Pub Date : 2022-11-01DOI: 10.18860/jrmm.v2i1.14467
A. Laila, Usman Pagalay, Heni Widayani
The spread of hepatitis B virus (HBV) infection has been widely studied using the deterministic SIR model, in which individuals who recover from acute infection have temporary immunity to the virus. However, this deterministic model uses a constant rate of viral infection over time. This is not in accordance with the fact that the infection rate is a random parameter that depends on time. This study discusses the analysis of the stochastic model of hepatitis B virus transmission. The purpose of this study is to construct the SIR stochastic model by dividing the infection rate into two, namely the rate of acute and chronic infection following the Wiener process. The model is then searched for an analytical solution referring to the Ito formula. The analytical solution and the Wiener process are described by substituting parameter values in the form of acute and chronic infection rates (β+α), cure rate (γ), and initial values (S(0) and I(0)) to obtain the mean value (μ). and the standard deviation (σ) of dS(t) and dI(t). The results of the simulation show that the number of infected individuals (I(t)) will decrease rapidly if (γ) is greater but will increase rapidly if (β+α) and (I(0)) are greater.
{"title":"Analisis Model Stokastik Penularan Virus Hepatitis B","authors":"A. Laila, Usman Pagalay, Heni Widayani","doi":"10.18860/jrmm.v2i1.14467","DOIUrl":"https://doi.org/10.18860/jrmm.v2i1.14467","url":null,"abstract":"The spread of hepatitis B virus (HBV) infection has been widely studied using the deterministic SIR model, in which individuals who recover from acute infection have temporary immunity to the virus. However, this deterministic model uses a constant rate of viral infection over time. This is not in accordance with the fact that the infection rate is a random parameter that depends on time. This study discusses the analysis of the stochastic model of hepatitis B virus transmission. The purpose of this study is to construct the SIR stochastic model by dividing the infection rate into two, namely the rate of acute and chronic infection following the Wiener process. The model is then searched for an analytical solution referring to the Ito formula. The analytical solution and the Wiener process are described by substituting parameter values in the form of acute and chronic infection rates (β+α), cure rate (γ), and initial values (S(0) and I(0)) to obtain the mean value (μ). and the standard deviation (σ) of dS(t) and dI(t). The results of the simulation show that the number of infected individuals (I(t)) will decrease rapidly if (γ) is greater but will increase rapidly if (β+α) and (I(0)) are greater.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130243118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-01DOI: 10.18860/jrmm.v1i7.14512
Febry Noorfitriana Utami, A. Kusumastuti, Juhari Juhari
This study discusses numerical simulation using the Adams-Bashforth-Moulton (ABM) method of order 4 in the flying fox string mathematical model which is in the form of ordinary differential equations depending on time, consisting of two equations, namely the equation of the flying fox string y(t) and the angular equation of the flying fox string θ(t). This mathematical model is a model that has been constructed by Kusumastuti, et al (2017) and has been validated by comparing analytical solutions to its numerical solutions by Sari (2018). The analysis of the behavior of the Kusumastuti 2017 model conducted by Makfiroh (2020) shows that the phase portrait graph is in the form of a spiral with eigenvectors pointing towards the equilibrium point so that the mathematical model of the flying fox string vibration can be concluded as a valid mathematical model that is close to the actual situation. This study attempts to determine the numerical simulation of the deflection of the flying fox string y(t) and the numerical simulation of the angle of the flying fox string θ(t). The Runge-Kutta method of order 4 was used to generate 3 initial values for order 4 ABM. Next, a comparison of the y(t) and θ(t) solution graphs of order 4 ABM with the solution graph with Runge-Kutta of order 4 was performed in Sari 2018. The first simulation was carried out when h=1, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 fluctuated in the range of [0,0.09] with almost the same graphic profile, and the difference in the value of θ(t) ABM of order 4, and Runge-Kuta order 4 which is quite large with different graphic profiles. The second simulation was carried out when h=0.01, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 was fluctuating which also ranged from [0.0.09] with the same graphic profile, and the difference in the values of θ(t) ABM of order 4 and Runge -Kutta order 4 fluctuates in the range of [0,1] with the same graphic profile. So concluded that when h=0.01 comparison of ABM of order 4 and Runge-Kutta of order 4 is the best for displaying the graph profiles of y(t) and θ(t). Further research can explore numerical solutions using other methods.
