Jurnal Matematika, Statistika dan Komputasi
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Analysis of Open Unemployment Rates in Indonesia Based on GRDP and the Percentage of Poor Population Using Nonparametric B-Spline Regression
Full text linkOpen Unemployment Rate (OUR) is a crucial indicator of the condition of the job market and the economy in Indonesia. This research is to modeling and analyzes the impact of GRDP and the percentage of poor population to the OUR in Indonesia using nonparametric B-Spline regression. The study applied B-Spline model due to the model’s property of handling non-linear associations without imposing any distributional assumptions. The research a used secondary data sourced from BPS Indonesia in 2024, which included 38 provinces in Indonesia. The analysis outcomes show that optimal model is achieved when the order was set at 2 for both GRDP and the percentage of poor population with one knot set at GRDP (1.055) and two knots set at the percentage of poor population (6.813333 and 11.583333) which gave a minimum GCV produced at 1.577369. The model’s coefficient of determination value of 0.7454 indicates that the model can explain 74.54% of the variation in the OUR is explained by GRDP and the percentage of poor population, with the remaining 25.46% is impacted by factors beyond the model
Dynamic Analysis of the SIRS Model with a Type III Holling Function on the Corrosion Distribution of Bridge Reinforcement Steel in Coastal Areas
Full text linkThis study discusses the dynamics of corrosion spread on reinforced concrete bridge reinforcement in coastal areas using the SIRS mathematical model approach and considering the Holling type III function. The model built, can be seen how corrosion appears, spreads, and persists based on the influence of interaction parameters between healthy reinforcement and reinforcement that has experienced damage. In addition, this model can be analyzed dynamically including the equilibrium point, local stability and basic reproduction number. The simulation results show that when the basic reproduction number , corrosion cannot persist and the system will return to a corrosion-free condition. However, when , corrosion is able to spread and persist so that some of the reinforcing steel remains in a corroded condition. Parameter analysis shows that increasing the ratio of the corrosion propagation rate to the recovery rate significantly increases the likelihood of corrosion development and long-term persistence. This ratio represents the intensity of interaction between the reinforcement in good condition and the corroded reinforcemen
Inflation Forecasting for Riau Province: A Comparison of Parametric ARIMA with Nonparametric Nadaraya-Watson Kernel Regression and B-Spline Methods
Full text linkForecasting inflation is crucial for assisting in the creation of sound economic strategies, particularly in key regions like Riau Province, one of the country\u27s hubs for the production of crude oil and palm oil. The economic peculiarities of Riau, which set it apart from other regions, lead to inflation patterns in this province that tend to deviate from the national average. Forecasting techniques are crucial for decision-making that promotes stability and overall regional economic planning. The parametric ARIMA method and the nonparametric Nadaraya-Watson Kernel Regression and B-Spline are used in this study to forecast inflation in Riau Province in 2025. While ARIMA is based on certain model assumptions, nonparametric methods are more flexible and can capture more complex patterns. The forecasting results using RMSE, ME, MAE, and MASE showed that the Nadaraya-Watson method performed the best out of the three methods tested. The forecasting results with Nadaraya-Watson Kernel Regression showed a stable decline in inflation, from 0.0464% in March to 0.0191% in August 2025
MODEL SPATIAL AUTOREGRESSIVE MOVING AVERAGE DENGAN PEMBOBOT ROOK CONTIGUITY: (Studi Kasus: Indeks Pembangunan Manusia Kabupaten/Kota di Pulau Kalimantan)
No full textThe Spatial Autoregressive Moving Average (SARMA) model is a regression model developed from the classical regression model. The classical regression model produces inaccurate conclusions when used to model spatial data because the assumption of independent errors is not met. The SARMA model has advantages in modeling spatial data that has a spatial effect on the lag of the dependent variable and error. This study aims to obtain a SARMA model and factors that significantly influence the Human Development Index (HDI) of districts and cities in Kalimantan in 2022 based on the SARMA model. The spatial weighting used in SARMA modeling is rook contiguity. The results of the study show that the SARMA model can model the HDI of districts and cities in Kalimantan. The factors that significantly influence the HDI of districts and cities in Kalimantan are the poverty rate, the open unemployment rate, and the number of hospital facilities.Regresi spasial merupakan pengembangan dari model regresi linier dengan mempertimbangkan pengaruh faktor lokasi. Model regresi spasial yang digunakan adalah Spatial Autoregressive Moving Average (SARMA). Penelitian ini bertujuan mendapatkan model SARMA dan faktor-faktor yang berpengaruh signifikan terhadap Indeks Pembangunan Manusia (IPM) kabupaten/kota di Pulau Kalimantan Tahun 2022 berdasarkan model SARMA. Hasil penelitian menunjukkan bahwa terdapat autokorelasi spasial pada data IPM kabupaten /kota di Pulau Kalimantan yang diperoleh dari uji Indeks Moran’s. Berdasarkan Uji lagrange multiplier, data IPM kabupaten/kota di Pulau Kalimantan dapat dimodelkan dengan model SARMA. Faktor-faktor yang berpengaruh signifikan terhadap IPM kabupaten/kota di Pulau Kalimantan berdasarkan model SARMA adalah persentase penduduk miskin, tingkat pengangguran terbuka, dan jumlah fasilitas rumah sakit
Pendekatan Minimum Variance Quadratic Unbiased Estimation dalam Analisis Regresi Data Panel dengan Pendugaan Komponen Galat Dua Arah Menggunakan Metode Biggers
Full text linkPanel data that have missing observations can be known as incomplete panel data. The model used is a two-way error component. The missing data estimation used is the Biggers method. This study aims to model the incomplete panel data regression of two-way error components on Manufacturing Company Stock Return data. The method used for estimating the error variance component is Minimum Variance Quadratic Unbiased Estimation (MIVQUE) with parameter estimation using Maximum Likelihood (ML). The method was applied to IDX data for 10 companies from 2014-2021. The results obtained using the MIVQUE method are σ ̂_v^2= 0.1142, σ ̂_μ^2=-0.0107, and σ ̂_λ^2=0.0068, for the ML method produces β ̂_0=0.0304719 〖 β ̂〗_1= -0.021107, and β ̂_2=0.0087936. Based on these methods, if there is an increase in the Debt to Equity Ratio, there is a decrease in the value of stock returns, and vice versa for Net Profit Margin
Connectivity Indices of Coprime Graphs over Generalized Quaternion Groups of a Certain Order
Full text linkThe generalized quaternion group is a non-abelian group of order that exhibits certain structural similarities with the dihedral group. It is generated by two elements that satisfy specific defining relations. Meanwhile, a coprime graph is constructed by representing the elements of a group as vertices, where two vertices are adjacent if the orders of the corresponding elements are coprime. In this study, we investigate coprime graphs derived from generalized quaternion groups, particularly when the group order is given by , with being a prime number. Based on the structural properties of these graphs, we compute several connectivity indices, including the First and Second Zagreb indices, the Wiener index, the hyper-Wiener index, the Harary index, and the Szeged index
Prime Labeling of Special Graph Classes Constructed from Dutch Windmill Graphs
Full text linkLet G be a simple graph of order n. Prime labeling is a bijective function f:V(G)→{1,2,…,n} such that gcd(f(u),f(v))=1 for every pair of adjacent vertices u,v in G. A graph G that satisfies the definition of prime labeling is called a prime graph. The Dutch windmill graph D_r^n is a graph obtained by taking n copies of cycle graph C_r with a vertex in common. The double quadrilateral graph DQ is a graph constructed from two copies of C_4 and identifying one edge from each of them. The graph obtained by taking n copies of DQ and identifying one vertex of degree 3 from each of them as a common central vertex is called the double quadrilateral Dutch windmill graph DQ_n, for n≥1. Furthermore, graphs D_r^n and DQ_n becomes the base graph to construct two new graph classes, namely graph P_2 [D_r^n] and flower double quadrilateral graph FDQ_n. Both graph classes, constructed from the Dutch windmill graph, also contain even cycles. From previous research, it is known that graphs P_2 [D_4^n] and flower double quadrilateral graph FDQ_n have odd harmonious labeling. However, the determination of prime labeling on both classes is still an open problem. In this paper, we show that two classes of graphs constructed from Dutch windmill graphs with even cycles, namely graphs P_2 [D_4^n] and flower double quadrilateral graphs FDQ_n for n≥1 have a prime labeling. The result of this research shows that these graphs are prime graphs
The Generalized Riemann Integral
