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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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Norms on Quotient Spaces of The 2-Inner Product Space Harmanus Batkunde
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 2 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i2.29853

Abstract

This paper discussed about construction of some quotients spaces of the 2-inner product spaces. On those quotient spaces, we defined an inner product with respect to a linear independent set. These inner products was derived from the -inner product. We then defined a norm which induced by the inner product in these quotient spaces.
The total irregularity strength of m copies of the friendship graph Meilin Tilukay; Harmanus Batkunde
Tensor: Pure and Applied Mathematics Journal Vol 3 No 1 (2022): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol3iss1pp43-48

Abstract

This paper deals with the totally irregular total labeling of the disjoin union of friendship graphs. The results shows that the disjoin union of copies of the friendship graph is a totally irregular total graph with the exact values of the total irregularity strength equals to its edge irregular total strength.
Symmetric Functions with Respect to a Point (a,b) and Its Properties that Generalized from Properties of Odd Functions Natasian, Nehemia Trianto; Lesnussa, Yopi Andry; Batkunde, Harmanus
Tensor: Pure and Applied Mathematics Journal Vol 5 No 1 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss1pp9-16

Abstract

The function f: R \to R is said to be an odd function if f (-x) = -f(x) for every x \in R. The graph of an odd function is symmetry with respect to origin, or point (0,0) . The propose of this study is to observe some properties of symmetrical functions which are generalize from some properties of odd functions. Some of the results obtained include a linear combination of two functions symmetrical with respect to the point (a,b) is a functions of symmetrical with respect to the point (a,2b). An integral functions of symmetrical with respect to the point (a,b) on a closed interval [a-c,a+c] is 2bc for any real number c. Moreover product of scalars with functions of symmetrical with respect to the point (a,b) is a functions of symmetrical with respect to the point (a,\alpha b) for every \alpha real numbers. Furthermore the addition n-symmetrical of functions with respect to the point (a,b) is a series of functions of symmetrical with respect to the point (a,nb). he function is said to be an odd function if for every . The graph of an odd function is symmetry with respect to origin, or point . The propose of this study is to observe some properties of symmetrical functions which are generalize from some properties of odd functions. Some of the results obtained include a linear combination of two functions symmetrical with respect to the point is a functions of symmetrical with respect to the point . An integral functions of symmetrical with respect to the point on a closed interval is for any real number . Moreover product of scalars with functions of symmetrical with respect to the point is a functions of symmetrical with respect to the point for every real numbers. Furthermore the addition -symmetrical of functions with respect to the point is a series of functions of symmetrical with respect to the point .
The Digital Image Compression Using Wavelet Daubechies Transform Maitimu, Meldry W; Rumlawang, Francis Y; Tilukay, Meilin I; Batkunde, Harmanus
Tensor: Pure and Applied Mathematics Journal Vol 5 No 1 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss1pp27-32

Abstract

As a form of data representation, the obstacle faced when using digital images is the large volume of data required to represent the image. For that we need a technique that can reduce the volume of data, this thechnique is called compression. In this thesis, a very well-known wavelet transform method is chosen, namely Daubechies D4 wavelet transform, with four coefficients of scaling function, and four coefficients of wavelet function. Then implemented with MATLAB 2021 software as a programming tool to see the effect of quality on the transformed image.
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
Simeulue Earthquake Activity Analysis Using the MLE Method Wattimanela, Henry Junus; Puspito, Nanang Tyasbudi; Batkunde, Harmanus
Indonesian Journal of Geography Vol 57, No 1 (2025): Indonesian Journal of Geography
Publisher : Faculty of Geography, Universitas Gadjah Mada

