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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Pattimura Proceeding : Conference of Science and Technology
Zanu, Pebrudal
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Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Control & Systems Engineering Energy Engineering Materials Science & Nanotechnology Mathematics Physics

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KETAKSAMAAN HARDY DI RUANG HERZ HOMOGEN Pebrudal Zanu; Yudi Soeharyadi; Wono Setya Budhi
Pattimura Proceeding 2021: Prosiding KNM XX
Publisher : Pattimura University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1759.731 KB) | DOI: 10.30598/PattimuraSci.2021.KNMXX.99-106

Abstract

Ruang Herz pertama kali diperkenalkan untuk mengidentifikasi hasil transformasi Fourier dari kelas fungsi Lipschitz. Lu dan Yang membedakan ruang ini menjadi dua jenis berdasarkan dekomposisi spasial pada Rn \{0}dan Rn. Dekomposisi pada Rn \{0}berupa anulus2berpangkat. Sedangkan,padaRn berupabolasatuandananulus2berpangkat. Ruang Herz tersebut dinamakan dengan ruang Herz homogen dan non-homogen. Dalam makalah ini akan dibuktikan keterbatasan operator Hardy tipe Samko dan dualnya pada ruang Herz homogen. Pembuktian terlebih dahulu melalui kasus 1 < q ≤ p < ∞. Untuk kasus 1 < p ≤ q < ∞, bukti dilanjutkan dengan konsep dualitas
Spectral Analysis of a Cyclic Tank Mixing System Zanu, Pebrudal; Wahyu, Sri; Burhan, Mohammad Januar Ismail
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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.v11i1.41466

Abstract

In this paper, we study a cyclic mixing tank system consisting of n identical tanks arranged in a closed-loop configuration, each operating under constant volume with equal inflow and outflow rates. The model is further generalized to an m-layer structure, where each layer comprises n circularly interconnected tanks. Based on mass balance principles, the concentration dynamics are formulated as a linear system of first-order ordinary differential equations. By exploiting the structured form of the system matrix, we derive an explicit analytical solution and obtain a closed-form characterization of its spectrum. We show that the eigenvalues of the system are explicitly given by k,j = (-2 + e2i(k-1)/n), which inherently guarantees the decay of all modes. In particular, the solution exhibits a polynomial-exponential form associated with the multilayer cyclic tank. We also establish that the system is exponentially stable under conditions ensuring decay of all modes. Finally, we present numerical simulations to validate the analytical results and to illustrate the transient dynamics of the multilayer system.
Co-Authors Burhan, Moh. Januar Ismail Sri Wahyu Wono Setya Budhi Yudi Soeharyadi