{"title":"Simulasi Numerik Model Matematika Vibrasi Dawai Flying Fox Menggunakan Metode Adams-Bashforth-Moulton","authors":"Febry Noorfitriana Utami, A. Kusumastuti, Juhari Juhari","doi":"10.18860/jrmm.v1i7.14512","DOIUrl":"https://doi.org/10.18860/jrmm.v1i7.14512","url":null,"abstract":"This study discusses numerical simulation using the Adams-Bashforth-Moulton (ABM) method of order 4 in the flying fox string mathematical model which is in the form of ordinary differential equations depending on time, consisting of two equations, namely the equation of the flying fox string y(t) and the angular equation of the flying fox string θ(t). This mathematical model is a model that has been constructed by Kusumastuti, et al (2017) and has been validated by comparing analytical solutions to its numerical solutions by Sari (2018). The analysis of the behavior of the Kusumastuti 2017 model conducted by Makfiroh (2020) shows that the phase portrait graph is in the form of a spiral with eigenvectors pointing towards the equilibrium point so that the mathematical model of the flying fox string vibration can be concluded as a valid mathematical model that is close to the actual situation. This study attempts to determine the numerical simulation of the deflection of the flying fox string y(t) and the numerical simulation of the angle of the flying fox string θ(t). The Runge-Kutta method of order 4 was used to generate 3 initial values for order 4 ABM. Next, a comparison of the y(t) and θ(t) solution graphs of order 4 ABM with the solution graph with Runge-Kutta of order 4 was performed in Sari 2018. The first simulation was carried out when h=1, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 fluctuated in the range of [0,0.09] with almost the same graphic profile, and the difference in the value of θ(t) ABM of order 4, and Runge-Kuta order 4 which is quite large with different graphic profiles. The second simulation was carried out when h=0.01, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 was fluctuating which also ranged from [0.0.09] with the same graphic profile, and the difference in the values of θ(t) ABM of order 4 and Runge -Kutta order 4 fluctuates in the range of [0,1] with the same graphic profile. So concluded that when h=0.01 comparison of ABM of order 4 and Runge-Kutta of order 4 is the best for displaying the graph profiles of y(t) and θ(t). Further research can explore numerical solutions using other methods.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115917226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A decomposition of graph G is collection of subgraphs 〖{H_i}〗_(i=1)^n from G such that H_i [E_i] for E_i is a subset of E(G) and 〖{E_i}〗_(i=1)^n is a partition of E(G). The purpose of the research was to determine the decomposition of the banana tree graph B_(m,n), for m≥1 and n≥2. The research method used in this research is library research. The steps used to determine the decomposition of the banana tree graph B_(m,n) are as follow: (a) Draw a banana tree graph B_(m,n) and label each edge and vertex, (b) Determine the partition on the edges of the banana tree graph B_(m,n), (c) Induced subgraph of from partitions of the banana tree graph B_(m,n), (d) Determine the decomposition of the banana tree graph B_(m,n), (e) Tabulate a conjecture on the decomposition of the banana tree graph B_(m,n), (f) Construct theorem of the decomposition theorem of of the banana tree graph B_(m,n) and its proof. The result of the reasearch is with m≥1 and n≥2, because banana tree graph B_(m,n) is decomposed by the complete graph 〖mK〗_2-decomposition.