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22146/ijg.91332

Abstract

The territory of Indonesia is prone to a high level of tectonic earthquake vulnerability including In Simeulue Regency, one of the regions of Aceh Province. Therefore, this study aimed to analyze level of tectonic earthquake activity in Simeulue Regency and its surroundings divided into four Sub Regions (I, II, III, and IV). The data used spanned 1940-2020 and were sourced from the ISC with the criteria of the depth being <60km and a magnitude of 3Mw. The seismic features were elucidated through descriptive statistics, while the determination of 'a' and 'b' values for individual Sub Region was accomplished by using the maximum likelihood estimation (MLE) method. The results showed that the highest distribution of earthquakes was at a depth of 15-44.9 km and magnitude at intervals of 3.0-4.9 Mw, specifically in Sub Region III. The largest Mc value was found in Sub Region I, while Sub Region III had high seismic activity and rock heterogeneity. In addition, this area had a large seismicity index and the shortest return period at intervals of magnitude 3.0≤M<4.0. Sub Region I on the other hand had a longer seismicity index at intervals of magnitudes 4.0≤M<5.0,5.0≤M<6.0, and M≥6.0.Received:2023-12-02  Revised:2024-01-11 Accepted:2024-12-07 Published:2025-04-27
ALJABAR-C* DAN SIFATNYA BATKUNDE, HARMANUS; Persulessy, Elvinus R.
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 6 No 1 (2012): BAREKENG : Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (306.489 KB) | DOI: 10.30598/barekengvol6iss1pp19-22

Abstract

These notes in this paper form an introductory of C*-algebras and its properties. Some results on more general Banach algebras and C*-algebras, are included. We shall prove and discuss basic properties of Banach Algebras, C*-algebras, and commutative C*-algebras. We will also give important examples for Banach Algebras, C*-algebras, and commutative C*-algebras.
ALJABAR-C* KOMUTATIF Batkunde, Harmanus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 7 No 1 (2013): BAREKENG : Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (430.033 KB) | DOI: 10.30598/barekengvol7iss1pp31-35

Abstract

These notes in this paper will discuss about C*-algebras commutative and its properties. The theory of algebra-*, Banach-* algebra, C*-algebras and *-homomorphism are included. We also give some examples of commutative C*-algebras. We shall prove and discuss some important properties of commutative C*-algebras and *-homomorphism.
KARAKTERISTIK RUANG HAUSDORFF KOMPAK Tomasoa, M.; Talakua, Mozart W.; Sinay, Lexy J.; Batkunde, Harmanus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 9 No 2 (2015): BAREKENG : Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (361.306 KB) | DOI: 10.30598/barekengvol9iss2pp85-88

Abstract

Misal (𝐻. 𝜏) adalah suatu ruang topologi, 𝐻 disebut ruang Hausdorff jika untuk setiap 𝑥, 𝑦 ∈ 𝐻 dimana 𝑥 ≠ 𝑦 terdapat dua himpunan buka 𝑈, 𝑉 ∈ 𝜏 dan 𝑈 ∩ 𝑉 = ∅ sedemikian sehingga 𝑥 ∈ 𝑈 dan 𝑦 ∈ 𝑉. Selanjutnya dengan memanfaatkan sifat kekompakan dalam suatu ruang topologi maka akan ditinjau karakteristik suatu ruang Hausdorff yang dilengkapi oleh sifat kekompakan ini. Lebih lanjut, suatu ruang Hausdorff yang dilengkapi dengan sifat kompak disebut ruang Hausdorff kompak
FUNGSIONAL LINEAR-2 DALAM RUANG NORM-2 Batkunde, Harmanus; Tilukay, Meilin I.; Rumlawang, Francis Y.
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 10 No 1 (2016): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (480.184 KB) | DOI: 10.30598/barekengvol10iss1pp1-7

Abstract

Ruang norm-2 merupakan perluasan dari ruang norm yang telah kita kenal. Ruang norm-2 dan perumumannya ruang norm-n (𝑛≥2), pertama kali diperkenalkan oleh Gähler pada tahun 1960-an, [3, 4, 5, 6]. Kemudian Misiak di tahun 1989 memperkenalkan ruang hasil kali dalam-n (𝑛≥2) [16]. Setelah itu, banyak peneliti yang mengkaji sifat-sifat ataupun aspek-aspek dalam ruang norm-2 maupun ruang norm-n. Hal ini dapat dilihat pada beberapa penelitian dalam [1,2,7,8,9,10,11,12,13,14,15,18,19]. Dalam penelitian ini aspek yang akan ditinjau adalah fungsional linear-2 terbatas pada ruang norm-2. Untuk meninjau beberapa sifatnya, sebelumnya akan diperkenalkan fungsional linear-2 di ruang norm-2 dengan beberapa tipe keterbatasn. Berdasarkan tipe keterbatasan ini akan dibentuk ruang-ruang dual. Ruang-ruang dual ini memuat semua fungsional linear-2 masing-masing berdasarkan tipe keterbatasannya. Selanjutnya akan ditunjukkan bahwa ruang-ruang dual ini ekuivalen.
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