International Journal of Mathematical, Engineering and Management Sciences
Fuzzy numbers have many applications in various mathematical models in both linear and nonlinear ... more Fuzzy numbers have many applications in various mathematical models in both linear and nonlinear forms. In the form of a nonlinear system, fuzzy nonlinear equations can be constructed in the form of matrix equations. Unfortunately, the matrix equations used to solve the problem of dual fully fuzzy nonlinear systems are still relatively few found in the publication of research results. This article attempts to solve a dual fully fuzzy nonlinear equation system involving triangular fuzzy numbers using Broyden’s method. This article provides the pseudocode algorithm and the implementation of the algorithm into the MATLAB program for the iteration process to be carried out quickly and easily. The performance of the given algorithm is the fastest in finding system solutions and provides a minimum error value.
Recent Advances in Computer Science and Communications
Background: Various methods can be used to solve dual fully fuzzy linear systems. The main choice... more Background: Various methods can be used to solve dual fully fuzzy linear systems. The main choice involves identifying which method produces the most accurate and efficient solutions. Objective: This article describes a procedure to solve the dual fully fuzzy linear systems based on the Jacobi method, which is done using a computer program. Methods: The Jacobi method is an approximate method used to solve dual fully fuzzy linear systems involving the arithmetic concept of triangular fuzzy numbers. The process of the Jacobi method begins with inputting the initial value to obtain a solution with a relatively small error. This requires that the equations of the system be diagonally dominant. Results: The solution obtained from a dual fully fuzzy linear system using the Jacobi method is a single solution that has a minimal error. Conclusion: The solutions of the given examples can be obtained easily by applying the Jacobi method algorithm using MATLAB.
International Journal of Mathematical, Engineering and Management Sciences
The use of mathematical concepts of mapping in cryptography provides advantages in securing text ... more The use of mathematical concepts of mapping in cryptography provides advantages in securing text or image data. The qualitative properties of mapping can preserve data that is kept confidential. Two of the essential properties in the mapping are the reversible and the preserving area. In this article, besides constructing a linear mapping derived from a second-order QRT difference equation and examining its qualitative properties, the coding procedure is used to encrypt text and fractal images based on the two-dimensional linear maps. For the digital text and image security algorithms, we developed the pseudo code algorithm implemented in Mathematica®. The proposed encoding technique will be compared with a 2D mKdV linear map to demonstrate its efficacy.
Abstrak Penelitian ini bertujuan untuk mensintesis polimer yang berfungsi sebagai senyawa pembawa... more Abstrak Penelitian ini bertujuan untuk mensintesis polimer yang berfungsi sebagai senyawa pembawa, yakni kopoli (eugenol-etilen glikol dimetakrilat, EGDMA) atau co-EEGDMA. Sintesis yang melibatkan antara eugenol dengan EGDMA sebagai agen sambung silang ini dilakukan dengan cara polimerisasi menggunakan katalis boron trifl ouro dietil eter. Polimer hasil sintesis ini kemudian dikarakterisasi menggunakan FTIR, SEM dan H-NMR. Co-EEGDMA bersama dengan dua senyawa lainnya, yaitu polivinil klorida (PVC) dan dibenzil eter (DBE). Komponen tersebut merupakan komponen dalam pembuatan membran yang digunakan untuk transport fenol. Komponen tersebut diuji dengan menggunakan metode polymer inclusion membrane (PIM). Hasil karakterisasi terhadap co-EEGDMA menunjukkan bahwa polimerisasi eugenol dengan agen penyambung silang EGDMA telah berhasil disintesis. Hasil penelitian juga menunjukkan bahwa membran yang mengandung senyawa baru tersebut mampu digunakan untuk transpor fenol secara berulang. Abstr...
Cryptography is the science and study of methods of protecting data in computer and communication... more Cryptography is the science and study of methods of protecting data in computer and communication systems from unauthorized disclosure and modification. Mathematical principles play important role in cryptography. Encryption-decryption algorithm using a mapping can be done for encoding a digital image, such as 2D Arnold’s Cat Map. In this article, we show a procedure (encryption-decryption algorithm) for protecting a digital image through 2D linear map that derived from modified ∆∆ sine-Gordon map.