{"title":"DEKOMPOSISI GRAF POHON PISANG Bm,n","authors":"Alfi Istijap Aji Sailendra, Evawati Alisah, Achmad Nasichuddin","doi":"10.18860/jrmm.v2i1.14671","DOIUrl":"https://doi.org/10.18860/jrmm.v2i1.14671","url":null,"abstract":"A decomposition of graph G is collection of subgraphs 〖{H_i}〗_(i=1)^n from G such that H_i [E_i] for E_i is a subset of E(G) and 〖{E_i}〗_(i=1)^n is a partition of E(G). The purpose of the research was to determine the decomposition of the banana tree graph B_(m,n), for m≥1 and n≥2. The research method used in this research is library research. The steps used to determine the decomposition of the banana tree graph B_(m,n) are as follow: (a) Draw a banana tree graph B_(m,n) and label each edge and vertex, (b) Determine the partition on the edges of the banana tree graph B_(m,n), (c) Induced subgraph of from partitions of the banana tree graph B_(m,n), (d) Determine the decomposition of the banana tree graph B_(m,n), (e) Tabulate a conjecture on the decomposition of the banana tree graph B_(m,n), (f) Construct theorem of the decomposition theorem of of the banana tree graph B_(m,n) and its proof. The result of the reasearch is with m≥1 and n≥2, because banana tree graph B_(m,n) is decomposed by the complete graph 〖mK〗_2-decomposition.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129751815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-01DOI: 10.18860/jrmm.v2i1.14619
Mohamad Abdul Ba'is, Hairur Rahman, Erna Herawati
Hӧlder inequality is a basic inequality in functional analysis. The inequality used for proofing other inequalities. In this research, the development of the application of the Hӧlder inequality in the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent. The integral Hӧlder inequality is used because the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent is a function space.This research shows the sufficient condition of Hӧlder inequality in Lebesgue spaces with variable exponent and the Morrey spaces with variable exponent according to the norm of the function and its characteristics.
{"title":"Syarat Cukup Ketaksamaan Holder di Ruang Lebesgue dengan Variabel Eksponen","authors":"Mohamad Abdul Ba'is, Hairur Rahman, Erna Herawati","doi":"10.18860/jrmm.v2i1.14619","DOIUrl":"https://doi.org/10.18860/jrmm.v2i1.14619","url":null,"abstract":"Hӧlder inequality is a basic inequality in functional analysis. The inequality used for proofing other inequalities. In this research, the development of the application of the Hӧlder inequality in the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent. The integral Hӧlder inequality is used because the Lebesgue spaces with variable exponent and Morrey spaces with variable exponent is a function space.This research shows the sufficient condition of Hӧlder inequality in Lebesgue spaces with variable exponent and the Morrey spaces with variable exponent according to the norm of the function and its characteristics.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127831257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-01DOI: 10.18860/jrmm.v2i1.14712
Miftakhul Rosidah, Heni Widayani, Usman Pagalay
Cervical cancer caused by Human Papillomavirus (HPV) is a serious health problem in Indonesia. The spread of HPV is still an unresolved problem even though a vaccine has been found and screening has been carried out in health facilities in Indonesia. In this study, the dynamic analysis of the HPV spread model was studied by categorizing the population into 6 sub-populations, namely the susceptible individual population (S(t)), the vaccinated individual population (V(t)), the infected individual population who were not aware 〖(I〗_u (t)), population of infected and screened individuals 〖(I〗_s (t)), population of individuals exposed to cervical cancer (C(t)), and population of cured individuals (R(t)). The model describes the dynamic rate of HPV spread which has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The results of this study indicate that the disease-free equilibrium point is unstable, meaning that there is still a possibility that infection will occur in the population. The numerical simulation illustrates that the percentage of individuals who are vaccinated will reduce the increase in the number of unconscious infected individuals and individuals with cervical cancer. Increasing the screening rate in the population will also reduce the number of unconsciously infected individuals and individuals with cervical cancer.
