Matrix Science Mathematic (MSMK)

ANALYTICAL APPROXIMATION FOR THE NONLINEAR DYNAMICS OF ERK ACTIVATION IN THE PRESENCE OF COMPETITIVE INHIBITOR

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msmk.01.2020.10.13

ABSTRACT

ANALYTICAL APPROXIMATION FOR THE NONLINEAR DYNAMICS OF ERK ACTIVATION IN THE PRESENCE OF COMPETITIVE INHIBITOR

Journal: Matrix Science Mathematic (MSMK)
Author: Yudi Ari Adi, M. Irawan Jayadi, Agung Budiantoro

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.10.13

The extracellular signal-regulated protein kinase (ERK), a subfamily of Mitogen-Activated Protein Kinase (MAPK) pathways, is one of the most important signals in the regulation of many biological processes. Deregulated of MAPK signaling pathways has been observed in human cancers with potential involvement in most of all cellular processes leading to tumorigenesis so that it became a potential target for therapy in cancer patients. In this paper, we discuss a Mathematical model of ERK activation in the presence of a small molecule inhibitor that competes with RAS. We present analytical expressions for the concentration of RAS, complex RAS-ERK, complex RAS-Inhibitor, and activated ERK in terms of dimensionless parameters using He’s Homotopy Perturbation Method (HPM). The analytical results are compared with numerical simulation and satisfactory agreement is obtained.
Pages 10-13
Year 2020
Issue 1
Volume 4

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msmk.01.2020.06.09

ABSTRACT

ON NEW WAYS OF VARIOUS IDEALS IN TERNARY SEMIGROUPS

Journal: Matrix Science Mathematic (MSMK)
Author: M. Palanikumar, K. Arulmozhi

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.06.09

We discuss tri-quasi ideals and bi-quasi ideals in ternary semigroups and give some characterizations. The intersection of left, lateral and right ideals is a tri-ideal and product of left, lateral and right ideals is again a tri-ideal. We also discuss m-tri-ideals towards some characterizations in terms of tri-ideals. Some relevant counter examples are also indicated.
Pages 06-09
Year 2020
Issue 1
Volume 4

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msmk.01.2020.01.05

ABSTRACT

ANALYTIC APPROXIMATE SOLUTION OF RABIES TRANSMISSION DYNAMICS USING HOMOTOPY PERTURBATION METHOD

Journal: Matrix Science Mathematic (MSMK)
Author: Muhammad Sinan

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.01.05

In this paper, we consider a mathematical model of Rabies disease which is an infectious disease. The model we are considering is a system of nonlinear ordinary differential equations and it is difficult to find an exact solution. He’s Homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear ordinary differential equations. The findings obtained by HPM are compared with a nonstandard finite difference (NSFD) and Runge-Kutta fourth order (RK4) methods. Some plots are presented to show the reliability and simplicity of the method.
Pages 1-5
Year 2020
Issue 1
Volume 4

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msmk.02.2019.17.21

ABSTRACT

FINITE ELEMENT METHOD FOR SOLVING NONLINEAR RANDOM ORDINARY DIFFERENTIAL EQUATIONS

Journal: Matrix Science Mathematic (MSMK)
Author: Ibrahim Elkott, Ibrahim.L. El-Kalla, Ahmed Elsaid, Reda Abdo

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2019.17.21

In this paper we utilize the finite element method for solving random nonlinear differential equations. In the proposed technique, the nodal coefficients are formulated as functions of the random variable. At certain values of random variable, curve fitting is used to construct the approximate nodal solution. Several numerical examples are presented, and the approximate mean solutions are compared with the exact mean solution to illustrate the ability and effectiveness of this method.
Pages 17-21
Year 2019
Issue 2
Volume 3

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msmk.02.2019.11.16

ABSTRACT

LAPLACE ADOMIAN DECOMPOSITION METHOD FOR SOLVING A MODEL OF CHRONIC MYELOGENOUS LEUKEMIA (CML) AND T CELL ASSOCIATION

Journal: Matrix Science Mathematic (MSMK)
Author: Faiz Alam

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2019.11.16

In this article, it is our purpose that we examine as well as analyze Chronic Myelogenous Leukemia (CML) a mathematical model, a white blood cells cancer. This model shows the association between naive T cells, effector T cells and CML cancer cells in the body, using a system of differential equations which give the rate of change of these three-cell population. We implement a Laplace Adomian Decomposition Method to compute an approximate solution of the considered model. We try to obtain analytic solution for CML model in the form of series that rapidly converges. Further, we also provide some result and stability of the propose model.
Pages 11-16
Year 2019
Issue 2
Volume 3

