We derive a detailed determination of the solution formula for the compressible viscous fluid flo... more We derive a detailed determination of the solution formula for the compressible viscous fluid flow in three dimensional Euclidean space using Fourier transform. For the further research, we can not only generalized the model problem to the N-dimensional Euclidean space (N>3) but also we can estimate the solution operator families of the model problem.
Quadratic Assignment Problem (QAP) is often encountered with facility layout issues. Facility lay... more Quadratic Assignment Problem (QAP) is often encountered with facility layout issues. Facility layout is a matter of assigning n facilities to n locations to minimize the total cost of the assignment. The QAP application examined in this research is the layout of the production facilities at PT. Slamet Langgeng. The search for QAP solutions uses the Ant System algorithm by examining three pheromone update algorithms, namely the Ant Cycle, Ant Density, and Ant Quantity algorithms. The simulation of the three algorithms in the completion of QAP uses the help of Matlab 7.0.4 software. Based on the results of the QAP completion simulation, the best QAP solution offered by the Ant Cycle, Ant Density, and Ant Quantity algorithms produce different minimum distances. The best QAP solution with the smallest minimum distance is offered by the Ant Cycle algorithm of 4,967.2 m for 1,000 iterations. The QAP solution has the same minimum distance with an optimal distance of 4,967.2 m so that the l...
Operations Research: International Conference Series
The complicated case of scheduling courses at the Mathematics and Natural Sciences Faculty of Mat... more The complicated case of scheduling courses at the Mathematics and Natural Sciences Faculty of Mathematics Study Program, Universitas Jenderal Soedirman, is a topic that is quite interesting to discuss and find a solution to using a mathematical method. In fact, manual course scheduling without a method is prone to scheduling errors such as class schedule clashes, clashes in the use of lecture rooms and so on, so a more efficient method of scheduling courses is needed. Scheduling lectures with the backtracking algorithm is a systematic and efficient method of scheduling lectures with influencing factors such as the number of courses, number of sessions, number of rooms, and lecture time. Algorithm backtracking is an algorithm based on Depth First Search to find solutions to problems more efficiently. The back tracking algorithm performs a systematic search for solutions to all possible solutions at each node based on recursive Depth First Search. Depth First Search is a search method...
Tlagayasa Village is located in Bobotsari District, Purbalingga Regency. Most of the Tlagayasa vi... more Tlagayasa Village is located in Bobotsari District, Purbalingga Regency. Most of the Tlagayasa villagers work as farmers. The absence of a guarantee of harvest results will pose a risk of crop failure for farmers so that it will result in reduced income for farmers. Mothers Fostering Family Welfare (PKK) and teenage children in Tlagayasa village need to be empowered so that they can help increase family income. PKK members can empowered in producing floor cleaners, while teenage children are empowered in marketing. The activity begins with socialization, training making of floor cleaners, monitoring production and marketing of floor cleaners through social media. The result of this activity is the establishment of a floor cleaning home-industry "Bening" and website as an information medium containing village potential and floor cleaning promotions
Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertice... more Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ0), m(µ1), …, m(µn-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements are µ0, µ1, …, µn-1 for the first row, and m(µ0), m(µ1), …, m(µn-1) for the second row. In this paper, we will discuss Laplacian spectrum of the directed windmill graph () with k ≥ 1. The determination of the Laplacian spectrum in this study is to determine the characteristic polynomial of the Laplacian matrix from the directed windmill graph () with k ≥ 1. Keywords: Characteristic polynomial, directed windmill graph, Laplacian matrix, Laplacian spectrum.MSC2020 :05C50
Jurnal Ilmiah Matematika dan Pendidikan Matematika
Hill Cipher is a symmetric cryptographic algorithm that can be used to encrypt and decrypt. Hill ... more Hill Cipher is a symmetric cryptographic algorithm that can be used to encrypt and decrypt. Hill Cipher has several advantages including the key used to encrypt and decrypt is a square matrix of size n x n which has a multiplicative inverse because the inverse is the key used to decrypt. This study discusses the design of encryption and decryption program using with Java. The resulting program is capable of encrypting and decrypting with key 2 x 2, 3 x 3 , and 4 x 4.
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP), May 18, 2020
Lucas triangle is an array of coeficients of a polynomial forming a pattern which is similar to P... more Lucas triangle is an array of coeficients of a polynomial forming a pattern which is similar to Pascal triangle. This research studies Lucas triangle and its properties. The research results show that every row in Lucas triangle is begun by the number 1 and is ended by the number 2, the sum of the first n terms of number of 1th column is equal to the number at th row, 2nd column. Besides, the number at nth row and th column of Lucas triangle is for , the sum of the first n terms of number of jth column is equal to the number at th row, column for . The number of Lucas triangle is the sum of two number terms in preceded row, that is the number at th row, and the number at th row, . Then, the sum of coefficients of each row of Lucas triangle is .
Travelling Salesman Problem (TSP) is a problem to find the shortest path a salesman visitS all th... more Travelling Salesman Problem (TSP) is a problem to find the shortest path a salesman visitS all the cities exactly once, and return to the starting city. In this reseacrh, the methods for TSP used are the nearest insertion method, the cheapest insertion method, and the farthest insertion method. With help the function of Software R to creat a minimum TSP Program from three insertion methods.The TSP results for same number of point using three insertion methods do not always have the same weight and route but depending on the data used.
