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All Journal Indonesian Journal of Geography CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan Contemporary Mathematics and Applications (ConMathA) InPrime: Indonesian Journal Of Pure And Applied Mathematics Tensor: Pure and Applied Mathematics Journal Parameter: Jurnal Matematika, Statistika dan Terapannya Amalgamasi: Journal of Mathematics and Applications PENGAMATAN: Jurnal Pengabdian Masyarakat untuk Ilmu MIPA dan Terapannya
Batkunde, Harmanus
MATHEMATIC DEPARTMENT FACULTY OF MATHEMATICS AND NATURAL SCIENCES UNIVERSITY OF PATTIMURA
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Pembinaan Penyelesaian Soal-soal Kompetisi Sains Nasional Bidang Matematika untuk Guru dan Siswa SMA Negeri 2 Ambon Dahoklory, Novita; Rumlawang, Francis Y.; Patty, Henry W. M.; Batkunde, Harmanus; Tilukay, Meilin I.; Patty, Dyana
PENGAMATAN: Jurnal Pengabdian Masyarakat untuk Ilmu MIPA dan Terapannya Vol 1 No 2 (2023): PENGAMATAN: Jurnal Pengabdian Masyarakat untuk Ilmu MIPA dan Terapannya
Publisher : Jurusan Matematika FMIPA Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/pengamatanv1i2p56-62

Abstract

Pengadaan Olimpiade Sains merupakan program yang penting dalam mengembangkan kemampuan siswa untuk berpikir kreatif dan kritis dalam memecahkan masalah. Hal ini menjadi tolak ukur penting dalam mengembangkan daya saing siswa kedepannya. Namun tingkat kesulitan yang disajikan dalam soal olimpiade cenderung tinggi jika dibandingkan dengan materi rutin yang diajarkan guru di sekolah. Oleh karena itu, guru matematika perlu meningkatkan kompetensi melalui kegiatan-kegiatan yang bertujuan meningkatkan inovasi dan kreativitas guru dalam memecahkan soal-soal olimpiade matematika. Divisi Aljabar dan Analisis Jurusan Matematika Universitas Pattimura berinisiatif melakukan pendampingan bagi guru matematika pada lembaga pendidikan SMA Negeri 2 Ambon. Kegiatan ini bertujuan untuk memberikan pendampingan bagi siswa dan guru matematika sebagai pembina olimpiade untuk dapat mengingkatkan kemampuan mencakup teori bilangan, aljabar, geometri, dan kombinatorika yang merupakan materi olimpiade matematika yang rutin disajikan dari tahun ke tahun. Selain itu, kegiatan ini juga memiliki luaran panduan olimpiade Kompetisi Sains Nasional tingkat SMA bidang Matematika sehingga diharapkan guru matematika dapat berinovasi dalam rangka persiapan siswa mengikuti olimpiade.
Notes on 2-Normed Spaces Through Their Quotient Spaces Rumlawang, Francis Yunito; Hernita, Hernita; Lesnussa, Yopi Andry; Batkunde, Harmanus
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.v10i2.35824

Abstract

In this paper, we defined new norms in 2-normed spaces derived from the 2-norm with respect to its quotient spaces. Moreover, these norms were used to observe some aspects of 2-normed spaces namely, a Convergent sequence, a Cauchy sequence, completeness, a closed set, and a bounded set. Furthermore, we used these aspects to prove the Fixed-Point Theorem in a 2-Banach Space.
THE SUFFICIENT CONDITIONS FOR A MULTIPLICATIVE DERIVATION IN THE JORDAN RING TO BE ADDITIVE Adrianus, Karen Isye; Batkunde, Harmanus; Patty, Dyana
Parameter: Jurnal Matematika, Statistika dan Terapannya Vol 4 No 1 (2025): Parameter: Jurnal Matematika, Statistika dan Terapannya
Publisher : Jurusan Matematika FMIPA Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/parameterv4i1pp95-110

Abstract

Derivation is a mapping from a set to itself. There are two types of derivations in rings: ordinary derivation and Jordan derivation. Given a triangular matrix ring T, a non-associative ring can be formed, known as a Jordan ring T. Subsequently, on the Jordan ring T, a derivation can be defined, referred to as derivation in the Jordan ring T. This paper provides the conditions that must be met for a multiplication derivation on the Jordan ring T to be additive. Furthermore, the ring T must be 2-torsion-free so that the derivation on the Jordan ring becomes a Jordan derivation on the ring T.
Kekonvergenan Barisan di Ruang Bernorma-2 Berdasarkan Norma Ruang Kuosiennya Adjid, Sasnia Febriani; Batkunde, Harmanus; Wattimena, Abraham Zacharia
Amalgamasi: Journal of Mathematics and Applications Vol. 1 No. 1 (2022): Amalgamasi: Journal of Mathematics and Applications
Publisher : Universitas Pasifik Morotai

