). Also, we show that MIQ is an abstract intelligence and soft concept of artificial intelligence. Finally, we conclude that the fuzzy sets can better represent MIQ instead of probabilistic and numerical methods.

In this paper we introduce an approach to increase integration rate of elements of a current source circuit. Framework the approach we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized.