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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
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.
Arjuna Subject : -
Articles 438 Documents
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Exploring the (h, m)-Convexity for Operators in Hilbert Space Maulana, Ekadion; Karim, Corina; Kurniawaty, Mila
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.32099

Abstract

This study examines the concept of operator (h, m)-convexity within the context of Hilbert spaces, aiming to advance the understanding of operator convex functions. Operator convex functions play a pivotal role in various mathematical disciplines, particularly in optimization and the study of inequalities. The paper introduces the notion of an operator (h, m)-convex function, which generalizes existing classes of operator convexity, and explores its fundamental properties. The methodological framework relies on a theoretical analysis of bounded operators and their relationships with other forms of operator convex functions. Key findings demonstrate that, under certain conditions, the product of two operator convex functions retains operator convexity. Furthermore, the study establishes convergence results for matrix (h, m)-convex functions. These contributions enhance the theoretical foundation of operator convexity, offering a basis for future research and applications. The results not only deepen the understanding of operator (h, m)-convex functions but also support the development of sharper inequalities, thereby broadening the applicability of operator convexity within mathematical analysis.
Comparing Outlier Detection Methods: An Application on Indonesian Air Quality Data Anwar Fitrianto; Amalia Kholifatunnisa; Anang Kurnia
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29434

Abstract

There are many methods for detecting outliers, but only a few methods consider data distribution. This research compares outlier detection method on univariate data with a skewed distribution. Outlier detection methods used in this research are Tukey's boxplot, adjusted boxplot, sequential fences, and adjusted sequential fences. It identifies areas of concern due to poor air quality during the Implementation of Micro-Community Activity Restrictions. The study used Indonesian air quality index data.The adjusted boxplot method performs best based on the number of outliers detected, error rate, accuracy, precision, specificity, sensitivity, and robustness. Adjusted boxplot and adjusted sequential fences can detect tails that contain outliers accurately because the skewness coefficient makes them more robust. Meanwhile, Tukey's boxplot and sequential fences are poor methods since they couldn’t detect correctly true outliers. Based on the results, adjusted boxplot is the best method. Then, areas that need attention due to poor air quality include South Sumatera, South Sulawesi, West Java, Riau, North Sumatera, Jambi, Jakarta, and East Java.
Comparative Analysis of Machine Learning Algorithms on Family Wellness Classification Budiarti, Retno; Hemarani, Febri; Reza, Mohammad; Mulyasari, Rindi Melati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.28259

Abstract

Family welfare is a state in which a family can experience happiness, have a decent quality of life, and be sufficient in meeting primary and secondary needs in family life. One factor that influences family welfare is the amount of per capita expenditure. This study aims to compare the performance of three machine learning algorithms, namely KNN (K-Nearest Neighbors), random forest, and naive Bayes, in classifying the status of families per province in Indonesia as prosperous or not prosperous. The data used in this study is demographic and social statistics data from the years 2017-2021, obtained from the bps.go.id website. The first statistical analysis conducted is principal component analysis (PCA) with 9 predictor variables. PCA produces four principal components which are then used in the KNN, random forest, and naive Bayes methods. The analysis results from the KNN, random forest, and naive Bayes methods each yield an F1-score of 65.46%, 68%, and 69.44%, respectively.
Estimation of Gompertz Mortality Parameter Models on Indonesian Population Mortality Table 2023 Andika Putra, Muhammad Rafael; Nurjannah, Nurjannah; Kurniawaty, Mila
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33319

