CAUCHY: Jurnal Matematika Murni dan Aplikasi
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Articles
438 Documents
<![CDATA[The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group ]]>
<![CDATA[Evi Yuniartika Asmarani]]>;
<![CDATA[Sahin Two Lestari]]>;
<![CDATA[Dara Purnamasari]]>;
<![CDATA[Abdul Gazir Syarifudin]]>;
<![CDATA[Salwa Salwa]]>;
<![CDATA[I Gede Adhitya Wisnu Wardhana]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.16991
<![CDATA[Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if or for a positive integer and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group where with prime numbers and an natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group where where is prime and an m natural number respectively is .]]>
<![CDATA[Systematic Literature Review on Adjustable Robust Shortest Path Problem ]]>
<![CDATA[Wida Nurul Fauziyah]]>;
<![CDATA[Diah Chaerani]]>;
<![CDATA[Herlina Napitupulu]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17648
<![CDATA[In real-world optimization problems, effective path planning is important. The Shortest Path Problem (SPP) model is a classical operations research that can be applied to determine an efficient path from the starting point to the end point in a plan. However, in the real world, uncertainty is often encountered and must be faced. Significant uncertainty factors in the problem of determining the shortest path are problems that are difficult to predict, therefore new criteria and appropriate models are needed to deal with uncertainty along with the required efficient solution. The uncertainty factor can be formulated using an uncertain SPP optimization model, assuming parameters that are not known with certainty but are in an uncertain set. Problems with uncertainty in mathematical optimization can be solved using Robust Optimization (RO). RO is a methodology in dealing with the problem of data uncertainty caused by errors in data measurement. The uncertainty in the linear optimization problem model can be formed by loading the uncertainty that only exists in the constraint function by assuming its uncertainty using the Robust Counterpart (RC) methodology. In this paper, we will review the literature on the two-stage optimization model for the SPP problem using an Adjustable Robust Counterpart (ARC).]]>
<![CDATA[Determination of Term Life Insurance Premiums with Varying Interest Rates Following The CIR Model and Varying Benefits Value ]]>
<![CDATA[Dian Puspita]]>;
<![CDATA[I Gusti Putu Purnaba]]>;
<![CDATA[Donny Citra Lesmana]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.20542
<![CDATA[Term life insurance is an insurance that provides protection for a certain period that has been agreed upon in the policy. The policy is an agreement that contains the participant's obligation to pay premiums contributions to the insurance company and the insurance company's obligation to pay benefits in the event of a risk to the insurance participant as agreed in the policy. Interest rates will influence the calculation of premium value and benefits in the long term. So we need a model of interest rates that will change by time. One of the models that can be used is the CIR model. This research purposes to simulate the CIR model that will be carried out to determine interest rates for calculating term life insurance premiums for five years, with premiums paid at the beginning of the 1/m interval or monthly premium payments and benefits paid at the end of the 1/m interval when the participant dies. The case that will be discussed is when the benefit various. The results of this study are the CIR model can be applied to calculate the term life insurance premiums for five years and the premium calculation results show that the amount of the premium increase every year with varying benefits.]]>
<![CDATA[A Fractional-Order Leslie-Gower Model with Fear and Allee Effect ]]>
<![CDATA[Adin Lazuardy Firdiansyah]]>;
<![CDATA[Dewi Rosikhoh]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17336
<![CDATA[In this manuscript, we investigate the dynamics behavior of a fractional-order Leslie-Gower model by considering fear effect in the prey and Allee effect in predators. Firstly, all possible equilibrium points are analyzed by identifying the conditions of their existence and local stability. Here, we find four equilibrium points, where two local stable points and two unstable points. Furthermore, we also investigate the stability changing caused by Hopf bifurcation when the order of derivative changes. Finally, we perform several simulations to support our analysis results. ]]>
<![CDATA[On the study of Rainbow Antimagic Coloring of Special Graphs ]]>
<![CDATA[Dafik Dafik]]>;
<![CDATA[Riniatul Nur Wahidah]]>;
<![CDATA[Ermita Rizki Albirri]]>;
<![CDATA[Sharifah Kartini Said Husain]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17836
<![CDATA[Let be a connected graph with vertex set and edge set . The bijective function is said to be a labeling of graph where is the associated weight for edge . If every edge has different weight, the function is called an edge antimagic vertex labeling. A path in the vertex-labeled graph , with every two edges satisfies is said to be a rainbow path. The function is called a rainbow antimagic labeling of , if for every two vertices , there exists a rainbow path. Graph admits the rainbow antimagic coloring, if we assign each edge with the color of the edge weight . The smallest number of colors induced from all edge weights of edge antimagic vertex labeling is called a rainbow antimagic connection number of , denoted by . In this paper, we study rainbow antimagic connection numbers of octopus graph , sandat graph , sun flower graph , volcano graph and semi jahangir graph Jn.]]>
<![CDATA[Confidence Intervals for the Mean Function of a Compound Cyclic Poisson Process in the Presence of Power Function Trend ]]>
<![CDATA[Muhammad, Faisal]]>;
<![CDATA[Mangku, I Wayan]]>;
<![CDATA[Silalahi, Bib Paruhum]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.15989
<![CDATA[We consider the problem of estimating the mean function of a compound cyclic Poisson process in the presence of power function trend. The objectives of this paper are: (i) to construct confidence interval for the mean function of a compound cyclic Poisson process with significance level , (ii) to prove that the probability that the mean function contained in the confidence interval converges to , and (iii) to observe, using simulation study, that the probabilities of the mean function contained in the confidence intervals for bounded length of observation interval. The main results are a confidence interval for the mean function and a theorem about convergence of the probability that the mean function contained in confidence interval. The simulation study shows that the probability that the mean function contained in the confidence interval is in accordance with the theorem. The contribution of this study is to provide information for users regarding confidence interval for the mean function of a compound cyclic Poisson process in the presence of power function trend.]]>
