Pada postingan ini disajikan tentang penelitian matematika dan pendidikan matematika. Penelitian berikut merupakan penelitian pada rentang tahun 2021 hingga 2023.
2023
Boundedness of the Hardy-Littlewood maximal operator, fractional integral operators, and Calderon-Zygmund operators on generalized weighted Morrey spaces
Abstract: In this paper we investigate the boundedness of three classical operators, namely the Hardy-Littlewood maximal operator, fractional integral operators, and Calderon-Zygmund operators, on generalized weighted Morrey spaces and generalized weighted weak Morrey spaces. We prove that each of the three operators is bounded on these function spaces under some assumptions.
Link: researchgate or https://www.kjm-math.org/article_182725.html
On the boundedness of Mikhlin Operator on Generalized Morrey Spaces
Abstract: In this paper we investigate the boundedness of Mikhlin perators on generalized Morrey spaces. The results show that the operators are bounded on generalized Morrey spaces under some assumptions.
Link: researchgate or https://ejurnal.undana.ac.id/index.php/JD/article/view/12400
2022
Penerapan Teori Residu dalam Penentuan Nilai Eksak dari Deret Tak Hingga
Abstract: Teorema Residu memiliki penerapan yang menarik pada berbagai bidang matematika. Penerapan tersebut seperti pada evaluasi transformasi Fourier, transformasi Mellin dan penentuan nilai integral tak wajar yang melibatkan fungsi yang tergolong relatif rumit seperti pada integral Dirichlet dan integral Fresnel. Selain penerapan-penerapan tersebut dalam penentuan nilai eksak integral, teori residu juga mempunyai penerapan pada penentuan nilai eksak dari suatu deret tak hingga yang konvergen. Pada penelitian ini, diturunkan kemudian dibuktikan sebuah aturan untuk menentukan nilai eksak dari suatu deret tak hingga yang memenuhi syarat-syarat tertentu. Metode penelitian yang digunakan berupa kajian literatur. Peneliti mengumpulkan sumber-sumber ilmiah baik berupa artikel ilmiah maupun buku-buku yang kemudian dianalisis untuk mencapai tujuan penelitian. Hasil penelitian memberikan syarat cukup terkait dengan penggunaan rumus yang diperoleh, yaitu barisan $(\sup{|f(z)|:z \in C_N})$ yang merupakan barisan dengan indeks konvergen dengan cepat ke nol serta analitik kecuali untuk berhingga banyaknya pola. Dari hasil yang diperoleh tersebut, peneliti juga melakukan perhitungan mengenai nilai eksak dari fungsi zeta-riemann di bilangan genap positif sebagai salah satu aplikasi dari aturan tersebut.
Link: researchgate or https://iptek.its.ac.id/index.php/limits/article/view/10652
On The Boundedness Properties of the Generalized Fractional Integrals on the Generalized Weighted Morrey Spaces
Abstract: Morrey Spaces were first introduced by C.B. Morrey in 1938. Morrey space can be considered as a generalization of the Lebesgue spaces. Morrey spaces were then generalized become the generalized Morrey spaces, the weighted Morrey spaces, and the generalized weighted Morrey spaces. One of the studies on Morrey spaces is the boundedness of certain operators on the spaces. One of the operators is the fractional integral. The boundedness of fractional integrals on the classical Morrey spaces, the weighted Morrey spaces, the generalized Morrey spaces, and the generalized weighted Morrey spaces had been known. One of the extensions of fractional integrals is generalized fractional integral. The operator was bounded on the generalized Morrey spaces. The purpose of this study is to investigate the boundedness of generalized fractional integrals on the generalized weighted Morrey spaces. The weight used is Muckenhoupt class. The results obtained show that the generalized fractional integral is bounded from generalized weighted Morrey space to another generalized weighted Morrey space under some assumptions. The main result obtained then implies the boundedness of the generalized fractional maximal operator on generalized weighted Morrey spaces under the same assumptions.
Link: researchgate or https://ojs.unm.ac.id/JMathCoS/article/view/36040
2021
Students’ Factual Understanding on the concept of Limit
Abstract: This research aims to describe the factual understanding of the concept of the formal definition of limit. This is a descriptive qualitative research with 8 students. The data gathered by using test and interview. The instruments is a conceptual understanding test. We divide the factual understanding into three main concepts: (1) students’ understanding on the symbol of ε and δ in the definition, (2) students’ understanding on the meaning of the absolute value in the definition, and (3) students’ understanding on the implication statement in the definition. Each elaborate to some categories to get the ideas on how students understand about the concept. The results reveals that most students have incomplete understanding about the definition of limit function.
Link: researchgate or https://iopscience.iop.org/article/10.1088/1742-6596/1899/1/012148
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