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55098/amalgamasi.v1.i1.pp33-43

Abstract

Konsep ruang bernorma-2 merupakan perumuman dari konsep ruang bernorma. Struktur dari ruang bernorma-2 telah banyak diteliti sejak dikenalkan oleh S. Gahler pada tahun 1964. Tujuan dari penelitian ini mengkaji kekonvergenan barisan di ruang bernorma-2 dengan memanfaatkan norma di ruang-ruang kuosiennya. Dua kelas yang berisi ruang-ruang kuosien akan dikonstruksi. Norma-norma di ruang kuosien pada tiap kelas ini akan menjadi pendekatan dalam mengkaji kekonvergenan barisan di ruang bernorma-2. Diperoleh bahwa kekonvergenan barisan ditinjau dengan menggunakan norma dari tiap kelas akan ekuivalen
The Total Irregularity Strength of a Comb Product of Stars Tilukay, Meilin Imelda; Batkunde, Harmanus
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 6 No. 2 (2024)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v6i2.42188

Abstract

A totally irregular total k-labeling λ: V U E → {1, 2, ⋯ , k} of a graph G is a labeling where the weights of all distinct vertices and edges are unique. The weight w(x) of a vertex x is defined as the sum of its label and the labels of all edges incident to it, while the weight w(e) of an edge e is the sum of its label and the labels of its two endpoints. The minimum k for which G admits such a labeling is known as the total irregularity strength of G, denoted ts(G). This study focuses on determining ts(G) for specific classes of trees, including the comb product of stars, where the contact vertex is the central vertex of one star, and the triple star graph.Keywords: comb product; star; total irregularity strength; totally irregular total labeling graph. AbstrakPelabelan k-total tak teratur total λ: V U E → {1, 2, ⋯ , k} dari suatu graf G adalah suatu pelabelan sedemikian sehingga bobot setiap titik dan sisi masing-masing berbeda. Bobot  suatu titik w(x)  adalah jumlah label titik x dan label setiap sisi yang terkait ke x, dan bobot suatu sisi w(e) adalah jumlah label sisi e dan kedua titik yang terkait ke e. Nilai minimum k sehingga suatu graf G memiliki pelabelan tersesebut dikenal sebagai nilai ketakteraturan total dari G, dinotasikan dengan ts(G). Pada artikel ini, ditentukan nilai ketakteraturan total dari suatu kelas graf pohon, yaitu hasil operasi comb dari graf bintang, dimana titik tetapnya adalah titik pusat graf bintang, dan graf bintang tripel. Kata Kunci: hasil operasi comb; graf bintang, nilai ketakteraturan total; pelabelan total tak teratur total. 2020MSC: 05C78
Necessary Condition for Boundedness of Stein-Weiss Operator on Orlicz-Morrey Spaces Al Hazmy, Sofihara; Masta, Al Azhary; Fatimah, Siti; Batkunde, Harmanus
Journal of the Indonesian Mathematical Society Vol. 31 No. 4 (2025): DECEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i4.1963

Abstract

This study aims to find necessary conditions for the boundedness of Stein-Weiss Operator on Orlicz-Morrey spaces. It is well known that the Orlicz-Morrey space is the generalization of the Lebesque space. In particular, by considering power function as Young’s function and zero as Morrey Space index, the Orlicz-Morrey space is a Lebesgue space itself. Orlicz-Morrey space and several operators in the space have been studied intensively by several researchers. In this study, we find a necessary condition for the boundedness of the Stein-Weiss operator on Orlicz-Morrey spaces. The technique to achieve our purpose is by substituting dilation of a radial function on a ball into inequality of boundedness assumption, and some basic properties of Young’s function. {Due to the properties of the dilation, the result will be presented as an inequality involving suitable parameters}. As a result we get the necessary condition. As a discussion, we try to find several examples that satisfy the inequalities. The most important, the result shows that there is a significant factor to see the boundedness of the Stein-Weiss operator on Orlicz-Morrey spaces. Since { Stein-Weiss operator is a generalization of fractional integral operator, the result shows that it generalize the boundedness of fractional integral on Orlicz space.
Co-Authors Adjid, Sasnia Febriani Adrianus, Karen Isye H. W. M. Patty Hernita, Hernita Maitimu, Meldry W Masta, Al Azhary Meilin Imelda Tilukay Nanang Tyasbudi Puspito Natasian, Nehemia Trianto Novita Dahoklory Patty, Dyana Persulessy, Elvinus R. Rumlawang, Francis Y Rumlawang, Francis Y. RUMLAWANG, FRANCIS YUNITO Sinay, Lexy J. Siti Fatimah Talakua, Mozart W. Tomasoa, M. Wattimanela, Henry Junus Wattimena, Abraham Zacharia Yopi Andry Lesnussa