Indonesian Journal of Mathematics and Applications
The Indonesian Journal of Mathematics and Applications is a journal managed by Universitas Brawijaya, Malang, Indonesia, that is published twice a year (in March and September). IJMA is devoted to research articles of the highest quality in all areas of mathematics and its applications, statistics, and data science. The journal covers the following topics: Mathematical Analysis, Algebra, Biomathematics, Industrial Mathematics, Operasion Research, and Optimization, Data Sciences/Soft computing, Mathematical Physics, Financial Mathematics and Actuarial Sciences, Statictics. Upon its submission, the Editor-in-Chief decides on the suitability of the paper’s content for the aim and scope of the IJMA. If the Editor in Chief considers the paper is suitable, then the paper will be sent for peer reviewing by two peer reviewers. The Indonesian Journal of Mathematics and Applications maintains double anonymity, so neither the peer reviewers nor the author(s) can be identified by one another. The peer reviewers are respected scholars in the areas. The Indonesian Journal of Mathematics and Applications is an open access, peer-reviewed journal that considers articles describing novel computational algorithms and software, models and tools, including statistical methods, machine learning, and artificial intelligence, as well as systems biology.
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<![CDATA[Some Basic Results in ν-Normed Spaces ]]>
<![CDATA[Rohman, Minanur]]>;
<![CDATA[İlker Eryılmaz]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications (IJMA) ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
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DOI: 10.21776/ub.ijma.2023.001.01.1
<![CDATA[In this paper, we introduce the notion of a directed preserving generator (d.p.g.) from R into R. This d.p.g. can be used to construct new fields which generally have the same properties as R, except that some properties are affected by d.p.g. itself. With this new field, a ν-normed space will be formed. Some of the basic properties of this normed space are also discussed.]]>
<![CDATA[On the Inverse of a Square Matrix Using Logarithm ]]>
<![CDATA[Rellon, Louie Resti]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications (IJMA) ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
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DOI: 10.21776/ub.ijma.2023.001.01.2
<![CDATA[Assume that A is an n n matrix with real numbers as entries and the determinant of A ≠ 0. In this study, we established the results of getting the inverse of a matrix A using the logarithmic method and used some examples to discuss the necessity of getting the inverse of a matrix using the logarithm for both positive and negative determinants in terms of a given determinant of a matrix A. If the det A > 0, we have , where . However, if the det A < 0, we have , where .]]>
<![CDATA[Vector-Reservoir Transmission in A Japanese Encephalitis Model ]]>
<![CDATA[Lisa R. Sari]]>;
<![CDATA[Puji Andayani]]>;
<![CDATA[Sekarsari U. Wijaya]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications (IJMA) ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
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DOI: 10.21776/ub.ijma.2023.001.01.3
<![CDATA[In this paper, a model for characterizing the dynamics of vector-borne diseases is put out, emphasizing Japanese encephalitis. The susceptible-infectious-recovered (SIR) model for the host population and the susceptible-infectious (SI) model for the vector and reservoir populations are used to examine the role of host-vector-reservoir dynamics and their interplay. The standard incidence rate represents the probability of an actual disease contact. The model has two equilibrium points: an endemic equilibrium point that only exists under specific circumstances and a disease-free equilibrium point that always exists. The stability analysis of the model’s equilibrium point has been established. The basic reproduction number is calculated using the next-generation matrix method. A sensitivity analysis on models supported by numerical simulations is provided to demonstrate the critical parameter that affects the spread of disease.Our findings indicate that vector-reservoir transmission is the primary cause of endemic. Controlling vector-reservoir transmission lowers the likelihood of human infection and creates disease-free settings.]]>
<![CDATA[Application of Simulated Annealing Method on Tabarru-Fund Valuation using Inflator by Vasicek Model Approach Based on Profit and Loss Sharing Scheme ]]>
<![CDATA[Selvi Faristasari]]>;
<![CDATA[Adhitya Ronnie Effendie]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications (IJMA) ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
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DOI: 10.21776/ub.ijma.2023.001.01.4
<![CDATA[Currently, the financial services industry is dominated by conventional banks and individuals that apply the system of interest or an excess of loans. In Islam, this excess is referred to as usury, which is prohibited by Islamic law because, in practice, usury makes borrowers poorer as they cannot pay such high-interest installments. Not to mention, late payments are subject to penalties that will continue to accumulate if the borrower is unable to pay the next installment. From these facts, this system is prohibited by Islamic Law because there are harmed parties. Therefore, this research discusses mathematical models in the form of Islamic investment business loans for micro-economic traders by implementing a profit and loss sharing system. Tabarru-fund is a set of funds derived from borrowers’ contributions used to overcome conditions when they experience losses in certain conditions. In this mathematical model, the tabarru-fund acts as the premium that must be paid if the borrower is still profitable after the principal installments have paid off. This sharia model with tabarru funds is obtained by calculating the premium which involves the problem of minimizing the remaining tabarru funds in a certain period. The future value of the trader's profit rate will be projected using the Vasicek Model approach which previously determined the parameter estimation using OLS regression and then the data is generated using Monte Carlo simulation so that the sharia inflator is obtained. This sharia inflator plays a role in the optimization process of minimizing the remaining tabarru-fund which will be solved by the Simulated Annealing (SA) algorithm.]]>
<![CDATA[Finite Difference Scheme for Nonlinear Finite Grating without and with Defect ]]>
