Eigen Mathematics Journal
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Co-Existing Point of Equilibrium in Discretization of Fractional-Order Prey and Predator Model
Get PDFIn this work, a discretization process of a fractional-order prey and predator model is discussed. The aim of this work is to describe the population phenomenon which contains prey and predator. In this research, the prey and predator model by Ghosh et al. (2017) is used. The model has an unique form because it contains prey refuge and additional food to predator. In order to give more details on prey and predator population, the model then modified into fractional order and then discretized. The discretization model has three points of equilibrium and one of them named co-existing point of equilibrium. The numerical simulation is used to perform the stability. The numerical simulation is controlled by using mathematical programming language. It resulted that the co-existing point of equilibrium tends to be stable or converge if a small value of (time step) is selected. Otherwise, if a larger value of is selected, then oscillatory is appeared which means the point of equilibrium become unstable or diverge
Pemeriksaan Uji Kenormalan dengan Kolmogorov-Smirnov, Anderson-Darling dan Shapiro-Wilk
No full textThe normal distribution is an important assumption for many statistical methods. The t-distribution is similar to the normal distribution, but there are differences in variance and free degree depending on the sample size. Normality testing usually uses Kolmogorov-Smirnov, Anderson-Darling, and Shapiro-Wilk tests. Simulating was performed on data derived from normal distributions, t-distributions, and exponential distributions. In the N(10,2) generation data, it was found that the Shapiro-Wilk method was better than other methods, while in a large sample, it was found that the Anderson-Darling method was better than the other methods. The data for the generation of the distribution of t(1) shows that the cumulative value of rejecting is close to 100%, meaning the data is not normally distributed. In a near-normal t(20) distribution, but not a normal data gain, Anderson-Darling and Shapiro-Wilk test performance showed good results. Meanwhile, in the t(100) generation data, the result was obtained that the most consistent cumulative value was the Anderson-Darling method. Furthermore, the Exp(1) data generator produces a cumulative value of rejecting close to 100%, with the most consistent method being Kolmogorov-Smirnov. So it can be known that the normality test selection depends on the number of samples and the data distribution.Distribusi normal adalah asumsi penting untuk banyak metode statistik. Pengujian normalitas biasanya menggunakan beberapa metode seperti kolmogorov-smirnov, Anderson-Darling dan tes Shapiro-Wilk. Pengujian simulasi dengan menghasilkan data dari distribusi normal, distribusi- t dan distribusi eksponensial. Pada data bangkitan diperoleh bahwa metode Shapiro-Wilk lebih baik dari metode lainnya, sedangkan pada sampel besar didapatkan bahwa metode Anderson-Darling lebih baik dari metode yang lainnya. Data bangkitan distribusi menunjukkan nilai kumulatif menolak mendekati 100% yang artinya data tidak berdistribusi normal. Sedangkan pada data bangkitan karena nilai derajat bebas ( semakin konsisten terhadap maka menyebabkan distribusi data mendekati normal dan diperoleh hasil bahwa nilai kumulatif yang paling konsisten adalah metode Anderson-Darling. Selanjutnya pada bangkitan data menghasilkan nilai kumulatif menolak mendekati 100% dengan metode yang paling konsisten adalah Kolmogorov-Smirnov. Sehingga dapat diketahui bahwa pemilihan uji normalitas sangat bergantung pada jumlah sampel dan sebaran datanya
Pipeline Network Optimization using Hybrid Algorithm between Simulated Annealing and Genetic Algorithms
Get PDFThe pipeline network is one of the most complex optimization problems consisting of several elements: reservoirs, pipes, valves, etc. The pipeline network is designed to deliver water to consumers by considering the demand and adequate pressure on the water pipe network. The main problem in designing reliable pipelines is the cost. The amount of cost that most influences the design of pipelines is the diameter of the pipe used. Therefore, this study aims to combine (hybrid) simulated annealing algorithm with genetic algorithm to optimize water pipe networks. The simulated annealing algorithm is the main algorithm in finding the optimal cost.Meanwhile, the genetic algorithm will assist in the pipeline update process using the roulette wheel selection. Simulation data is used to test the hybrid algorithm performance compared to the standard simulated annealing algorithm. The results show that the simulated annealing hybrid algorithm is able to get a more optimal cost in designing a water pipe network compared to the standard simulated annealing algorithm. Keywords: Optimization, Epanet 2.0, Simulated Annealing, and Genetic Algorith