Abstract— In the process of learning mathematics, there are high school mathematics materials tha... more Abstract— In the process of learning mathematics, there are high school mathematics materials that are difficult for students to understand. For this reason, learning aids are needed. There are several mathematics learning aids that can be used to help when solving mathematical problems, especially geometry, both simple and complex, including Geogebra, Mathematica and Maple. The use of Geogebra software was chosen because this software is available for free only on the internet. From the initial survey conducted to a number of teachers with samples of high school teachers in Lampung province it appears that their knowledge of the use of Geogebra as a learning medium in mathematics lessons, obtained that 90% of respondents answered that they had never used Geogebra in solving mathematical problems. In general, they know that the use of computers is very necessary to facilitate their work. For example, processing student grades, making transparency for learning media, making reports o...
The ethylene glycol dimethacrylate (EGDMA) is crosslinking agents which can be used to extend the... more The ethylene glycol dimethacrylate (EGDMA) is crosslinking agents which can be used to extend the polymer chain and increase the active side. This paper describes the evaluation of Polymer Inclusion Membrane (PIM) containing the derivatives of polyeugenol as carrier with respect to the physical properties of carrier and the optimization of phenol transport. The polymerization results between eugenol and EGDMA is copoly(eugenol-ethylene glycol dimethacrylate, co-EEGDMA). Subsequently the synthesized polymer is used as a carrier for phenol transport using PIM method. The optimization parameters performed are the effect of pH on the source phase, the NaOH concentration in the receiving phase, and the influence of transport time. The result was performed by looking at the physical properties of carrier including rendemen, melting point and solubility, then characterization of carrier and membrane were performed using FT-IR and SEM. The result of analysis and characterization proves that...
Perkembangan sektor industri yang cukup pesat dapat menimbulkan masalah lingkungan yang cukup ser... more Perkembangan sektor industri yang cukup pesat dapat menimbulkan masalah lingkungan yang cukup serius, karena limbah industri, termasuk polutan senyawa organik misalnya fenol akan masuk ke lingkungan. Fenol bersifat korosif dan karsinogenik, oleh karena itu fenol digolongkan sebagai bahan beracun dan berbahaya, sehingga proses pemisahan dan recovery fenol dari air limbah merupakan hal yang sangat penting untuk melindungi dan melestarikan lingkungan. Monomer diena sering digunakan dalam kopolimerisasi untuk memperoleh struktur tertaut silang (cross linked) dalam hasil akhir. Taut silang ini dapat terjadi tergantung pada reaktifitas reaktif dari ikatan rangkap diena. Tujuan jangka panjang dari penelitian adalah diperoleh suatu desain dan teknologi pemisahan fenol berbasis Motode Polymer Inclusion Membrane Sebagai Upaya Penanggulangan Limbah Fenol. Target khusus pada penelitian ini adalah sintesis polimer berbasis senyawa alam eugenol yang telah di tautsilang dengan etilen glikol dimeta...
A rocket is a spacecraft, guided missile, or flying vehicle that boosted by a chemical reaction r... more A rocket is a spacecraft, guided missile, or flying vehicle that boosted by a chemical reaction resulting from the combustion of propellant in the rocket motor. One of the essential parameters in the development of rocket motors is design optimization to improve the propulsion performance of the rocket. Increasing the propulsion performance of the rocket will increase the flight performance of the rocket, in terms of its maximum range or the altitude of the rocket trajectory. This study examined the determination of the design parameter values of a rocket motor by looking at it as an optimization problem with constraints. The problem studied was limited to the case of the second-stage rocket motor. A genetic algorithm was used to solve the resulting optimization problem of propellant grain configuration cases and a characteristic method for designing the bell nozzle. The results obtained indicated an increase in total impulse by 10% compared to the results before optimization.
This paper investigates the projection on the population of Bandar Lampung City in 2017 - 2030 th... more This paper investigates the projection on the population of Bandar Lampung City in 2017 - 2030 through a mathematical modeling approach. Here, we use four growth mathematical models particularly simple linear regression model, exponential model, logistic model and demographic transition model. The best approximation is chosen based on the smallest Mean Absolute Percentage Error (MAPE) value of the four models compared to the actual data. By using population data from 1995 - 2011, the results show that the model which gives the smallest MAPE is exponential model and the largest MAPE is demographic transition model.