{"title":"ANALISIS DINAMIK PENYEBARAN HUMAN PAPILLOMAVIRUS DENGAN PENGARUH VAKSINASI DAN SKRINING","authors":"Miftakhul Rosidah, Heni Widayani, Usman Pagalay","doi":"10.18860/jrmm.v2i1.14712","DOIUrl":"https://doi.org/10.18860/jrmm.v2i1.14712","url":null,"abstract":"Cervical cancer caused by Human Papillomavirus (HPV) is a serious health problem in Indonesia. The spread of HPV is still an unresolved problem even though a vaccine has been found and screening has been carried out in health facilities in Indonesia. In this study, the dynamic analysis of the HPV spread model was studied by categorizing the population into 6 sub-populations, namely the susceptible individual population (S(t)), the vaccinated individual population (V(t)), the infected individual population who were not aware 〖(I〗_u (t)), population of infected and screened individuals 〖(I〗_s (t)), population of individuals exposed to cervical cancer (C(t)), and population of cured individuals (R(t)). The model describes the dynamic rate of HPV spread which has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The results of this study indicate that the disease-free equilibrium point is unstable, meaning that there is still a possibility that infection will occur in the population. The numerical simulation illustrates that the percentage of individuals who are vaccinated will reduce the increase in the number of unconscious infected individuals and individuals with cervical cancer. Increasing the screening rate in the population will also reduce the number of unconsciously infected individuals and individuals with cervical cancer.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130958256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-30DOI: 10.18860/jrmm.v1i6.14561
Nur Misbahul Arfiana, Evawati Alisah, Dewi Ismiarti
The most developed forecasting method currently is the time series, which uses a quantitative approach with past data as a reference for future forecasting. Fuzzy time series is a solution that uses time series data by applying fuzzy methods in forecasting. This research using fuzzy time series is applied on data from the sale of the Republic of Indonesia Employee Cooperative (KPRI) Selorejo District, Blitar Regency in 2015-2021. This study describes the problem of forecasting the results of cooperative sales using the Fuzzy Time Series (FTS) which was developed with the High Order. The development of the method is done by improving the FTS method with mathematical rules and is applied to the stages of the process of forecasting the results of cooperative sales. Testing the results of the High Order Fuzzy Time Series forecasting using the best Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE) accuracy values . The High Order Fuzzy Time Series consists of second order FTS, third order FTS and fourth order FTS. The results of the calculation of the smallest accuracy values are found in the fourth-order FTS, namely MSE of 19,333,658,980,372, MAPE of 11%, and MAE of 267,749. So it can be concluded that the fourth-order FTS is the best method in this study.
{"title":"Penerapan Metode Fuzzy Time Series Chen Orde Tinggi Pada Peramalan Hasil Penjualan (Studi Kasus: KPRI “Serba Guna” Kecamatan Selorejo Kabupaten Blitar)","authors":"Nur Misbahul Arfiana, Evawati Alisah, Dewi Ismiarti","doi":"10.18860/jrmm.v1i6.14561","DOIUrl":"https://doi.org/10.18860/jrmm.v1i6.14561","url":null,"abstract":"The most developed forecasting method currently is the time series, which uses a quantitative approach with past data as a reference for future forecasting. Fuzzy time series is a solution that uses time series data by applying fuzzy methods in forecasting. This research using fuzzy time series is applied on data from the sale of the Republic of Indonesia Employee Cooperative (KPRI) Selorejo District, Blitar Regency in 2015-2021. This study describes the problem of forecasting the results of cooperative sales using the Fuzzy Time Series (FTS) which was developed with the High Order. The development of the method is done by improving the FTS method with mathematical rules and is applied to the stages of the process of forecasting the results of cooperative sales. Testing the results of the High Order Fuzzy Time Series forecasting using the best Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE) accuracy values . The High Order Fuzzy Time Series consists of second order FTS, third order FTS and fourth order FTS. The results of the calculation of the smallest accuracy values are found in the fourth-order FTS, namely MSE of 19,333,658,980,372, MAPE of 11%, and MAE of 267,749. So it can be concluded that the fourth-order FTS is the best method in this study.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115261563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-30DOI: 10.18860/jrmm.v1i6.14594
Nur Fatin Mufinnun, Hairur Rahman, M. N. Jauhari
Prediction is a branch of science that is used to predict events that may occur in the future based on past events. One of the developed prediction methods, Backpropagation Neural Network, a method that has a good level of effectiveness. This study aims to determine the model and the accuracy of the model in predicting the total sales of the Toyota Avanza and to find out the results of sales predictions for the next 12 months by analyzing the number of sales in January 2010 to October 2021. The prediction model for the number of Toyota Avanza sales using the Backpropagation Neural Network is 12-13-1, where there are 12 variables in the input layer, 13 variables in the hidden layer and 1 variable in the output layer with a learning rate value of 0.5 and momentum 0. The predictions for the number of Toyota Avanza sales for 12 months are at an average upper limit of 6215 and an average lower limit of 3415 with a MAPE value of 9,39135%, so that the model can be said to be very good.