APPLICATION OF EXPONENTIAL SMOOTHING METHOD TO FORECASE THE AMOUNT OF RICE PRODUCTION IN TANATE RIAJA DISTRICT, BARRU REGENCY
No full textExponential smoothing is a forecasting method with data that tends to fluctuate. Rice production is one of the data with these properties. This study discusses the agricultural production, the variable used to predict the level of rice production in Tanete Rilau District, Barru Regency . This study aims to predict the total production of rice plants from 2021 to 2025. The analysis results show that the forecast values for the entire production of rice plants from 2021 to 2025 are 24016.6, 24613.14, 25018.36, 25342.54, and 25601.88, respectively. It can be seen that rice production forecasting using the exponential smoothing method fluctuates yearly.This study discusses the agricultural production of rice plans. The variabel used to predict the level of rice production in Tanete Riaja District, Barru Regency, are as the total production of rice plants. This research is an applied research with double exponential smoothing method. The purpose of this study was to determine the amount of rice production in Tanete Riaja District, Barru Regency in 2021 to 2025. The results of forecasting the amount of rice production ini 2021 were 24134.18 tons, in 2022 25235.25 tons, in 2023 26336.32 tons, in 2024 it will be 27437.38 ton, and in 2025 it will be 28538.45 ton. Based on the results of forecasting the amount of rice production, it can be concluded that from year to year increased
Analisis Pengendalian Kualitas Air Minum dalam Kemasan Menggunakan Metode FMEA dan Penerapan Kaizen (Study Kasus di PT.Lombok Pusaka Adam, Jelantik Lombok Tengah)
No full textClean water is one of the basic needs with unlimited use, even in the economic field. The opportunities provided can be utilized by companies that produce bottled drinking water. The existence of defective products is obtained in production so that the need for quality analysis of the product is still within the control limits on the P chart. This is done by knowing the highest value in the influential failure mode. So that suggestions for improvement with Kaizen can be given. Based on the control P chart obtained, all points of defective products in the production process are within control limits with a UCL limit of 0.00804 and an LCL limit of 0.00602. This indicates that the defective product is statistically controlled. The Failure Mode and Effect Analysis (FMEA) method assigns a priority value to each failure mode, and the value is the Risk Priority Number (RPN). The biggest RPN is that the cover does not stick to the surface of the cup, with an RPN value of 240. The proposed improvement using the Kaizen method is to increase inspections and routine repairs on the machine.The clean water is one of the basic needs with unlimited use even in the economic field. The opportunities provided can be utilized by companies that produce bottled drinking water (AMDK). The existence of defective products is obtained in production so that the need for quality analysis of the product is still within the control limits on the P chart. This is done by knowing the highest value in the influential failure mode. So that suggestions for improvement with kaizen can be given. Based on the control P chart obtained, all points of defective products in the production process are within control limits with a UCL limit of 0.00804 and an LCL limit of 0.00602. This indicates that the defective product is statistically controlled. The FMEA method assigns a priority value to each failure mode. The value is the Risk Priority Number (RPN). The biggest RPN is that the cover does not stick to the surface of the cup, with an RPN value of 240. The proposed improvement using the Kaizen method is to increase inspections and routine repairs on the machine. Keywords: Failure Mode and Effect Analysis (FMEA), Kaizen, Quality Control, Statistical Process Control (SPC
Pengembangan Metode Iterasi Petviashvili dalam Penentuan Solusi Gelombang Stasioner pada Persamaan Bertipe Schrödinger Nonlinear dengan Fungsi Potensial V(x)
