Journal of Advanced Mathematical Modeling
https://jamm.scu.ac.ir/
Journal of Advanced Mathematical Modelingendaily1Tue, 26 Dec 2023 00:00:00 +0330Tue, 26 Dec 2023 00:00:00 +0330Minimization of HIV Infection among Nigerian Women through the Use of Microbicides: An Insight from Mathematical Modeling
https://jamm.scu.ac.ir/article_18740.html
A recent report indicated that one hundred and thirty thousand Nigerians were lately infected with HIV with the majority of infections resulting from unguarded vaginal sex. About two-thirds of new HIV infections in adults exist in women. Male circumcision and male condoms limit the danger of HIV infection, but the adoption of these procedures is beyond the control of Nigerian women due to gender inequality and gender-based violence against women in the country. In an attempt to provide a mathematical framework to examine a potential female-controlled strategy of HIV acquisition in Nigeria, a mathematical model is modified and analyzed for the transmission of HIV by incorporating pre-exposure prophylaxis (PrEP) in the form of a microbicide. The solutions of the model are proved to be positive. The critical points of the model and the epidemic threshold known as the reproduction number are also derived. The restricted case of total compliance to the use of the microbicide is analyzed by proving the global stability of the disease-free equilibrium (DFE) of the model. The general case which permits individuals to default the microbicide is also investigated by proving the global stability of the endemic equilibrium (EE) of the model. Numerical simulation is carried out to verify the analytical results and the results of the simulation show that strict compliance and consistent use of the microbicide may tend HIV acquisition among Nigerian women to zero.Numerical Solution of Fokker-Planck-Kolmogorov Time Fractional Differential Equations Using Legendre Wavelet Method Along with convergence and error analysis
https://jamm.scu.ac.ir/article_18725.html
The aim of this paper is to numerically solve the Fokker-Planck-Kolmogorov fractional-time differential equations using the Legendre wavelet. Also, we analyzed the convergence of function approximation using Legendre wavelets. Introduced the absolute value between the exact answer and the approximate answer obtained by the given numerical methods, and analyzed the error of the numerical method. This method has the advantage of being simple to solve. The results revealed that the suggested numerical method is highly accurate and effective. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. The simulation was carried out using MATLAB software. In this paper and for the first time, the authors presented results on the numerical simulation for classes of time-fractional differential equations. The authors applied the reproducing Legendre wavelet method for the numerical solutions of nonlinear Fokker-Planck-Kolmogorov time-fractional differential equation.The method presented in the present study can be used by programmers, engineers and other researchers in this field.Exact solutions of (3+1)-dimensional wave equation via Lie brackets of symmetries
https://jamm.scu.ac.ir/article_18739.html
&lrm;In this paper the Lie symmetry method and Lie brackets of vector fields are used in order to find some new solutions of (3+1)-dimensional sourceless wave equation&lrm;. &lrm;The obtained solutions are classified to two categories; polynomial and non-polynomial exact solutions&lrm;. &lrm;Because of the properties of the Lie brackets and the symmetries&lrm;, &lrm;a generalized method is implemented for constructing new solutions from old solutions&lrm;. &lrm;We demonstrate the generation of such polynomial and non-polynomial solutions through the medium of the group theoretical properties of the equation&lrm;. &lrm;It in noteworthy that this method could be used when the equations has two special kind of symmetries which will be mentioned below&lrm;.Analysis of the behavior of the corona virus in the body of an infected person with the help of dynamic systems
https://jamm.scu.ac.ir/article_18822.html
In general, the process of the spread of any virus in the human body consists of five stages, which include attachment of the virus to the host cell, penetration, preparation for reproduction, reproduction and propagation. However, different viruses have different life cycles. In this article, we will model the behavior of the corona virus in the body of each affected person and analyze the behavior of this virus in the body using dynamic systems. For this purpose, we study the dynamics of the evolutionary competition between the strategy of the corona virus and the body&rsquo;s immune cells, especially lymphocytes T and B.Local higher derivations on Hilbert C*-modules
https://jamm.scu.ac.ir/article_18827.html
&lrm;A sequence of continuous linear mappings $\{\Phi_n\}_{n=0}^\infty$ form a Hilbert C* -&lrm;module&lrm; M into M is called a local higher derivation if for each $a\in\mathfrak{M}$ there is a continuous higher derivation $\{\varphi_{a,n}\}_{n=0}^\infty$ &lrm;on&lrm; M such that $\Phi_n(a)=\varphi_{a,n}(a)$ for each non-negative integer n&lrm;. &lrm;In this paper w&lrm;e show that if M is a Hilbert C* -&lrm;module&lrm; such that every local derivation on M is a derivation, then each local higher derivation on M&lrm; is a higher derivation&lrm;. Also, we prove that each local higher derivation on a unital C*-algebra is automatically continuous&lrm;.Postmodern Criminology and Dynamic Mathematical Modeling of Crime
https://jamm.scu.ac.ir/article_18834.html
Crime control and security are among the essential needs of development in any society. One of the frequently used theories of criminology that its birth was in the 1990s is postmodern or eclectic criminology. Postmodern criminology through combining different scientific theories, including mathematics tries to do a comprehensive analysis of crime. Nowadays, mathematical models are used to study the dynamic behavior of many phenomena and processes in engineering sciences, basic sciences and humanities. Mathematical modeling is one of the important tools of scientists in controlling and predicting the future of various dynamic phenomena. In the field of law and especially in criminology, these models are very useful for evaluating crime control strategies. In this article, using a new mathematical model, we deal with mass dynamic modeling and its analysis.An eigenvalue optimization problem for Dirichlet-Laplacian with a drift
https://jamm.scu.ac.ir/article_18750.html
In this paper, we prove a monotonicity result related to the principal eigenvalue for Dirichlet-Laplacian with a drift operator in a punctured ball.Karamzadeh's captivating thoughts and elegant solutions to some popular and classical results revisited:
Some comments and explanations
https://jamm.scu.ac.ir/article_18812.html
In this note, we intend to explain and interpret the proofs of some of the classic mathematical facts and results that are made easy by the beautiful mind of Karamzadeh, who has an incredible love for mathematics and has been enthusiastically busy for years concerning its popularization. These results are readable for every person who likes mathematics.