Abstract

The research article discuss Gompertz Mortality Law parameter estimation using several methods to get the best models. The data based from Indonesian population mortality table or called Tabel Mortalitas Penduduk Indonesia (TMPI) 2023. Parameter estimation using several methods, includes Nonlinear Least Square (NLLS) with the Gauss-Newton algorithm, Weighted Least Squares (WLS), and Poisson Regression. Model validation is done by calculating root mean square error (RMSE) to determine the most accurate method. The analysis includes calculation of values in the mortality table, transformation of the gompertz model, estimated parameters with each method, and RMSE calculation. In the WLS method, the estimation is carried out by transformation of natural logarithms from the force of mortality function, then minimizes the number of squares of error, with ?? as weight and forming the ?? function and maximizing the logordered function on Poisson regression. Model accuracy is assessed from the suitability between the ?? function value of the model results with the ?? value in TMPI, both visually and mathematically through RMSE. The analysis results show that the NLLS method with the Gauss-Newton algorithm produces the most accurate Gompertz model.
Combination of Extreme Learning Machine and Binary Bat Algorithm for Customer Churn Prediction Arifin, Arifin; Anam, Syaiful; Marsudi, Marsudi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.31815

Abstract

AbstractOne of the important assets in a company is customers. Customers determine the company's stability because they are source of income and determine the company's competitiveness. It shows the importance of predicting which customers have the potential to switch to another company. These predictions can be done using Machine Learning (ML). One of ML methods is the Extreme Learning Machine (ELM). The advantages of ELM compared to other methods are fast computing time, ease of use, and can reach a global optimum. However, ELM has weaknesses when solving problems with high-dimensional datasets, so feature selection is required. The Binary Bat Algorithm (BBA) is a swarm intelligence method that can be used to optimize ELM performance. The advantages of BBA compared to other are few parameters and much better in effectiveness or accuracy. This research was carried out with preprocessing data, training data and testing data. The research results showed that ELM-BBA is better than ELM and ELM-Binary Particle Swarm Optimization (BPSO) in evaluation metric values. However, ELM-BBA tended to be slower than ELM-BPSO. The best results on evaluation metrics achieved by ELM-BBA were 0.97, 0.97, 0.96, and 0.97 in accuracy, precision, recall, and F1 score, respectively.
Reversible Self-Dual Codes over Finite Field Hidayat, Ardi Nur; Krisnawati, Vira Hari; Alghofari, Abdul Rouf
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29116

Abstract

Reversible self-dual code is a linear code which combine the properties from self-dual code and reversible code. Previous research shows that reversible self-dual codes have only been developed over field of order 2 and order 4. In this article, we construct reversible self-dual code over any finite field of order F_q ,  with natural number q=2.  We first examine and prove some of fundamental properties of reversible self-dual code over . After a thorough analysis these, we obtain a new generator matrix of reversible self-dual code.  A new generator matrix is derived from existing self-dual and reversible self-dual code over . It will be shown that a new reversible self-dual over  can be constructs from one and more existing code by specific algebraic methods. Furthermore, using this construction, we determine the minimum distance of reversible self-dual code and ensuring its optimal performance in various applications.
Dynamical Analysis of Modified Mathematical Model of Social Media Addiction Juhari, Juhari; Fikrina, Zulfa Akfi; Alisah, Evawati; Sujarwo, Imam
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29225

Abstract

In this study, there is no division between addiction in the mild and severe stages. Therefore, it is necessary to divide the stages of addiction because the healing is clearly different. Therefore, in this study, a modified dynamic analysis of the Social Media addiction model is carried out to obtain a valid model that can be implemented in real life. This study aims to find the stability of changes in the Addicted variable which is divided into two, namely Social Media addiction in the mild stage and Social Media addiction in the severe stage  There are six models that have been modified in this study, namely, individuals who do not have Social Media but are vulnerable to addiction , individuals who have Social Media but are not yet at the addiction stage , individuals infected with Social Media addiction in the mild stage , individuals infected with Social Media addiction in the severe stage , individuals who are recovering from Social Media addiction , individuals who are completely recovered from Social Media addiction . The steps of dynamic analysis include determining the equilibrium point, analyzing the stability of the equilibrium point, finding the basic reproduction number, numerical simulation of all variables. The results showed that the population of individuals infected with Social Media addiction in the mild stage  was at a value of 1.6112 with t = 4 years while the population of individuals infected with Social Media addiction in the severe stage  was at a value of 36.542 with t = 4 years. This study provides information that the dynamic analysis carried out on the modified mathematical model of Social Media addiction shows a stable condition.
Clustering and Mixture Model Analysis of Human Development Index in Papua: A Study Based on Educational Data (2010–2023) Sroyer, Alvian; Morin, Henderina; Reba, Felix; Wororomi, Jonathan; Languwuyo, Agustinus
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32988