{"title":"Implementasi Backpropagation Neural Network pada Prediksi Jumlah Penjualan Toyota Avanza di Indonesia","authors":"Nur Fatin Mufinnun, Hairur Rahman, M. N. Jauhari","doi":"10.18860/jrmm.v1i6.14594","DOIUrl":"https://doi.org/10.18860/jrmm.v1i6.14594","url":null,"abstract":"Prediction is a branch of science that is used to predict events that may occur in the future based on past events. One of the developed prediction methods, Backpropagation Neural Network, a method that has a good level of effectiveness. This study aims to determine the model and the accuracy of the model in predicting the total sales of the Toyota Avanza and to find out the results of sales predictions for the next 12 months by analyzing the number of sales in January 2010 to October 2021. The prediction model for the number of Toyota Avanza sales using the Backpropagation Neural Network is 12-13-1, where there are 12 variables in the input layer, 13 variables in the hidden layer and 1 variable in the output layer with a learning rate value of 0.5 and momentum 0. The predictions for the number of Toyota Avanza sales for 12 months are at an average upper limit of 6215 and an average lower limit of 3415 with a MAPE value of 9,39135%, so that the model can be said to be very good. ","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123378229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-30DOI: 10.18860/jrmm.v1i6.14531
Ahmed Syarief Marzuki, Juhari Juhari, E. Alisah
Distribution is the action or process of supplying goods to stores and other businesses that sell to consumers. If a product or service is distributed from a company, it requires adequate means of transportation and usually requires too large distribution costs. Delivery of goods at this company does not use mathematical methods in calculating its distribution to several places correctly. The purpose of this research is to create an optimal, efficient and effective distribution model for this company by applying the North West Corner Method and the Modified Distribution Method in July, August and September 2021. North West Corner Method for the initial solution and Modified Distribution Method as the optimal solution is a variation of the Stepping Stone method. The results of this research show that the distribution costs incurred by the company after being calculated using the North West Corner Method and the Modified Distribution Method are Rp. 6,961,779, - from Rp. 7,000,000. Then these two methods are able to help companies save distribution costs incurred.
{"title":"Optimasi Distribusi Biaya Transportasi Melalui Metode Modified Distribution","authors":"Ahmed Syarief Marzuki, Juhari Juhari, E. Alisah","doi":"10.18860/jrmm.v1i6.14531","DOIUrl":"https://doi.org/10.18860/jrmm.v1i6.14531","url":null,"abstract":"Distribution is the action or process of supplying goods to stores and other businesses that sell to consumers. If a product or service is distributed from a company, it requires adequate means of transportation and usually requires too large distribution costs. Delivery of goods at this company does not use mathematical methods in calculating its distribution to several places correctly. The purpose of this research is to create an optimal, efficient and effective distribution model for this company by applying the North West Corner Method and the Modified Distribution Method in July, August and September 2021. North West Corner Method for the initial solution and Modified Distribution Method as the optimal solution is a variation of the Stepping Stone method. The results of this research show that the distribution costs incurred by the company after being calculated using the North West Corner Method and the Modified Distribution Method are Rp. 6,961,779, - from Rp. 7,000,000. Then these two methods are able to help companies save distribution costs incurred.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126220891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-30DOI: 10.18860/jrmm.v1i6.14517
Nurul Hafidhoh Anwar, M. N. Jauhari, Dewi Ismiarti
