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A CLOSER LOOK AT A PATH DOMINATION NUMBER IN GRID GRAPHS 网格图中路径支配数的进一步研究
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2023-07-02 DOI: 10.14710/jfma.v6i1.16608
Leomarich F. Casinillo
{"title":"A CLOSER LOOK AT A PATH DOMINATION NUMBER IN GRID GRAPHS","authors":"Leomarich F. Casinillo","doi":"10.14710/jfma.v6i1.16608","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.16608","url":null,"abstract":"This article exposes the combinatorial formula that determines the pathdomination number in a grid graph and discusses some of its properties. Seven propertiesare derived regarding the path domination number of grid graphs. Furthermore, some additional properties as direct consequences of the derived main properties are alsodiscussed.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364352","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}
引用次数: 0
ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS 一些图的强积的反相邻矩阵
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2023-07-02 DOI: 10.14710/jfma.v6i1.16653
Aluysius Sutjijana, Dea Alvionita Azka
{"title":"ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS","authors":"Aluysius Sutjijana, Dea Alvionita Azka","doi":"10.14710/jfma.v6i1.16653","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.16653","url":null,"abstract":"Let G be an undirected graphs with no multiple edges. There are many ways to represent a graph, and one of them is in a matrix form, by constructing an antiadjacency matrix. Given a connected graph G with  vertex set $V$ consisting of n members, an antiadjacency matrix of the graph G is a matrix B of order n times n such that if there is an edge that connects vertex v_i to vertex v_j (v_i sim v_j ) then the element of i^{th} row and b^{th} column of B is 0, otherwise 1. In this paper we investigate some properties of antiadjacency matrices for some strong product of two graphs. Our results are general forms of the antiadjacency matrix of the strong product of path graphs P_m with P_n for m, nge 3, and cycle graphs C_m with C_m for m ge 3.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364356","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}
引用次数: 0
FRACTIONAL MATHEMATICAL MODEL OF HIV AND CD4+ T-CELLS INTERACTIONS WITH HAART TREATMENT 艾滋病毒和 cd4+ t 细胞与哈特治疗相互作用的分数数学模型
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2023-07-02 DOI: 10.14710/jfma.v6i1.17174
Muhammad Rifki Nisardi, Kasbawati Kasbawati, Restu Ananda Putra
{"title":"FRACTIONAL MATHEMATICAL MODEL OF HIV AND CD4+ T-CELLS INTERACTIONS WITH HAART TREATMENT","authors":"Muhammad Rifki Nisardi, Kasbawati Kasbawati, Restu Ananda Putra","doi":"10.14710/jfma.v6i1.17174","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.17174","url":null,"abstract":". This study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order α. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number (𝑅 0 ) . Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model. The result of this study could assist for future improvement, especially for fractional modelling.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364390","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}
引用次数: 0
ARTIFICIAL NEURAL NETWORK APPLICATION IN MODELING MORTALITY OF COVID-19 PATIENTS IN INDONESIA 人工神经网络在印度尼西亚 COVID-19 患者死亡率建模中的应用
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2023-07-02 DOI: 10.14710/jfma.v6i1.17861
Rika Fitriani, Ruth Cornelia Nugraha
{"title":"ARTIFICIAL NEURAL NETWORK APPLICATION IN MODELING MORTALITY OF COVID-19 PATIENTS IN INDONESIA","authors":"Rika Fitriani, Ruth Cornelia Nugraha","doi":"10.14710/jfma.v6i1.17861","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.17861","url":null,"abstract":". The Indonesian government and public healthcare system have been under massive pressure due to increased infections and mortality rates among Covid-19 patients. An appropriate model is needed to model the mortality of Covid-19 patients in Indonesia to help the Indonesian government develop the right policy for dealing with the Covid-19 pandemic. Artificial neural networks are increasingly popular in various research fields. Artificial neural networks can detect specific patterns in mortality modeling. In this study, we use artificial neural networks to model the mortality rate of Covid-19 patients in Indonesia. We try combinations of activation functions, learning rates, and hidden layers for the best predictions. We compare the prediction accuracy of artificial neural networks with that of the Holt-Winters method. The results showed that the best model of artificial neural networks produced an RMSE of 3.0530. In contrast, the Holt-Winters method produced an RMSE of 664.9022. Therefore, the artificial neural networks performed better than the Holt-Winters method in analyzing mortality data of Covid-19 patients in Indonesia.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364404","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}