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msmk.02.2019.08.10

ABSTRACT

ON THE MATLAB TECHNIQUE BY USING LAPLACE TRANSFORM FOR SOLVING SECOND ORDER ODE WITH INITIAL CONDITIONS EXACTLY

Journal: Matrix Science Mathematic (MSMK)
Author: Bawar Mohammed Faraj and Faraedoon Waly Ahmed

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2019.08.10

In this paper Matlab technique has been presented that is approach to exact solution for second order ODE with constant coefficients and initial condition by using Laplace transformation. Matlab function has been constructed to estimate and compute exact solution of second order ordinary differential equations with initial conditions generally, the results of the program shows the elapsed time, exact solution and it’s figures.
Pages 8-10
Year 2019
Issue 2
Volume 3

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msmk.01.2019.20.24

ABSTRACT

ANALYTICAL APPROXIMATE SOLUTION OF NON-LINEAR PROBLEM BY HOMOTOPY PERTURBATION METHOD (HPM)

Journal: Matrix Science Mathematic (MSMK)
Author: Ihtisham ul Haq

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2019.20.24

In this article, we want to find the analytic approximate solution of nonlinear problems by using Homotopy Perturbation Method. Using the Homotopy Perturbation Method once we express the nonlinear problem into infinite number of sub linear problems and then obtain the solution of linear problems.
Pages 20-24
Year 2019
Issue 1
Volume 3

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msmk.01.2019.17.19

ABSTRACT

COMPARATIVE STUDY OF MATHEMATICAL MODEL OF EBOLA VIRUS DISEASE VIA USING DIFFERENTIAL TRANSFORM METHOD AND VARIATION OF ITERATION METHOD

Journal: Matrix Science Mathematic (MSMK)
Author: Ghazala Nazir, Shaista Gul

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2019.17.19

This study investigates the application of differential transformation method and variational iteration method in finding the approximate solution of Ebola model. Variational iteration method uses the general Lagrange multiplier to construct the correction functional for the problem while differential transformation method uses the transformed function of the original nonlinear system. The result revealed that both methods are in complete agreement, accurate and efficient for solving systems of ODEs.
Pages 17-19
Year 2019
Issue 1
Volume 3

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msmk.01.2019.13.16

ABSTRACT

NUMERICAL SOLUTION OF FRACTIONAL BOUNDARY VALUE PROBLEMS BY USING CHEBYSHEV WAVELET METHOD

Journal: Matrix Science Mathematic (MSMK)
Author: Hassan Khan, Muhammad Arif, Syed Tauseef Mohyud-Din

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2019.13.16

In this paper Chebyshev Wavelets Method (CWM) is applied to obtain the numerical solutions of fractional fourth, sixth and eighth order linear and nonlinear boundary value problems. The solutions of the fractional order problems are shown to be convergent to the integer order solution of that problem. The computational work is done successfully with the help of the proposed algorithm and hence this algorithm can be extended to other physical problems. High level of accuracy is obtained by the present method.
Pages 13-16
Year 2019
Issue 1
Volume 3

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msmk.02.2018.40.49

ABSTRACT

EXTREMAL IOTA ENERGY OF A SUBCLASS OF TRICYCLIC DIGRAPHS AND SIDIGRAPHS

Journal: Matrix Science Mathematic (MSMK)
Author: Fareeha Jamal, Mehtab Khan/span>

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2018.40.49

The iota energy of an n-vertex digraph D is defined by Ec (𝐷) = ∑ 􀀀1 |Im(𝑧 k)|, where z1, . . ., zn are eigenvalues of D and Im(zk) is the imaginary part of eigenvalue zk . The iota energy of an n-vertex sidigraph can be defined analogously. In this paper, we define a class Fn of n-vertex tricyclic digraphs containing five linear subdigraphs such that one of the directed cycles does not share any vertex with the other two directed cycles and the remaining two directed cycles are of same length sharing at least one vertex. We find the digraphs in Fn with minimal and maximal iota energy. We also consider a similar class of tricyclic sidigraphs and find extremal values of iota energy among the sidigraphs in this class.
Pages 40-49
Year 2018
Issue2 2
Volume 2

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