Dynamics of oxidation reaction using reverse flow reactor (RFR) are given by a set of convection ... more Dynamics of oxidation reaction using reverse flow reactor (RFR) are given by a set of convection - diffusion equations that containing the non-linear term corresponding to the reaction rate and provided with certain initial and boundary conditions. In this paper, we investigate the dynamic profiles of temperature and feed concentration on oxidation process using numerical simulation approach. Here we assume the process satisfies 1-D pseudo-homogeneous model and the feed gas form is square wave function. Several different operation parameters have simulated to see the influence towards temperature and feed concentration profile. The results show that period function, small switching time, medium gas velocity and small specific reactor wall surface will make the reactor operated longer.
Polimer baru yang berfungsi sebagai senyawa pembawa, yakni kopoli (Eugenol-etilen glikol dimetakr... more Polimer baru yang berfungsi sebagai senyawa pembawa, yakni kopoli (Eugenol-etilen glikol dimetakrilat, EGDMA) atau co-EEGDMA telah disintesis. Sintesis yang melibatkan antara eugenol dengan EGDMA sebagai agen sambung silang ini dilakukan dengan cara polimerisasi menggunakan katalis boron triflouro dietil eter. Polimer hasil sintesis ini kemudian dikarakterisasi menggunakan FTIR, SEM dan H-NMR. Co-EEGDMA bersama dengan dua senyawa lainnya, yaitu polivinil klorida (PVC) dan dibenzil eter (DBE) yang merupakan komponen dalam pembuatan membran selanjutnya di uji kemampuannya yang digunakan untuk transpor fenol menggunakan metode polymer inclusion membrane (PIM). Hasil karakterisasi terhadap co-EEGDMA menunjukkan bahwa polimerisasi eugenol dengan agen penyambung silang EGDMA telah berhasil disintesis. Hasil penelitian juga menunjukkan bahwa membran yang mengandung senyawa baru tersebut mampu digunakan untuk transpor fenol secara berulang.
This article examine mathematical model of propellant grain configuration to obtain the appropria... more This article examine mathematical model of propellant grain configuration to obtain the appropriate burning area in sonda rocket. Sonda roket is experimental rocket that created by Pustekroket LAPAN to support research on space sector with altitude as the target of assessment. Burning area for hollow grain, wagon wheel grain, star grain are analysed analytically through mathematical modelling. Than the results are compared by manual calculation using SolidWork. The results show that burning area of three types of grain did not show a significant difference between these two methods.
Methane (CH4) is one of the most dangerous greenhouse gases in the atmosphere. A reverse flow rea... more Methane (CH4) is one of the most dangerous greenhouse gases in the atmosphere. A reverse flow reactor is utilized to convert CH4 to carbon dioxide (CO2) as a means of reducing the effect of global warming. The dynamics of its dependent variables can be stated by a set of convective-diffusion equations. In this article, we examined analytical solutions of temperature dynamics and methane conversion for a 1-D pseudo homogeneous model without refrigeration by using the homotopy analysis method. The results show that temperature and conversion of methane will go to constant when time goes to infinity. ABSTRAK: Metana (CH4) merupakan salah satu gas rumah hijau paling berbahaya di atmosfera. Reaktor aliran balik telah dipakai bagi menukar CH4 kepada CO2 bagi mengurangkan kesan pemanasan global. Dinamik pemboleh ubah bersandar ini dapat diterangkan melalui satu set persamaan konvektif-difusi. Artikel ini akan mengkaji penyelesaian analisis dinamik suhu dan penukaran metana bagi model 1-D p...
Journal of Research in Mathematics Trends and Technology
In this paper, we propose an analytical solution of convective-diffusion equation that derived fr... more In this paper, we propose an analytical solution of convective-diffusion equation that derived from an oxidation reaction in a chemical reactor. Here, concentration of feed gas as dependent variable. In this study, the reaction are assumed to be a one-dimensional pseudo homogeneous model and it is evaluated at a certain reaction rate. By rescaling process, the nonlinear term of the reaction rate can be approximated by a linear term, resulting a linear convective-diffusion equation with an initial condition and a set of boundary conditions. Here, we present an analytic solution of the initial condition and the boundary conditions using the homotopy perturbation method. The results show that at the end of the reactor, the solution is in agreement with numerical solution of the initial and boundary conditions.
