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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 533 Documents
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A Multiplicative Extension of Weighted Hadamard Fractional Integrals Almeer Naufal Hakim; Marjono Marjono; Corina Karim
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.43122

Abstract

This paper presents an innovative category of weighted Hadamard fractional integral operators situated within the paradigm of multiplicative calculus. The operator introduced herein broadens the traditional weighted Hadamard fractional integral by integrating the multiplicative framework of non-Newtonian calculus, thereby establishing a cohesive linkage between weighted fractional analysis and multiplicative fractional calculus. We delineate the formulation of both the left- and right-sided multiplicative weighted Hadamard fractional integral operators and explore their core analytical characteristics. Specifically, a multiplicative linearity property is demonstrated, the continuity of the logarithmic representation of the operator is affirmed, and boundedness results are extracted in weighted Lebesgue-type spaces through the application of Hölder's inequality. Furthermore, we establish that the proposed operators comply with a semigroup property, which ensures alignment with the classical framework of fractional integration. These findings illustrate that the introduced operators maintain crucial structural attributes of weighted fractional integrals while seamlessly extending them to the multiplicative context. The theoretical framework developed herein lays a foundational basis for subsequent explorations in multiplicative fractional calculus, fractional integral inequalities, and associated applications within the realm of mathematical analysis.
Spatial Heterogeneity of Poverty Determinants in Indonesia A Hierarchical Geographically Weighted Regression Approach Debora Dwi Kurniawati; Henny Pramoedyo; Suci Astutik
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42956

Abstract

This study employs the Hierarchical Geographically Weighted Regression (HGWR) model to analyze poverty determinants in Indonesia, addressing spatial heterogeneity and hierarchical data structures simultaneously. Using data across 34 provinces and 508 regencies/cities, the HGWR model with a Gaussian kernel (bandwidth = 15) substantially outperforms the global Ordinary Least Squares (OLS) regression, increasing the R2 value from 0.502 to 0.754. The Moran's I test on the global model residuals (0.2216, p 0.001) justifies the urgency of accounting for spatial nonstationarity, while the HGWR post-estimation residuals show that spatial autocorrelation is successfully eliminated (-0.000641, p = 0.416). At the regency/city level, adjusted per capita expenditure and the poverty line significantly reduce the poverty headcount rate, whereas the average years of schooling shows no significant localized effect. At the provincial level, the Human Development Index (HDI) consistently reduces poverty (mean coefficient of -0.8082) but exhibits substantial spatial variation, where the impact is strongest in eastern Indonesia (coefficients -0.95) and weakest in Java (coefficients -0.65). Conversely, expected years of schooling exhibits a positive mean coefficient (3.4755), with its positive effects highly concentrated in Java. These findings conclude that poverty reduction strategies in Indonesia must be place-based rather than uniform, prioritizing provincial HDI improvements in eastern Indonesia where the marginal returns of development policy are highest.
A Generalization Euclidean Algorithm Approach for Solving Multi-Variable Linear Diophantine Equations Ikhsan Abdul Ro'uf; Hery Susanto; I Made Sulandra
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.43242

Abstract

Multi-variable linear Diophantine equations of the form a1x1 + a2x2 + + anxn = b, where ai, b Z, have various applications in many fields, including cryptography, chemistry, and statistics, where they can be used to determine public and private keys, balance chemical equations, and model scheduling problems, respectively. The equation has infinitely many integer solutions if gcd(a1, a2, , an) divides b. Two well-known algorithms for finding solutions are the Smith normal form and integer lattice methods. This paper presents an alternative approach for obtaining the general solution of the equation. The proposed method applies the generalized Euclidean algorithm to compute gcd(a1, a2, , an), followed by a back-substitution process through the algorithm's steps to express the greatest common divisor as a linear combination of a1, a2, , an. This linear combination is then multiplied by b/gcd(a1, a2, , an) to obtain a particular solution of the equation. Finally, the general solution is constructed from the resulting particular solution.

Page 54 of 54 | Total Record : 533

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