No full textThis research discusses a numerical method for determining the stationary waves as a solution of Nonlinear Schrödinger (NLS) equations. In general, solutions for the partial differential equations can be solved analytically. However, most the solutions of the nonlinear wave equations are difficult to determine analytically. Therefore, a numerical approach is needed to determine the solution of the NLS equation. One of the numerical methods can be used to find the solution of the NLS equation is the Petviashvili iteration method. For case study, the NLS equation has been generated by the theory of Bose-Einstein condensation which contain potential function . To solve this problem, we generalized Petviashvili iteration method to determine the stationary waves solution easily. The most interesting result for this study is by modification of Petviashvili iteration method, we can make it easier to find a stationary solution for the nonlinear Schrodinger equation which containing the Bose-Einstein condensation potential function .Penelitian ini membahas metode numerik untuk menentukan gelombang stasioner sebagai solusi dalam persamaan Nonlinier Schrödinger (NLS). Secara umum, solusi untuk persamaan diferensial parsial dapat diselesaikan secara analitik. Namun, sebagian besar solusi persamaan gelombang nonlinier sulit ditentukan secara analitik. Oleh karena itu, diperlukan sebuah pendekatan numerik untuk menentukan solusi persamaan bertipe NLS. Salah satu metode numerik yang dapat digunakan untuk menentukan solusi persamaan bertipe NLS adalah metode iterasi Petviashvili. Pada studi kasus, persamaan NLS telah dibangkitkan oleh teori kondensasi Bose-Einstein yang mengandung fungsi potensial . Untuk mengatasi masalah ini, kami melakukan pengembangan metode iterasi Petviashvili agar dapat dimanfaatkan untuk menentukan solusi stasioner yang diharapkan. Hasil yang paling menarik dari penelitian ini adalah dengan modifikasi metode iterasi Petviashvili, kita dapat dengan mudah menentukan solusi gelombang stasioner untuk persamaan Schrodinger nonlinier yang memuat fungsi potensial pada teori kondensasi Bose-Einstein
Analisis Faktor Untuk Pemetaan Karakteristik pada Percobaan Dekafeinasi Kopi Robusta
No full textIn recent years, there has been a positive trend in coffee consumption in Indonesia. Coffee that was initially identical to older man's drinks is starting to be liked by teenagers and children because coffee contains caffeine which can have an addictive effect. Coffee has various benefits, such as preventing drowsiness, antioxidants, improving brain performance, and reducing fatigue. However, drinking a lot of coffee than your body can tolerate will cause symptoms of insomnia, excessive anxiety, and increased blood pressure. Various experiments have been made to reduce the caffeine content in coffee (decaffeination), one of which is mixing coffee with chayote juice (Sechium edule). Furthermore, this article classified the characteristics of decaffeinated products, caffeine content, moisture content, total acid titration, ash content, hue color, and L value. Using factor analysis, it is known that the characteristics can be mapped into three principal components. The first principal component consists of variables of caffeine content, water content, and hue color value. The second principal component consists of ash content and total acid content titration variables, and the third principal component, this factor, consists only of the characteristic L. It is also known that these three main components can explain 74.2% of the diversity of origin.In recent years, there has been a positive trend in coffee consumption in Indonesia. Dringking coffee which were originally identical as oldmans drinks, is starting to be liked by teenagers to children. This is because coffee contains caffeine which can have an addictive effect. Drinking coffee in the right dose can have positive effects for the drinker, such as stimulating the ability of brain function and also as an antioxidant. However, if you drink more coffee than your body can tolerate, it will cause symptoms of insomnia, excessive anxiety and increased blood pressure. Various attempts have been made to reduce the caffeine content in coffee (decaffeination), one of which is by mixing coffee with chayote juice (Sechium edule) as has been done by Paramartha (2021). Furthermore, this article classifies the characteristics of decaffeinated products, caffeine content, moisture content, total acid content of titration, ash content, hue color, and L value. By using factor analysis, it is known that the characteristics can be mapped into three main factors, where the first main factor consists of variables of caffeine content, water content, and hue color value. The second main factor consists of variables of ash content, and total acid content titration, and the third major factor, this factor consists only of the characteristic L. It is also known that 74.2% of the diversity of origin can be explained by the three main factors
