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 Skew Circulant dengan Entri Bilangan Pell-Lucas
Abstrak: Matriks skew circulant adalah matriks persegi yang entrinya bergeser satu kolom secara berurutan ke kanan dan semua entri yang berada di bawah diagonal utama akan bernilai negatif, sehingga untuk mengetahui seluruh entri matriks skew circulant dapat dilihat dari salah satu baris dari matriks tersebut. Entri-entri pada matriks skew circulant dapat menggunakan entri dengan berbagai barisan bilangan, salah satunya adalah bilangan Pell-Lucas. Pada karya ilmiah ini diformulasikan determinan dan invers matriks skew circulant dengan entri bilangan Pell-Lucas. Pembuktian formulasi determinan matriks skew circulant dengan entri bilangan Pell-Lucas diperoleh dari penerapan serangkaian operasi baris dasar sehingga diperoleh matriks segitiga atas. Sedangkan, formulasi inversnya diperoleh dengan membuat matriks-matriks representasi dari hasil serangkaian operasi baris dasar dan operasi kolom dasar., Skew circulant matrix is a square matrix whose entries are shifted one column sequentially to the right and all entries below the main diagonal will be negative, so to find out all the entries of the skew circulant matrix can be seen from any row of the matrix. The entries in the skew circulant matrix can be filled in various sequences of numbers such as Pell-Lucas numbers. In this research, the determinant and inverse of the skew circulant matrix with Pell-Lucas numbers entries are formulated. The proof of the determinant formulation of the skew circulant matrix with Pell-Lucas numbers entries is explained by applying a series of elementary row operations to get the upper triangular matrix. While the proof of the inverse formulation is explained by constructing representational matrices of the results of the series of elementary row operations and elementary column operations.
Keyword: determinant, inverse, Pell-Lucas number, skew circulant matrix

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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