A vertex coloring of a graph , is an assigments of colors to the vertices of , such that no two adjacent vertices are assigned the same color. The least number of colors needed for an vertices coloring of a graph is the chromatic number, denoted by . A graph is said to be planar if it can be drawn in the plane so that no edges crossing except at endpoints. A dual graph is constructed from the planar graph. Each region in planar graph can be represented by a vertex of the dual graph. Two vertices are connected if the region represented by these vertices are neugbours and have a common border. A diamond graph denoted by , can be used to model structure networks. In this study, it is shown that the chromatic number of dual diamond graph is χ(〖Br_n〗^* )={█(3,n=2 and n≥4@4,n=3.)┤
{"title":"Bilangan Kromatik Titik dari Dual Graf Berlian","authors":"Nurul Hafidhoh Anwar, M. N. Jauhari, Dewi Ismiarti","doi":"10.18860/jrmm.v1i6.14517","DOIUrl":"https://doi.org/10.18860/jrmm.v1i6.14517","url":null,"abstract":"A vertex coloring of a graph , is an assigments of colors to the vertices of , such that no two adjacent vertices are assigned the same color. The least number of colors needed for an vertices coloring of a graph is the chromatic number, denoted by . A graph is said to be planar if it can be drawn in the plane so that no edges crossing except at endpoints. A dual graph is constructed from the planar graph. Each region in planar graph can be represented by a vertex of the dual graph. Two vertices are connected if the region represented by these vertices are neugbours and have a common border. A diamond graph denoted by , can be used to model structure networks. In this study, it is shown that the chromatic number of dual diamond graph is χ(〖Br_n〗^* )={█(3,n=2 and n≥4@4,n=3.)┤","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122773974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-30DOI: 10.18860/jrmm.v1i6.14591
W. Faizah, Muhammad Khudzaifah, Dewi Ismiarti
DNA Cryptography is one of new algortihm in cryptography that is used to encrypt the data by converting the DNA code into binary code. Encryption process is expected to produce a random and unreadable ciphertext. This research aims to determine the result of encryption frequency analysis of the ciphertext obtained from the encryption process using DNA Cryptography and Digraph Transformation algorithm. The formation of a symmetric key is carried out for the encryption and decryption process in DNA Cryptography, and modular arithmetic in Digraph Transformation algorithm. The encryption process produces ciphertext in the form of letters and symbols because if involves the use of an ASCII table. Frequency analysis is done by comparing the frequency of occurence of letters in the ciphertext with frequency of occurence of letters in English. The conclusion for this research is that the ciphertext looks random, not easy to read, and hard to guess. For the future work, researcher can change the choice of binary code combinatory in DNA Cryptographic algorithms, increase the character vocabulary in the Digraph Transformation algorithm, and use various languages to code.
{"title":"Analisis Frekuensi Ciphertext dengan Algoritma Kriptografi DNA dan Transformasi Digraf","authors":"W. Faizah, Muhammad Khudzaifah, Dewi Ismiarti","doi":"10.18860/jrmm.v1i6.14591","DOIUrl":"https://doi.org/10.18860/jrmm.v1i6.14591","url":null,"abstract":"DNA Cryptography is one of new algortihm in cryptography that is used to encrypt the data by converting the DNA code into binary code. Encryption process is expected to produce a random and unreadable ciphertext. This research aims to determine the result of encryption frequency analysis of the ciphertext obtained from the encryption process using DNA Cryptography and Digraph Transformation algorithm. The formation of a symmetric key is carried out for the encryption and decryption process in DNA Cryptography, and modular arithmetic in Digraph Transformation algorithm. The encryption process produces ciphertext in the form of letters and symbols because if involves the use of an ASCII table. Frequency analysis is done by comparing the frequency of occurence of letters in the ciphertext with frequency of occurence of letters in English. The conclusion for this research is that the ciphertext looks random, not easy to read, and hard to guess. For the future work, researcher can change the choice of binary code combinatory in DNA Cryptographic algorithms, increase the character vocabulary in the Digraph Transformation algorithm, and use various languages to code.","PeriodicalId":270235,"journal":{"name":"Jurnal Riset Mahasiswa Matematika","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126705155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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