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A FAST COMPUTATION FOR EIGENVALUES OF CIRCULANT MATRICES WITH ARITHMETIC SEQUENCE Guritman, Sugi; Jaharuddin; Mas'oed, Teduh Wulandari; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.1.69-80

Abstract

In this article, we derive simple formulations of the eigenvalues, determinants, and also the inverse of circulant matrices whose entries in the first row form an arithmetic sequence. The formulation of the determinant and inverse is based on elementary row and column operations transforming the matrix to an equivalent diagonal matrix so that the formulation is obtained easily. Meanwhile, for the eigenvalues formulation, we simplify the known result of formulation for the general circulant matrices by exploiting the properties of the cyclic group induced by the set of all roots of as the set of points in the unit circle in the complex plane, and also by considering the specific property of arithmetic sequence. Then, we construct an algorithm for the eigenvalues formulation. This algorithm shows a better computation compared to the previously known result for the general case of circulant matrices.
DETERMINAN, INVERS, DAN NILAI EIGEN MATRIKS SKEW-CIRCULANT DENGAN ENTRI BARISAN GEOMETRI Azhari, Mirza Farhan; Wulandari Mas'oed, Teduh; Guritman, Sugi; Jaharuddin; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 2 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.2.129-140

Abstract

Matriks skew-circulant adalah matriks segi yang entri terakhir setiap baris berpindah ke posisi utama dan berganti tanda disertai pergeseran semua entri lainnya ke posisi berikutnya. Dalam artikel ini, entri dari matriks circulant berupa entri barisan bilangan geometri. Tujuannya adalah merumuskan suatu formulasi sederhana dari determinan, invers, dan nilai eigen dari suatu matriks skew circulant. Formulasi determinan ditentukan dengan menerapkan serangkaian operasi baris dasar dan kolom dasar sampai diperoleh matriks diagonal. Langkah untuk mencari invers dilakukan dengan mengadaptasi metode dalam mencari determinan dan ekuivalensi baris dan kolom pada matriks. Dalam mencari nilai eigen digunakan konsep akar kesatuan (roots of unity) dan subgrup siklik.
OPTIMASI PENJADWALAN BISKITA TRANS PAKUAN BOGOR DI KORIDOR-2 DENGAN INTEGER LINEAR PROGRAMMING Mayyani, Hidayatul; Syahrul; Supriyo, Prapto Tri; Aman, Amril; Siswandi; Septianto, Fendy; Julianto, Mochamad Tito
MILANG Journal of Mathematics and Its Applications Vol. 21 No. 1 (2025): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.21.1.35-43

Abstract

Kota Bogor merupakan salah satu kota yang berada di provinsi Jawa Barat dengan jumlah penduduk yang banyak. Sejalan dengan perubahan waktu, jumlah penduduk kota Bogor bertambah, sehingga menyebabkan mobilitas semakin meningkat dan juga menyebabkan kemacetan. Salah satu upaya Pemerintah Kota Bogor untuk mengatasi kemacetan adalah dengan melakukan pergantian angkutan kota menjadi bentuk angkutan massal perkotaan dengan konsep Bus Rapid Transit yang diberi nama BisKita Trans Pakuan Bogor. Dalam paper ini dibahas masalah optimasi penjadwalan BisKita Trans Pakuan Bogor pada Koridor 2 berdasar Integer Linear Programming yang diselesaikan menggunakan bantuan software MiniZinc. Model dibangun dengan memperhatikan partisi waktu, rute bus, banyaknya bus yang beroperasi, jam kerja pramudi (pengemudi), banyaknya pramudi serta lamanya perjalanan dalam tiap partisi waktu. Hasil luaran model berupa optimasi banyaknya rit bus dan biaya operasional minimum yang dikeluarkan oleh perusahaan. Banyaknya rit yang dihasilkan selanjutnya digunakan untuk menyusun jadwal keberangkatan bus.
ANALISIS IMPLEMENTASI KURIKULUM MERDEKA BELAJAR PADA PEMBELAJARAN SEJARAH LOKAL DI SMA NEGERI 2 NANGA TAYAP KABUPATEN KETAPANG: STUDI KASUS PADA KELAS XI IPS Siswandi; Syaifulloh, Muhammad
Puteri Hijau : Jurnal Pendidikan Sejarah Vol. 10 No. 2 (2025): PUTERI HIJAU: JURNAL PENDIDIKAN SEJARAH
Publisher : Department of History Education, Faculty of Social Science, Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/ph.v10i2.56512