<![CDATA[Dynamic Analysis of the Susceptible-Exposed-Infected-Hospitalized-Critical-Recovered-Dead (SEIHCRD) ]]>
<![CDATA[Juhari, Juhari]]>;
<![CDATA[Kurnia, Silvi]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v8i2.22812
<![CDATA[This study discusses the dynamic analysis of the Susceptible–Exposed–Infected–Hospitalized–Critical–Recovered–Dead (SEIHCRD) model using the fourth order Runge-Kutta method. The data used in this study is original data on Infected, Hospitalized and Critical cases in Indonesia from August to October 2021. Dynamic analysis of the model is carried out by determining disease-free and endemic equilibrium points, local stability analysis of disease-free and endemic equilibrium points, and determine the basic reproduction number. The result of this analysis is that the number of new infection cases in Indonesia will decrease over time and the COVID-19 outbreak will end. Then a numerical simulation was carried out using the fourth order Runge-Kutta method in dealing with COVID-19 cases in Indonesia. The simulations and calculations show that the rate of contact of susceptible individuals with infected individuals is 0.06 per day, the rate of movement of individuals in the Exposed class to the Infected class is 0.14 per day, the probability of infected individuals being hospitalized with a value of 0.95, the probability that COVID-19 patients become critical and enter the Intensive Care Unit (ICU) with a value of 0.485, and the probability of a critical patient dying with a value of 0.25 affects the slope of Infected, Hospitalized and Critical cases in Indonesia. Where Infected cases will be sloping with an absolute error value of 28%, Hospitalized cases with an absolute error value of 20% and Critical cases with an absolute error value of 33%. This research provides information that it is estimated that the daily infection cases of COVID-19 will decrease and be close to zero. So that infected patients who must be hospitalized and admitted to the Intensive Care Unit (ICU) are also decreasing, it is hoped that the COVID-19 pandemic will not happen again]]>
<![CDATA[A Monte Carlo Simulation Study to Assess Estimation Methods in CFA on Ordinal Data ]]>
<![CDATA[Fitriyati, Nina]]>;
<![CDATA[Wijaya, Madona Yunita]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.14434
<![CDATA[Likert-type scale data are ordinal data and are commonly used to measure latent constructs in the educational, social, and behavioral sciences. The ordinal observed variables are often treated as continuous variables in factor analysis, which may cause misleading statistical inferences. Two robust estimators, i.e., unweighted least square (ULS) and diagonally weighted least square (DWLS) have been developed to deal with ordinal data in confirmatory factor analysis (CFA). Using synthetic data generated in a Monte Carlo experiment, we study the behavior of these methods (DWLS and ULS) and compare their performance with normal theory-based ML and GLS (generalized least square) under different levels of experimental conditions. The simulation results indicate that both DWLS and ULS yield consistently accurate parameter estimates across all conditions considered in this study. The Likert data can be treated as a continuous variable under ML or GLS when using at least five Likert scale points to produce trivial bias. However, these methods generally fail to provide a satisfactory fit. Empirical studies in the field of psychological measurement data are reported to present how theoretical and statistical instances have to be taken into consideration when ordinal data are used in the CFA model.Keywords: confirmatory factor analysis, diagonally weighted least square, generalized least square, Likert data, maximum likelihood.]]>
<![CDATA[SEIR Mathematical Model with the Use of Hand Sanitizers to Prevent the Spread of Covid-19 Disease ]]>
<![CDATA[Misri, Muhamad Ali]]>;
<![CDATA[Qadr, Khelan Hussien]]>;
<![CDATA[Rahmatullah, Muhammad Avif]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v9i1.25754
<![CDATA[The SARS-CoV-2 coronavirus can spread through contact with contaminated surfaces. The use of hand sanitizer is claimed to reduce the risk of transmission. For this reason, this study aims to develop a model of the spread of COVID-19 using the SEIR model with the use of hand sanitizer for infected individuals. The individual population is divided into six compartments, namely two compartments for susceptible individuals who using hand sanitizer and not, one compartment for exposed individuals, two compartments for infected individuals who using hand sanitizer and not, and one compartment for individuals died and recovered. The results obtained two equilibrium points: the disease-free and endemic equilibrium point, and also the basic reproduction number. The existence of a disease-free equilibrium point is unconditional, while the endemic there exist when the basic reproduction number is more than one. Stability analysis of the disease-free equilibrium point is locally asymptotic stable when the basic reproduction number is less than one. Numerical simulations carried out also strengthen them. Finally, the results of basic reproduction number sensitivity analysis show that the basic reproduction number is strongly influenced by contact of the susceptible individuals with exposed and infected individuals, neglecting of hand sanitizer use, mortality and cure rates.]]>
<![CDATA[Characteristic of Quaternion Algebra Over Fields ]]>
<![CDATA[Faldiyan, Muhammad]]>;
<![CDATA[Carnia, Ema]]>;
<![CDATA[Supriatna, Asep K.]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17625
<![CDATA[Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space with bases and the elements of the algebra are members of the field. Each element in quaternion algebra has an inverse, despite the fact that the ring is not commutative. Based on this, the purpose of this study is to obtain the characteristics of split quaternion algebra and determine how it interacts with central simple algebra. The research method used in this paper is literature study on quaternion algebra, field and central simple algebra. The results of this study establish the equivalence of split quaternion algebra as well as the theorem relating central simple algebra and quaternion algebra. The conclusion obtained from this study is that split quaternion algebra has five different characteristics and quaternion algebra is a central simple algebra with dimensions less than equal to four.]]>