引用次数: 0
MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION 对具有两个不同感染阶段的结核病模型的数学分析
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2023-06-30 DOI: 10.14710/jfma.v5i2.15723
A. H. Permatasari, R. H. S. Utomo
{"title":"MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION","authors":"A. H. Permatasari, R. H. S. Utomo","doi":"10.14710/jfma.v5i2.15723","DOIUrl":"https://doi.org/10.14710/jfma.v5i2.15723","url":null,"abstract":"Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with  two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139367594","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}
引用次数: 0
BONUS MALUS SYSTEM FOR MOTORIZED VEHICLE INSURANCE USING GEOMETRIC DISTRIBUTIONS AND WEIBULL DISTRIBUTIONS 使用几何分布和威布尔分布的机动车辆保险奖金分红系统
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2023-06-30 DOI: 10.14710/jfma.v6i1.16505
Grisselia Rizky Sevina, J. Purwadi
{"title":"BONUS MALUS SYSTEM FOR MOTORIZED VEHICLE INSURANCE USING GEOMETRIC DISTRIBUTIONS AND WEIBULL DISTRIBUTIONS","authors":"Grisselia Rizky Sevina, J. Purwadi","doi":"10.14710/jfma.v6i1.16505","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.16505","url":null,"abstract":". The bonus malus system is one of the systems used to determine the premium amount for the next period based on the claim history of the policyholder. If the policyholder has no claims history or did not file a claim in the previous year, then the policyholder will get a bonus or in other words will get a reduction in the premium rate in the following period. Meanwhile, if the policyholder has a history of claims in the previous year, then the policyholder will be subject to a malus or must pay an increase in the premium rate in the following period. The purpose of this study is to calculate motor vehicle insurance premiums using the classic and optimal bonus malus method which takes into account the frequency of claims with a geometric distribution and the size of claims with a Weibull distribution. The results of this study indicate that the optimal bonus malus system is fairer for policyholders who renew their policies because the premium paid by the policyholder depends on the number of claims and the size of the claim, so that each policyholder will pay a different premium according to the number of claims.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139366413","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}
引用次数: 0
FREE CONVECTION FLOW OVER A HORIZONTAL POROUS FLAT PLATE WITH THE EFFECT OF MAGNETOHYDRODYNAMICS 受磁流体力学影响的水平多孔平板上的自由对流流动
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2021-11-30 DOI: 10.14710/jfma.v4i2.11719
Mohammad Ghani
{"title":"FREE CONVECTION FLOW OVER A HORIZONTAL POROUS FLAT PLATE WITH THE EFFECT OF MAGNETOHYDRODYNAMICS","authors":"Mohammad Ghani","doi":"10.14710/jfma.v4i2.11719","DOIUrl":"https://doi.org/10.14710/jfma.v4i2.11719","url":null,"abstract":"We are interested in study of the velocity (𝑓′) and temperature (𝜃) profiles for fluid flow over the surface of porous flat plate with the effect of magnetohydrodynamics. The dimensional equations are first transformed into the non-dimensional equations. Then, we transform the non-dimensional equations into the similar equations using stream functions. The numerical results are based on the discretization of similar equations using the finite difference method of Keller-Box. Based on the numerical results, the velocity profiles (𝑓′) decrease when the viscoelastic parameter (𝐾), Prandtl number (𝑃𝑟), magnetic parameter (𝑀), porosity parameter (𝑃) are increased. Moreover, the temperature profile (𝜃) is increased when the viscoelastic parameter (𝐾) and magnetic parameter (𝑀) are increased. However, the temperature profile (𝜃) decreases when Prandtl number (𝑃𝑟) and porosity (𝑃) are increased.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122129615","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}
引用次数: 0
ANALISIS AKURASI DARI PERBEDAAN FUNGSI KERNEL DAN COST PADA SUPPORT VECTOR MACHINE STUDI KASUS KLASIFIKASI CURAH HUJAN DI JAKARTA 分析雅加达降雨量分类个案支持机的内核和成本差异的准确性