Abstract

The purpose of this research is to analyze the distribution of the Human Development Index (HDI) in Papua based on the average length of schooling during the period 2010–2023 using the Gaussian Mixture Model (GMM) approach. Data from 27 districts are grouped into three clusters based on the distribution characteristics of each region. Weibull, Nakagami, and Generalized Extreme Value (GEV) distributions were selected to represent Cluster 1, Cluster 2, and Cluster 3, with parameter estimation using Maximum Likelihood Estimation (MLE). The results of the analysis show that Cluster 1 includes areas with low HDI such as Mamberamo Raya and Yahukimo, Cluster 2 reflects moderate HDI in areas such as Nduga and Tolikara, while Cluster 3 describes high HDI in districts such as Jayapura and Mimika. The mixture model that combines these three distributions provides an accurate representation of the HDI distribution pattern in Papua. Policy implications from these results include the development of cluster-based education programs to improve access to education in areas with low HDI, reduce educational disparities in areas with moderate HDI, and maintain sustainable development in areas with high HDI. This approach can be a reference for similar analyses in other regions with high development heterogeneity characteristics
Logistic Map with Feedback Control for Resilient Image Encryption Fahrurrozy, Mohammad; Suryanto, Agus; Darti, Isnani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.30783

Abstract

Images are one of many forms used to store important information that is easy to use and share, but they are vulnerable to cyber-attacks. An encryption effort is needed to secure the vital information in an image. In this paper, an encryption and decryption algorithm for grayscale and RGB images is proposed using logistic map with feedback control (LMFC). This 2D map which is an improvement from the popular one-dimensional logistic map also exhibits sensitive dependence on initial conditions, known as chaos. This phenomenon is verified through bifurcation diagram and the largest Lyapunov exponent. By using the largest Lyapunov exponent and the control parameters as secret key, LMFC generates two sequences of pseudo-random number related to the original image. Subsequently, a permutation process is proposed, utilizing permutation box to rearrange the pixel positions in the plain image. Finally, a diffusion process is proposed, utilizing XOR operations and keystreams created from the pseudo-random sequence to alter the pixel values, resulting in a visually distinct cipher image. Performance analysis of the proposed algorithm indicates resilience to various cryptanalysis and robust security, as it is sensitive to both secret keys and plain image. Additionally, the proposed decryption algorithm demonstrates the ability to reconstruct the original image with good quality from a cipher image, despite data changes or losses.
Hybrid Methods Random Forest and FOX-Inspired Optimization Algorithm for Selecting Features in Cervical Cancer Data Masbakhah, Afidatul; Sa'adah, Umu; Muslikh, Mohamad
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29582

Abstract

Cervical cancer is one of the number four causes of death among women worldwide, with about 604,000 new cases and 324,000 deaths each year. Human Papillomavirus infection is one of the main factors in almost 99% of cervical cancer cases. In addition to HPV, other risk factors such as smoking, long-term use of oral contraceptives, and weak immunity also play an important role. Along with the development of technology and in an effort to detect cervical cancer early, machine learning algorithms have been widely used to analyze the risk of cervical cancer, one of which is Random Forest (RF). One of the main challenges in early detection of cervical cancer is the large amount of irrelevant and redundant data, which can reduce the accuracy of predictions, making feature selection imperative. SI is able to combine new algorithms to improve performance in feature selection. One of the SI-based optimization algorithms is the FOX-Inspired Optimization Algorithm. The results of research that has been carried out using the RF-FOX hybrid method, the Num of pregnancies feature has proven to be the most influential factor in detecting the risk of cervical cancer in patients. In addition, other features such as First sexual intercourse, Number of sexual partners, age, and Hormonal Contraceptives also occupy the top five most influential features. Therefore, the hybrid RF-FOX method allows the performance of the model to be more optimized, thus helping in the identification of patients at risk of cervical cancer more precisely.

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