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All Journal Hilbert Journal of Mathematical Analysis Unnes Journal of Mathematics Education
Janny Lindiarni
Analysis and Geometri Group, Faculty of Mathematics and Natural Sciences Institute of Technology Bandung, Bandung 40132, Indonesia
Chemistry Control & Systems Engineering Education Engineering Mathematics Physics

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Construction of a Banach algebra in summable infinite matrices and its realization of the Gelfand transformation Lindiarni, Janny; Setya Budhi, Wono
Hilbert Journal of Mathematical Analysis Vol. 1 No. 2 (2023): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v1i2.11

Abstract

In this paper, we extend the construction of a Banach Algebra from summable sequences to summable matrices. We also find the representation of the Banach algebra as complex-valued continuous functions defined on a Hausdorff space.
On Invariant eigenvalues of Laplacian on complex star metric graphs Soeharyadi, Yudi; Lindiarni, Janny; Agustima, Pilipus Neri; Burhan, Mohammad Januar Ismail
Hilbert Journal of Mathematical Analysis Vol. 1 No. 2 (2023): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v1i2.13

Abstract

In this article eigenvalues of Laplacian acting on complex star metric graphs is considered. The operator is coupled with Neumann-Kirchhoff vertex condition, implying self adjointness of the operator. We exhibit the invariance of the eigenvalues over the number of the bonds of the star metric graphs. Moreover, the eigenvalues are also invariant over parallel bonds of the star metric multigraphs.
Using the History of Circle and Parabolic Segment Areas as Learning Alternatives in Integral Yuwono, Layli Rahmania; Lindiarni, Janny; Afgani, Rizal
Unnes Journal of Mathematics Education Vol. 13 No. 1 (2024): Reguler Issue
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/vw82bv85

Abstract

This article will present some classic problems in the Ancient Greece period: the ratio of the areas of two circles problem solved by Eudoxus and the area of a parabola segment problem solved by Archimedes. These problems can be used as alternative teaching resources to give the students an early understanding of the integral concept. This article focuses on finding alternatives for teaching integral material through theorems and historical understanding without calculus knowledge. This study used a systematic literature review method to analyze the mathematical content and the historical influences on their problem-solving methods. The literature sources were indirect sources such as journals, books, and other written literature. The results show that Eudoxus' principle has been a special limit problem since the period, helping solve the ratio of the areas of two circles problem, and there has been a special case of infinite geometric series solving the area of parabolic segment problem. This article gives some recommendations for the teachers at the end of the article, on how to give a representation of the propositions discussed in this article to the students so the students can understand the connections between the prior area problem (in which the area is bounded by its line segments) and the integral concept which will be learned.
Co-Authors Afgani, Rizal Agustima, Pilipus Neri Burhan, Moh. Januar Ismail Setya Budhi, Wono Yudi Soeharyadi Yuwono, Layli Rahmania