International Journal of Mathematical, Engineering and Management Sciences
Fuzzy numbers have many applications in various mathematical models in both linear and nonlinear ... more Fuzzy numbers have many applications in various mathematical models in both linear and nonlinear forms. In the form of a nonlinear system, fuzzy nonlinear equations can be constructed in the form of matrix equations. Unfortunately, the matrix equations used to solve the problem of dual fully fuzzy nonlinear systems are still relatively few found in the publication of research results. This article attempts to solve a dual fully fuzzy nonlinear equation system involving triangular fuzzy numbers using Broyden’s method. This article provides the pseudocode algorithm and the implementation of the algorithm into the MATLAB program for the iteration process to be carried out quickly and easily. The performance of the given algorithm is the fastest in finding system solutions and provides a minimum error value.
Recent Advances in Computer Science and Communications
Background: Various methods can be used to solve dual fully fuzzy linear systems. The main choice... more Background: Various methods can be used to solve dual fully fuzzy linear systems. The main choice involves identifying which method produces the most accurate and efficient solutions. Objective: This article describes a procedure to solve the dual fully fuzzy linear systems based on the Jacobi method, which is done using a computer program. Methods: The Jacobi method is an approximate method used to solve dual fully fuzzy linear systems involving the arithmetic concept of triangular fuzzy numbers. The process of the Jacobi method begins with inputting the initial value to obtain a solution with a relatively small error. This requires that the equations of the system be diagonally dominant. Results: The solution obtained from a dual fully fuzzy linear system using the Jacobi method is a single solution that has a minimal error. Conclusion: The solutions of the given examples can be obtained easily by applying the Jacobi method algorithm using MATLAB.
International Journal of Mathematical, Engineering and Management Sciences
The use of mathematical concepts of mapping in cryptography provides advantages in securing text ... more The use of mathematical concepts of mapping in cryptography provides advantages in securing text or image data. The qualitative properties of mapping can preserve data that is kept confidential. Two of the essential properties in the mapping are the reversible and the preserving area. In this article, besides constructing a linear mapping derived from a second-order QRT difference equation and examining its qualitative properties, the coding procedure is used to encrypt text and fractal images based on the two-dimensional linear maps. For the digital text and image security algorithms, we developed the pseudo code algorithm implemented in Mathematica®. The proposed encoding technique will be compared with a 2D mKdV linear map to demonstrate its efficacy.
Abstrak Penelitian ini bertujuan untuk mensintesis polimer yang berfungsi sebagai senyawa pembawa... more Abstrak Penelitian ini bertujuan untuk mensintesis polimer yang berfungsi sebagai senyawa pembawa, yakni kopoli (eugenol-etilen glikol dimetakrilat, EGDMA) atau co-EEGDMA. Sintesis yang melibatkan antara eugenol dengan EGDMA sebagai agen sambung silang ini dilakukan dengan cara polimerisasi menggunakan katalis boron trifl ouro dietil eter. Polimer hasil sintesis ini kemudian dikarakterisasi menggunakan FTIR, SEM dan H-NMR. Co-EEGDMA bersama dengan dua senyawa lainnya, yaitu polivinil klorida (PVC) dan dibenzil eter (DBE). Komponen tersebut merupakan komponen dalam pembuatan membran yang digunakan untuk transport fenol. Komponen tersebut diuji dengan menggunakan metode polymer inclusion membrane (PIM). Hasil karakterisasi terhadap co-EEGDMA menunjukkan bahwa polimerisasi eugenol dengan agen penyambung silang EGDMA telah berhasil disintesis. Hasil penelitian juga menunjukkan bahwa membran yang mengandung senyawa baru tersebut mampu digunakan untuk transpor fenol secara berulang. Abstr...
Cryptography is the science and study of methods of protecting data in computer and communication... more Cryptography is the science and study of methods of protecting data in computer and communication systems from unauthorized disclosure and modification. Mathematical principles play important role in cryptography. Encryption-decryption algorithm using a mapping can be done for encoding a digital image, such as 2D Arnold’s Cat Map. In this article, we show a procedure (encryption-decryption algorithm) for protecting a digital image through 2D linear map that derived from modified ∆∆ sine-Gordon map.