We derive a detailed determination of the solution formula for the compressible viscous fluid flo... more We derive a detailed determination of the solution formula for the compressible viscous fluid flow in three dimensional Euclidean space using Fourier transform. For the further research, we can not only generalized the model problem to the N-dimensional Euclidean space (N>3) but also we can estimate the solution operator families of the model problem.
Quadratic Assignment Problem (QAP) is often encountered with facility layout issues. Facility lay... more Quadratic Assignment Problem (QAP) is often encountered with facility layout issues. Facility layout is a matter of assigning n facilities to n locations to minimize the total cost of the assignment. The QAP application examined in this research is the layout of the production facilities at PT. Slamet Langgeng. The search for QAP solutions uses the Ant System algorithm by examining three pheromone update algorithms, namely the Ant Cycle, Ant Density, and Ant Quantity algorithms. The simulation of the three algorithms in the completion of QAP uses the help of Matlab 7.0.4 software. Based on the results of the QAP completion simulation, the best QAP solution offered by the Ant Cycle, Ant Density, and Ant Quantity algorithms produce different minimum distances. The best QAP solution with the smallest minimum distance is offered by the Ant Cycle algorithm of 4,967.2 m for 1,000 iterations. The QAP solution has the same minimum distance with an optimal distance of 4,967.2 m so that the l...
Operations Research: International Conference Series
The complicated case of scheduling courses at the Mathematics and Natural Sciences Faculty of Mat... more The complicated case of scheduling courses at the Mathematics and Natural Sciences Faculty of Mathematics Study Program, Universitas Jenderal Soedirman, is a topic that is quite interesting to discuss and find a solution to using a mathematical method. In fact, manual course scheduling without a method is prone to scheduling errors such as class schedule clashes, clashes in the use of lecture rooms and so on, so a more efficient method of scheduling courses is needed. Scheduling lectures with the backtracking algorithm is a systematic and efficient method of scheduling lectures with influencing factors such as the number of courses, number of sessions, number of rooms, and lecture time. Algorithm backtracking is an algorithm based on Depth First Search to find solutions to problems more efficiently. The back tracking algorithm performs a systematic search for solutions to all possible solutions at each node based on recursive Depth First Search. Depth First Search is a search method...
Tlagayasa Village is located in Bobotsari District, Purbalingga Regency. Most of the Tlagayasa vi... more Tlagayasa Village is located in Bobotsari District, Purbalingga Regency. Most of the Tlagayasa villagers work as farmers. The absence of a guarantee of harvest results will pose a risk of crop failure for farmers so that it will result in reduced income for farmers. Mothers Fostering Family Welfare (PKK) and teenage children in Tlagayasa village need to be empowered so that they can help increase family income. PKK members can empowered in producing floor cleaners, while teenage children are empowered in marketing. The activity begins with socialization, training making of floor cleaners, monitoring production and marketing of floor cleaners through social media. The result of this activity is the establishment of a floor cleaning home-industry "Bening" and website as an information medium containing village potential and floor cleaning promotions
Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertice... more Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ0), m(µ1), …, m(µn-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements are µ0, µ1, …, µn-1 for the first row, and m(µ0), m(µ1), …, m(µn-1) for the second row. In this paper, we will discuss Laplacian spectrum of the directed windmill graph () with k ≥ 1. The determination of the Laplacian spectrum in this study is to determine the characteristic polynomial of the Laplacian matrix from the directed windmill graph () with k ≥ 1. Keywords: Characteristic polynomial, directed windmill graph, Laplacian matrix, Laplacian spectrum.MSC2020 :05C50
Jurnal Ilmiah Matematika dan Pendidikan Matematika
Hill Cipher is a symmetric cryptographic algorithm that can be used to encrypt and decrypt. Hill ... more Hill Cipher is a symmetric cryptographic algorithm that can be used to encrypt and decrypt. Hill Cipher has several advantages including the key used to encrypt and decrypt is a square matrix of size n x n which has a multiplicative inverse because the inverse is the key used to decrypt. This study discusses the design of encryption and decryption program using with Java. The resulting program is capable of encrypting and decrypting with key 2 x 2, 3 x 3 , and 4 x 4.
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP), May 18, 2020
Lucas triangle is an array of coeficients of a polynomial forming a pattern which is similar to P... more Lucas triangle is an array of coeficients of a polynomial forming a pattern which is similar to Pascal triangle. This research studies Lucas triangle and its properties. The research results show that every row in Lucas triangle is begun by the number 1 and is ended by the number 2, the sum of the first n terms of number of 1th column is equal to the number at th row, 2nd column. Besides, the number at nth row and th column of Lucas triangle is for , the sum of the first n terms of number of jth column is equal to the number at th row, column for . The number of Lucas triangle is the sum of two number terms in preceded row, that is the number at th row, and the number at th row, . Then, the sum of coefficients of each row of Lucas triangle is .
Travelling Salesman Problem (TSP) is a problem to find the shortest path a salesman visitS all th... more Travelling Salesman Problem (TSP) is a problem to find the shortest path a salesman visitS all the cities exactly once, and return to the starting city. In this reseacrh, the methods for TSP used are the nearest insertion method, the cheapest insertion method, and the farthest insertion method. With help the function of Software R to creat a minimum TSP Program from three insertion methods.The TSP results for same number of point using three insertion methods do not always have the same weight and route but depending on the data used.
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