Judul: Determinan dan Invers Matriks Leslie Ganda dengan Formula Schur
Abstrak: Matriks Leslie ganda merupakan bentuk umum dari matriks Leslie, matriks companion, dan matriks companion ganda. Bentuk khusus komplemen Schur dapat digunakan pada formula Schur untuk mendapatkan rumus determinan dan invers. Tujuan dari penulisan karya ilmiah ini adalah mengkaji secara teoritis pembuktian formulasi determinan dan invers matriks Leslie ganda berdasarkan formula Schur. Pembuktian formula determinan dan invers matriks Leslie ganda dilakukan dengan mensubstitusi formula determinan dan invers matriks persegi menggunakan komplemen Schur., The doubly Leslie matrix is generalized of the Leslie matrix, the double companion matrix, and the companion matrix. The unique form of Schur complement can be used in Schur’s formula to obtain a formula of the determinant and inverse of doubly Leslie matrix. In this article, the proof of those formulation are discussed theoretically based on Schur’s formula. Proof of the determinant and inverse formulation perform by substitute the determinant and inverse of square matrix with Schur Complement.
Keyword: Komplemen Schur, Formula Schur, Determinan, Invers, Matriks Leslie Ganda

Judul: Determinan dan Invers Matriks Left Circulant dengan Entri Barisan Bilangan Jacobsthal-Lucas Menggunakan Metode OBD dan OKD.
Abstrak: Matriks persegi merupakan susunan bilangan dalam baris dan kolom membentuk persegi panjang yang pada umumnya digunakan dalam menyelesaikan persoalan matematis di kehidupan sehari-hari, terutama terkait dengan sistem persamaan linear. Metode untuk menentukan determinan dan invers matriks persegi dapat disederhanakan dalam bentuk suatu formulasi ketika struktur dan entrinya didefinisikan secara khusus. Maka dari itu, banyak penelitian dilakukan dalam mencari rumus sederhana dari determinan dan invers dengan beragam struktur dan entri khusus. Pada karya ilmiah ini, dicari rumus sederhana dari determinan dan invers matriks left circulant dengan entri barisan bilangan Jacobsthal-Lucas menggunakan metode operasi baris dan kolom dasar. Hasil penelitian menunjukkan bahwa terdapat sebuah formula umum yang dapat digunakan dalam mencari determinan dan invers matriks left circulant dengan entri barisan bilangan Jacobsthal-Lucas., A square matrix is an arrangement of numbers in rows and columns to form a square which is generally used in solving mathematical problems in daily life, especially those related to systems of linear equations. The method that is used to determine the determinant and inverse of a square matrix can be simplified in the form of a formulation when the structure and entries are specifically defined. Therefore, much research has been done to determine simple formulas of the determinant and inverse of square matrices with various special structure and entry. In this scientific work, we obtain simple formulas for the determinants and inverses of left circulant matrices with Jacobsthal-Lucas number entries using the elementary row and column operations method. The results showed that there is a general formula that can be used to find the determinant and inverse of left circulant matrices with the Jacobsthal-Lucas number entries.
Keyword: Jacobathal-Lucas, Matriks left circulant, Operasi baris dan kolom dasar, Jacobsthal-Lucas, left circulant matrix, elementary row and column operation

Judul: Biodegradasi Fenol Limbah Cair Industri Tekstil oleh Candida tropicalis
Abstrak: Large quantities of textile waste were produced during the operation of textile industry. It materials contained a high level of phenol compounds that results a serious environmental problem. One of microorganism that used phenol for carbon source is Candida tropicalis. In this studi, Candida tropicalis was used in an aerobic biodegradation process to reduce phenol concentration in order to optimum condition. Phenol concentration was determined by 4-aminoantipyrine method on 510 nm. Results showed that degradation rate is optimum at 30oC and a pH of 6. Phenol concentration in control not decrease during observation, meanwhile textile wastewater that inoculation Candida tropicalis decrease 30% for 6 hours with degradation rate 0.025 mg L-1 h-1. This degradation rate is lower than in pure phenol 12.5 mg L-1 h-1. The other results show that phenol disposed to degraded than to produce cell biomass that showing optical density of cell biomass is constant during observation.
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