Abstract— In the process of learning mathematics, there are high school mathematics materials tha... more Abstract— In the process of learning mathematics, there are high school mathematics materials that are difficult for students to understand. For this reason, learning aids are needed. There are several mathematics learning aids that can be used to help when solving mathematical problems, especially geometry, both simple and complex, including Geogebra, Mathematica and Maple. The use of Geogebra software was chosen because this software is available for free only on the internet. From the initial survey conducted to a number of teachers with samples of high school teachers in Lampung province it appears that their knowledge of the use of Geogebra as a learning medium in mathematics lessons, obtained that 90% of respondents answered that they had never used Geogebra in solving mathematical problems. In general, they know that the use of computers is very necessary to facilitate their work. For example, processing student grades, making transparency for learning media, making reports o...
The ethylene glycol dimethacrylate (EGDMA) is crosslinking agents which can be used to extend the... more The ethylene glycol dimethacrylate (EGDMA) is crosslinking agents which can be used to extend the polymer chain and increase the active side. This paper describes the evaluation of Polymer Inclusion Membrane (PIM) containing the derivatives of polyeugenol as carrier with respect to the physical properties of carrier and the optimization of phenol transport. The polymerization results between eugenol and EGDMA is copoly(eugenol-ethylene glycol dimethacrylate, co-EEGDMA). Subsequently the synthesized polymer is used as a carrier for phenol transport using PIM method. The optimization parameters performed are the effect of pH on the source phase, the NaOH concentration in the receiving phase, and the influence of transport time. The result was performed by looking at the physical properties of carrier including rendemen, melting point and solubility, then characterization of carrier and membrane were performed using FT-IR and SEM. The result of analysis and characterization proves that...
Perkembangan sektor industri yang cukup pesat dapat menimbulkan masalah lingkungan yang cukup ser... more Perkembangan sektor industri yang cukup pesat dapat menimbulkan masalah lingkungan yang cukup serius, karena limbah industri, termasuk polutan senyawa organik misalnya fenol akan masuk ke lingkungan. Fenol bersifat korosif dan karsinogenik, oleh karena itu fenol digolongkan sebagai bahan beracun dan berbahaya, sehingga proses pemisahan dan recovery fenol dari air limbah merupakan hal yang sangat penting untuk melindungi dan melestarikan lingkungan. Monomer diena sering digunakan dalam kopolimerisasi untuk memperoleh struktur tertaut silang (cross linked) dalam hasil akhir. Taut silang ini dapat terjadi tergantung pada reaktifitas reaktif dari ikatan rangkap diena. Tujuan jangka panjang dari penelitian adalah diperoleh suatu desain dan teknologi pemisahan fenol berbasis Motode Polymer Inclusion Membrane Sebagai Upaya Penanggulangan Limbah Fenol. Target khusus pada penelitian ini adalah sintesis polimer berbasis senyawa alam eugenol yang telah di tautsilang dengan etilen glikol dimeta...
A rocket is a spacecraft, guided missile, or flying vehicle that boosted by a chemical reaction r... more A rocket is a spacecraft, guided missile, or flying vehicle that boosted by a chemical reaction resulting from the combustion of propellant in the rocket motor. One of the essential parameters in the development of rocket motors is design optimization to improve the propulsion performance of the rocket. Increasing the propulsion performance of the rocket will increase the flight performance of the rocket, in terms of its maximum range or the altitude of the rocket trajectory. This study examined the determination of the design parameter values of a rocket motor by looking at it as an optimization problem with constraints. The problem studied was limited to the case of the second-stage rocket motor. A genetic algorithm was used to solve the resulting optimization problem of propellant grain configuration cases and a characteristic method for designing the bell nozzle. The results obtained indicated an increase in total impulse by 10% compared to the results before optimization.
This paper investigates the projection on the population of Bandar Lampung City in 2017 - 2030 th... more This paper investigates the projection on the population of Bandar Lampung City in 2017 - 2030 through a mathematical modeling approach. Here, we use four growth mathematical models particularly simple linear regression model, exponential model, logistic model and demographic transition model. The best approximation is chosen based on the smallest Mean Absolute Percentage Error (MAPE) value of the four models compared to the actual data. By using population data from 1995 - 2011, the results show that the model which gives the smallest MAPE is exponential model and the largest MAPE is demographic transition model.