<![CDATA[Purnomo, Reymond]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications (IJMA) ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
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DOI: 10.21776/ub.ijma.2023.001.01.5
<![CDATA[We present a simple numerical scheme based on finite difference method (FDM) with different boundary treatments to study the nonlinear optical response of finite one-dimensional grating with Kerr medium. For linear and nonlinear case, we use the second order numerical scheme for interior with different treatments of boundary conditions. The resulting of nonlinear system of equations is solved using Newton method with continuation method. To illustrate this method, we consider a periodic medium with and without defect. As the result, this method is able to show the bandgap and optical bistability phenomena for both mediums.]]>
<![CDATA[Some Basic Results in ν-Normed Spaces ]]>
<![CDATA[Rohman, Minanur]]>;
<![CDATA[İlker Eryılmaz]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
Show Abstract
|
Download Original
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DOI: 10.21776/ub.ijma.2023.001.01.1
<![CDATA[In this paper, we introduce the notion of a directed preserving generator (d.p.g.) from R into R. This d.p.g. can be used to construct new fields which generally have the same properties as R, except that some properties are affected by d.p.g. itself. With this new field, a ν-normed space will be formed. Some of the basic properties of this normed space are also discussed.]]>
<![CDATA[On the Inverse of a Square Matrix Using Logarithm ]]>
<![CDATA[Rellon, Louie Resti]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
Show Abstract
|
Download Original
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Original Source
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DOI: 10.21776/ub.ijma.2023.001.01.2
<![CDATA[Assume that A is an n n matrix with real numbers as entries and the determinant of A ≠ 0. In this study, we established the results of getting the inverse of a matrix A using the logarithmic method and used some examples to discuss the necessity of getting the inverse of a matrix using the logarithm for both positive and negative determinants in terms of a given determinant of a matrix A. If the det A > 0, we have , where . However, if the det A < 0, we have , where .]]>
<![CDATA[Vector-Reservoir Transmission in A Japanese Encephalitis Model ]]>
<![CDATA[Lisa R. Sari]]>;
<![CDATA[Puji Andayani]]>;
<![CDATA[Sekarsari U. Wijaya]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.21776/ub.ijma.2023.001.01.3
<![CDATA[In this paper, a model for characterizing the dynamics of vector-borne diseases is put out, emphasizing Japanese encephalitis. The susceptible-infectious-recovered (SIR) model for the host population and the susceptible-infectious (SI) model for the vector and reservoir populations are used to examine the role of host-vector-reservoir dynamics and their interplay. The standard incidence rate represents the probability of an actual disease contact. The model has two equilibrium points: an endemic equilibrium point that only exists under specific circumstances and a disease-free equilibrium point that always exists. The stability analysis of the model’s equilibrium point has been established. The basic reproduction number is calculated using the next-generation matrix method. A sensitivity analysis on models supported by numerical simulations is provided to demonstrate the critical parameter that affects the spread of disease.Our findings indicate that vector-reservoir transmission is the primary cause of endemic. Controlling vector-reservoir transmission lowers the likelihood of human infection and creates disease-free settings.]]>
<![CDATA[Application of Simulated Annealing Method on Tabarru-Fund Valuation using Inflator by Vasicek Model Approach Based on Profit and Loss Sharing Scheme ]]>
<![CDATA[Selvi Faristasari]]>;
<![CDATA[Adhitya Ronnie Effendie]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.21776/ub.ijma.2023.001.01.4
<![CDATA[Currently, the financial services industry is dominated by conventional banks and individuals that apply the system of interest or an excess of loans. In Islam, this excess is referred to as usury, which is prohibited by Islamic law because, in practice, usury makes borrowers poorer as they cannot pay such high-interest installments. Not to mention, late payments are subject to penalties that will continue to accumulate if the borrower is unable to pay the next installment. From these facts, this system is prohibited by Islamic Law because there are harmed parties. Therefore, this research discusses mathematical models in the form of Islamic investment business loans for micro-economic traders by implementing a profit and loss sharing system. Tabarru-fund is a set of funds derived from borrowers’ contributions used to overcome conditions when they experience losses in certain conditions. In this mathematical model, the tabarru-fund acts as the premium that must be paid if the borrower is still profitable after the principal installments have paid off. This sharia model with tabarru funds is obtained by calculating the premium which involves the problem of minimizing the remaining tabarru funds in a certain period. The future value of the trader's profit rate will be projected using the Vasicek Model approach which previously determined the parameter estimation using OLS regression and then the data is generated using Monte Carlo simulation so that the sharia inflator is obtained. This sharia inflator plays a role in the optimization process of minimizing the remaining tabarru-fund which will be solved by the Simulated Annealing (SA) algorithm.]]>
<![CDATA[Finite Difference Scheme for Nonlinear Finite Grating without and with Defect ]]>
<![CDATA[Purnomo, Reymond]]>
<![CDATA[ Indonesian Journal of Mathematics and Applications Vol. 1 No. 1 (2023): Indonesian Journal of Mathematics and Applications ]]>
Publisher : <![CDATA[Universitas Brawijaya ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
|
DOI: 10.21776/ub.ijma.2023.001.01.5
<![CDATA[We present a simple numerical scheme based on finite difference method (FDM) with different boundary treatments to study the nonlinear optical response of finite one-dimensional grating with Kerr medium. For linear and nonlinear case, we use the second order numerical scheme for interior with different treatments of boundary conditions. The resulting of nonlinear system of equations is solved using Newton method with continuation method. To illustrate this method, we consider a periodic medium with and without defect. As the result, this method is able to show the bandgap and optical bistability phenomena for both mediums.]]>