Prime submodul of an integer over itself
No full textOne of the sciences used in digital security systems is cryptography. Cryptography is closely related to the integer system, especially prime numbers. Prime numbers themselves have been abstracted a lot. One form of abstraction of prime numbers is the prime ideal. Previous studies have proven that an Ideal is said to be a prime ideal on if and only if I is constructed by a prime element. Other studies have also shown how the prime ideal develops. One of them is the research result of Dauns, where the prime ideal form is developed in the form of a prime submodule. A prime submodule is one of the objects in the module, which is an abstraction of prime numbers. Based on these things, it is exciting if the properties of the prime submodule are applied to other module forms, one of which is the integer module.One of the sciences used in digital security systems is cryptography. Cryptography is closely related to the integer system, especially prime numbers. Prime numbers themselves have been abstracted a lot. One form of abstraction of prime numbers is the prime ideal. Previous studies have proven that an Ideal is said to be a prime ideal on if and only if I is constructed by a prime element. Other studies have also shown how the prime ideal develops. One of them is the research result of Dauns, where the prime ideal form is developed in the form of a prime submodule. A prime submodule is one of the objects in the module, which is an abstraction of prime numbers. Based on these things, it is exciting if the properties of the prime submodule are applied to other module forms, one of which is the integer module
Application of the Poverty Equivalent Growth Rate (PEGR) Method (Case Study: Household Income Group in South Sulawesi 2016-2018)
Get PDFThe purpose of this study is to analyze pro-poor growth in South Sulawesi Province with an income dimension approach for the classification of urban and rural areas. This study reveals the poverty situation in South Sulawesi and the extent of the growth of the poor population. In addition, an overview of the effects of growth and distribution effects on changes in poverty is also obtained. Using SUSENAS data from South Sulawesi Province from 2016 to 2018, it was found that growth tends to have a greater impact on reducing poverty in rural areas than in urban areas based on the results of the Shapley decomposition. The results of calculating the degree of pro-poor growth with PEGR, show that income growth tends to be trickle-down from 2016 to 2017. The decline in the poverty rate did occur but the benefits of growth received by the poor were proportionally less than the non-poor. Income growth shows pro poor in the period from 2017 to 2018.The purpose of this study is to analyze pro-poor growth in South Sulawesi Province with an income dimension approach for the classification of urban and rural areas. This study reveals the poverty situation in South Sulawesi and the extent of the growth of the poor population. In addition, an overview of the effects of growth and distribution effects on changes in poverty is also obtained. Using SUSENAS data from South Sulawesi Province from 2016 to 2018, it was found that growth tends to have a greater impact on reducing poverty in rural areas than in urban areas based on the results of the Shapley decomposition. The results of calculating the degree of pro-poor growth with PEGR, show that income growth tends to be trickle-down from 2016 to 2017. The decline in the poverty rate did occur but the benefits of growth received by the poor were proportionally less than the non-poor. Income growth shows pro poor in the period from 2017 to 2018
Proving The Fermat Last Theorem for Case q≤n
Get PDFFermat's Last Theorem is a well-known classical theorem in mathematics. Andrew Willes has proven this theorem using the modular elliptic curve. However, the proposed proof is difficult for mathematicians and researchers to understand. For this reason, in this study, we provide evidence of several properties of Fermat's Last Theorem with a simple concept. We use Newton's Binomial Theorem, well-known in Fermat's time. In this study, we prove Fermat's Last Theorem for case . We also use the Newton’s Binomial theorem to verify several cases .