Full text linkRiemann integration theory integrates functions on a bounded interval as a Riemann sum approach (integral) where the fineness of the partitions is controlled by a number (norm) of the partition. In Generalized Riemann integral theory, the Riemann sum approach of functions is controlled by a gauge on tagged partition so that enabling integrating functions with much larger collections. Therefore, the theorems that apply to Generalized Riemann integral theory have differences in their hypotheses and conclusions. In this paper, theory of Generalized Riemann integral is studied by giving some examples of functions that are Generalized Riemann integrable such that they are not Riemann integrable; and proving some theorems that apply in this theory. The functions are integrable by constructing a gauge on the tagged partition of the interval such that the Riemann sum of the function is very close to some real number. Functions defined on a bounded interval that are Generalized Riemann integrable such that they are or not Riemann integrable have the general form of the function: a function f on [a,b] is continuous on [a,b]\Z and discontinuous on Z, where Z is a null set. Moreover, an unbounded function f on [a,b] is integrable, if the set Z where f is unbounded on Z is a countable set. Furthermore, these two criteria can be extended to infinite intervals, i.e. a function defined on an infinite interval can be Generalized Riemann integrable such that it is not Riemann integrable, if the set of discontinuous and unbounded points of the function is a null set. A sequence of integrable functions on an interval I that converges to a function on I, satisfies that this limit function is integrable if it satisfies that the existence of the dominating functions.Teori integrasi Riemann mengintegralkan fungsi pada interval terbatas sebagai pendekatan jumlah Riemann (integral) dimana kehalusan partisi-partisi dikendalikan oleh sebuah bilangan (norm) dari partisi. Pada teori integral Riemann Diperumum, pendekatan jumlah Riemann dari fungsi dikendalikan oleh gauge pada partisi tag sehingga memampukan mengintegralkan fungsi-fungsi dengan koleksi yang jauh lebih besar. Oleh karena itu, teorema-teorema yang berlaku pada teori integral Riemann Diperumum mempunyai perbedaan dalam hipotesis dan kesimpulannya. Pada makalah ini, dikaji teori integral Riemann Diperumum dengan memberikan beberapa contoh fungsi-fungsi yang terintegralkan Riemann Diperumum sedemikian sehingga tidak terintegralkan Riemann; dan membuktikan beberapa teorema yang berlaku dalam teori ini. Fungsi-fungsi tersebut dapat terintegralkan dengan mengkonstruksi sebuah gauge pada partisi tag dari suatu interval sehingga jumlah Riemann dari fungsi menuju (sangat dekat) ke suatu bilangan real. Fungsi-fungsi yang didefinisikan pada sebuah interval terbatas yang terintegralkan Riemann Diperumum sedemikian sehingga tidak terintegralkan Riemann memiliki bentuk umum fungsi: fungsi f pada [a,b] adalah kontinu pada [a,b]\Z dan diskontinu pada Z, dimana Z adalah suatu himpunan null. Kemudian sebuah fungsi tidak terbatas f pada [a,b] dapat terintegralkan, jika himpunan Z dimana f tidak terbatas pada Z adalah sebuah himpunan terhitung (countable). Lebih lanjut, dari kedua kriteria ini dapat diperluas ke interval tidak berhingga, yakni suatu fungsi yang didefinisikan pada interval tidak berhingga dapat terintegralkan Riemann Diperumum sedemikian sehingga tidak terintegralkan Riemann, jika himpunan-himpunan titik-titik diskontinu dan tidak terbatas dari fungsi adalah suatu himpunan null. Barisan fungsi-fungsi yang terintegralkan pada suatu interval I yang konvergen ke sebuah fungsi pada I, memenuhi bahwa fungsi limit ini adalah terintegralkan jika memenuhi adanya fungsi dominasi
Optimization of Stock Portfolio Investment based on K-Means Clustering using Markowitz Method (A case study: IDX-MES BUMN17 Index)
Full text linkA stock portfolio is a combination of two or more equity securities invested over a specific period and under certain conditions. This research analyzes stock combinations that can be formed into an optimal portfolio using the Markowitz method. The Markowitz method is employed to maximize returns and minimize the risk of a portfolio. The data used in this study consists of daily closing prices from the IDX-MES BUMN17 index, one of the indices in Indonesian Stock Exchange, between January 2023 and December 2023. Based on the results obtained, two recommended portfolios are identified, known as the Minimum Variance Portfolio (MVP) and Tangency Portfolio. The optimal portfolio can serve as an option depending on the investor\u27s risk profile
Computing The First Zagreb Index, The Wiener Index and The Gutman Index of The Power of Dihedral Group Using Python
Full text linkThis paper presents a computational study on three classical topological indices—the First Zagreb Index, Wiener Index, and Gutman Index—within the context of power graphs of the dihedral group , where is a positive integer representing half the order of the group. These indices are fundamental in mathematical chemistry and graph theory, serving as quantitative descriptors of graph structure and connectivity. The methodology involves constructing power graphs derived from and calculating the indices using Python programming, supported by the NetworkX, Matplotlib, and Gradio libraries. Numerical simulations were conducted for varying values of , revealing consistent algebraic patterns and insights into the structural complexity of the corresponding graphs. Additionally, an interactive Python-based interface is developed to facilitate real-time computation and visualization, thus promoting further exploration and application in algebraic graph theory