Abstract

Kurikulum Merdeka Belajar (KMB) merupakan terobosan baru dalam pendidikan Indonesia yang menekankan kebebasan belajar dan pengembangan karakter. Penelitian ini bertujuan untuk menganalisis implementasi KMB pada pembelajaran sejarah lokal di SMA Negeri 2 Nanga Tayap Kabupaten Ketapang dan mengidentifikasi faktor-faktor yang mendukung dan menghambatnya. Studi kasus dilakukan pada kelas XI IPS dengan metode kualitatif, melalui wawancara, observasi, dan dokumentasi. Hasil penelitian menunjukkan bahwa implementasi KMB pada pembelajaran sejarah lokal masih belum optimal. Faktor pendukungnya adalah antusiasme siswa dan dukungan kepala sekolah. Faktor penghambatnya adalah kurangnya pemahaman guru tentang KMB, keterbatasan sumber belajar, dan sarana prasarana yang belum memadai. Disarankan untuk memberikan pelatihan KMB kepada guru, mengembangkan sumber belajar lokal, dan meningkatkan sarana prasarana.Curriculum for Independent Learning (Kurikulum Merdeka Belajar or KMB) is a new breakthrough in Indonesian education that emphasizes freedom in learning and character development. This research aims to analyze the implementation of KMB in local history learning at SMA Negeri 2 Nanga Tayap, Ketapang Regency, and identify supporting and inhibiting factors. A case study was conducted in class XI IPS using a qualitative method, involving interviews, observations, and documentation.The research results indicate that the implementation of KMB in local history learning is not yet optimal. Supporting factors include student enthusiasm and school principal support. Inhibiting factors include teachers' lack of understanding about KMB, limited learning resources, and inadequate facilities. It is recommended to provide KMB training for teachers, develop local learning resources, and improve facilities.
Rationality of antibiotics prescription on pneumonia patients at the Indonesia Air Force Center Hospital (RSPAU) Dr. Suhardi Hardjolukito, Yogyakarta Burju Simanjuntak, Lamhot; Siswandi; Gugun Suhendra; Dewi Wulandari; Wulanria Nurfitrika; Weti Widayanti; Nurhasna Suhmita Sari; Ikhwan Dwi Wahyu Nugroho
Indonesian Journal of Pharmacology and Therapy Vol 5 No 2 (2024)
Publisher : Faculty of Medicine, Public Health, and Nursing Universitas Gadjah Mada and Indonesian Pharmacologist Association or Ikatan Farmakologi Indonesia (IKAFARI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22146/ijpther.9867

Abstract

Irrational antibiotic prescriptions on pneumonia patients is common in hospitals. This study aimed to evaluate the rationality of antibiotics prescription on pneumonia patients at the Indonesia Air Force Center Hospital (RSPAU) Dr. Suhardi Hardjolukito, Yogyakarta. It was a cross-sectional study using prescriptions for inpatients and outpatients suspected of community acquired pneumonia (CAP) submitted to the Medical Record Installation. All prescribed drugs, including their dosage, duration, route of administration, and demographic information of patients were extracted. The rationality of antibiotic use was then evaluated using the Gyssens and PCNE methods by assessing the antibiotic use with standard treatments based on the Clinical Pathway of RSPAU Dr. Suhardi Hardjolukito, Yogyakarta and the Guideline for the Use of Antibiotics of the Ministry of Health, Republic of Indonesia number 28 in 2021. A total of 124 pneumonia patient prescriptions were evaluated. The rationality of antibiotic prescriptions based on the Gyssens and PCNE criteria were 65.7% and 65.26%, respectively. The irrational of antibiotics based on the Gyssens method consisted of incomplete antibiotic prescription (2.90%), antibiotics not indicated (2.23%), medications prescribed cost more than substitute medications (8.20%), and less duration of medications (19.40%). Furthermore, the irrationality of antibiotics based on the PCNE method consisted of untreated symptoms or indications (8.33%), treatment issues related to cost-effectiveness (1.39%), too short duration of medications (23.61%), and incorrect medication administration or dosage interval timing (1.39%). In conclusion, in general, the antibiotics prescription on pneumonia patients at the RSPAU Dr. Suhardi Hardjolukito was rational. However, this rationality can still be improved.