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2021-11-30 DOI: 10.14710/jfma.v4i2.11691
Novia Pratiwi, Yudi Setyawan
{"title":"ANALISIS AKURASI DARI PERBEDAAN FUNGSI KERNEL DAN COST PADA SUPPORT VECTOR MACHINE STUDI KASUS KLASIFIKASI CURAH HUJAN DI JAKARTA","authors":"Novia Pratiwi, Yudi Setyawan","doi":"10.14710/jfma.v4i2.11691","DOIUrl":"https://doi.org/10.14710/jfma.v4i2.11691","url":null,"abstract":"Abstrak. Penelitian ini difokuskan pada perbandingan beberapa fungsi kernel, cost dan proporsi data training pada Support Vector Machine terhadap akurasi pengklasifikasian curah hujan di Jakarta. Fungsi-fungsi kernel linier, Gauss dan polynomial digunakan untuk memodifikasi metode Support Vector Machine guna menyelesaikan kasus nonlinier yang sering terjadi pada kondisi real.  Variabel yang digunakan dalam penelitian ini meliputi temperatur, kelembaban, penyinaran matahari dan kecepatan angin. Hasil analisis menunjukkan bahwa nilai support vector terkecil tidak memberikan akurasi yang tertinggi pada masing-masing fungsi kernel. Selain itu, proporsi dataset (training:testing) sebesar  90%:10% memberikan akurasi sedikit lebih tinggi dibandingkan dengan akurasi untuk proporsi 80%:20% untuk masing-masing fungsi kernel. Secara keseluruhan, akurasi tertinggi diperoleh pada proporsi 90%:10% oleh fungsi kernel linier dan polinom untuk cost 1 dan 1000 secara bersamaan yaitu 78,38%.Kata Kunci : Cost, Gauss, Kernel, linear, polynomial, Abstract. This research focuses on the comparison of several kernel functions, costs and proportions of data training on the Support Vector Machine to the accuracy of classifying rainfall in Jakarta. The linear, Gaussian and polynomial kernel functions were applied to modify the Support Vector Machine method to solve non-linear cases that often occur in actual conditions. The variables used in this study comprised of temperature, humidity, sunlight and wind speed. The analysis disclosed that the smallest support vector value did not provide the highest accuracy value for each kernel. In addition, the proportion of the dataset (training:testing) of 90%:10% provided a slightly higher accuracy compared to the accuracy for the proportion of 80%:20% for each kernel function. Overall, the highest accuracy attained at the proportion of 90%:10% by linear and polynomial kernel functions for cost 1 and 1000 simultaneously, which was 78.38%.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129726585","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}
引用次数: 0
ANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT 不同治疗效果下肺结核动力学模型分析
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2021-11-30 DOI: 10.14710/jfma.v4i2.12049
A. H. Permatasari, R. H. S. Utomo
{"title":"ANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT","authors":"A. H. Permatasari, R. H. S. Utomo","doi":"10.14710/jfma.v4i2.12049","DOIUrl":"https://doi.org/10.14710/jfma.v4i2.12049","url":null,"abstract":"A tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simulation was studied to illustrate the effect of the treatment on the spread of the tuberculosis disease. ","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115051745","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}
引用次数: 0
GENERAL UNCROSSING COVERING PATHS INSIDE THE AXIS-ALIGNED BOUNDING BOX 在轴对齐的边界框内的一般不交叉覆盖路径
Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2021-11-30 DOI: 10.14710/jfma.v4i2.12053
Marco Ripà
{"title":"GENERAL UNCROSSING COVERING PATHS INSIDE THE AXIS-ALIGNED BOUNDING BOX","authors":"Marco Ripà","doi":"10.14710/jfma.v4i2.12053","DOIUrl":"https://doi.org/10.14710/jfma.v4i2.12053","url":null,"abstract":"Given the finite set of n_1⋅n_2⋅...⋅n_k points G(n_1,n_2,...,n_k) in R^𝑘 such that n_k≥...≥n_2≥n_1∈Z+, we introduce a new algorithm, called MΛI, which returns an uncrossing covering path inside the minimum axis-aligned bounding box [0,n_1−1]×[0,n_2−1]×...×[0,n_k−1], consisting of 3⋅(n_1⋅n_2⋅...⋅n_k−1)−2 links of prescribed length n_k−1 units. Thus, for any n_k≥3, the link length of the covering path provided by our MΛI-algorithm is smaller than the cardinality of the set G(n_1,n_2,...,n_k). Furthermore, assuming k>2, we present an uncrossing covering path for G(3,3,...,3), comprising only 20*3^(k−3)−2 two units long edges, which is constrained by the axis-aligned bounding box [0,4−√3]×[0,4−√3]×[0,2]×...×[0,2].","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124673240","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}
引用次数: 4
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