Dynamics of oxidation reaction using reverse flow reactor (RFR) are given by a set of convection ... more Dynamics of oxidation reaction using reverse flow reactor (RFR) are given by a set of convection - diffusion equations that containing the non-linear term corresponding to the reaction rate and provided with certain initial and boundary conditions. In this paper, we investigate the dynamic profiles of temperature and feed concentration on oxidation process using numerical simulation approach. Here we assume the process satisfies 1-D pseudo-homogeneous model and the feed gas form is square wave function. Several different operation parameters have simulated to see the influence towards temperature and feed concentration profile. The results show that period function, small switching time, medium gas velocity and small specific reactor wall surface will make the reactor operated longer.
Polimer baru yang berfungsi sebagai senyawa pembawa, yakni kopoli (Eugenol-etilen glikol dimetakr... more Polimer baru yang berfungsi sebagai senyawa pembawa, yakni kopoli (Eugenol-etilen glikol dimetakrilat, EGDMA) atau co-EEGDMA telah disintesis. Sintesis yang melibatkan antara eugenol dengan EGDMA sebagai agen sambung silang ini dilakukan dengan cara polimerisasi menggunakan katalis boron triflouro dietil eter. Polimer hasil sintesis ini kemudian dikarakterisasi menggunakan FTIR, SEM dan H-NMR. Co-EEGDMA bersama dengan dua senyawa lainnya, yaitu polivinil klorida (PVC) dan dibenzil eter (DBE) yang merupakan komponen dalam pembuatan membran selanjutnya di uji kemampuannya yang digunakan untuk transpor fenol menggunakan metode polymer inclusion membrane (PIM). Hasil karakterisasi terhadap co-EEGDMA menunjukkan bahwa polimerisasi eugenol dengan agen penyambung silang EGDMA telah berhasil disintesis. Hasil penelitian juga menunjukkan bahwa membran yang mengandung senyawa baru tersebut mampu digunakan untuk transpor fenol secara berulang.
This article examine mathematical model of propellant grain configuration to obtain the appropria... more This article examine mathematical model of propellant grain configuration to obtain the appropriate burning area in sonda rocket. Sonda roket is experimental rocket that created by Pustekroket LAPAN to support research on space sector with altitude as the target of assessment. Burning area for hollow grain, wagon wheel grain, star grain are analysed analytically through mathematical modelling. Than the results are compared by manual calculation using SolidWork. The results show that burning area of three types of grain did not show a significant difference between these two methods.
Methane (CH4) is one of the most dangerous greenhouse gases in the atmosphere. A reverse flow rea... more Methane (CH4) is one of the most dangerous greenhouse gases in the atmosphere. A reverse flow reactor is utilized to convert CH4 to carbon dioxide (CO2) as a means of reducing the effect of global warming. The dynamics of its dependent variables can be stated by a set of convective-diffusion equations. In this article, we examined analytical solutions of temperature dynamics and methane conversion for a 1-D pseudo homogeneous model without refrigeration by using the homotopy analysis method. The results show that temperature and conversion of methane will go to constant when time goes to infinity. ABSTRAK: Metana (CH4) merupakan salah satu gas rumah hijau paling berbahaya di atmosfera. Reaktor aliran balik telah dipakai bagi menukar CH4 kepada CO2 bagi mengurangkan kesan pemanasan global. Dinamik pemboleh ubah bersandar ini dapat diterangkan melalui satu set persamaan konvektif-difusi. Artikel ini akan mengkaji penyelesaian analisis dinamik suhu dan penukaran metana bagi model 1-D p...
Journal of Research in Mathematics Trends and Technology
In this paper, we propose an analytical solution of convective-diffusion equation that derived fr... more In this paper, we propose an analytical solution of convective-diffusion equation that derived from an oxidation reaction in a chemical reactor. Here, concentration of feed gas as dependent variable. In this study, the reaction are assumed to be a one-dimensional pseudo homogeneous model and it is evaluated at a certain reaction rate. By rescaling process, the nonlinear term of the reaction rate can be approximated by a linear term, resulting a linear convective-diffusion equation with an initial condition and a set of boundary conditions. Here, we present an analytic solution of the initial condition and the boundary conditions using the homotopy perturbation method. The results show that at the end of the reactor, the solution is in agreement with numerical solution of the initial and boundary conditions.
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