Judul: Dekomposisi Nilai Singular pada Matriks Kompleks Toeplitz Bidiagonal Atas.
Abstrak: Dekomposisi nilai singular merupakan salah satu metode faktorisasi matriks berdasarkan nilai singular dan vektor singularnya. Dekomposisi nilai singular bertujuan untuk memfaktorisasi suatu matriks �������� berukuran �������� × �������� menjadi bentuk �������������������������������� dengan �������� merupakan matriks berukuran �������� × �������� , �������� merupakan matriks berukuran �������� × �������� dan �������� merupakan matriks berukuran �������� × ��������. Pada karya ilmiah ini, dibahas dekomposisi nilai singular pada matriks kompleks Toeplitz bidiagonal atas berukuran �������� × (�������� + 1).
Keyword: dekomposisi nilai singular, matriks Toeplitz, matriks bidiagonal atas, matriks kompleks

Judul: Invers Drazin dari Matriks Toeplitz Singular
Abstrak: Matriks Toeplitz adalah matriks yang setiap unsur pada diagonal utama bernilai sama dan setiap unsur pada subdiagonal yang bersesuaian dengan diagonal utama juga bernilai sama. Matriks singular adalah matriks yang tidak bisa ditentukan inversnya. Akan tetapi, dapat diupayakan untuk ditentukan inversnya menggunakan invers matriks yang diperumum. Invers Drazin merupakan salah satu jenis invers matriks yang diperumum. Pada karya ilmiah ini ditentukan invers Drazin dari matriks Toeplitz singular dengan menggunakan metode Leverrier Faddeev. Kemudian, ditentukan invers Drazin dari matriks Toeplitz singular yang direpresentasikan sebagai penjumlahan segitiga bawah dan segitiga atas matriks Toeplitz berdasar pada teorema Gohberg dan Semencul., Toeplitz matrix is a matrix in with element on the main diagonal has the same value and on the subdiagonal corresponding to the main diagonal also has the same value. Singular matrix is a matrix that has no inverse. However, it can be attempted to determine the inverse using a generalized inverse matrix. Inverse Drazin is a type of generalized matrix inverse. This paper discussed the inverse Drazin for a singular Toeplitz matrix using the Leverrier Faddeev method. Then, the Drazin inverse of the singular Toeplitz matrix which is represented as a sum of products of lower and upper triangular Toeplitz matrix based on Gohberg and Semencul theorem.
Keyword: inverse Drazine, singular Toeplitz matrix

Judul: Macroalgae development as feeding stimulants for the adult sea urchin (Tripneustes gratilla Linnaeus 1758)
Abstrak: Development of artificial feed for somatic growth and gonad quality is one of the focus of research on sea urchin aquaculture activities. Palatability is important factor when developing artificial feed for aquaculture diets. This study investigated the effects of macroalgae (Sargassum polycystum, Gracilaria lichenoides, and Ulva reticulata) as feeding stimulants to artificial diets consumption and gonad profile for the adult sea urchin Tripneustes gratilla, by three feeding trials. Previously starved T. gratilla were held in replicated (3X) 50 L aquaria with recirculation water system (in the first feeding trial) and flow through water system (in the second and third feeding trial). In the first feeding trial, preference of T. gratilla for dried macroalgae was assessed in choice feeding experiment. T. gratilla displayed significant preference for the agar containing dried U. reticulata at 20% agar weight over nine other diets treatment when they were offered simultaneously. Total protein, energy and the ratio of protein to energy in the dried macroalgae had no correlation on agar consumption by T. gratilla. Three artificial diets were made by incorporating one of each of these dried macroalgae at 5% feed weight used in the second feeding trial. Although no significant difference in artificial diets containing dried macroalgae, urchins fed diets containing dried macroalgae consumed more than basal diet when they were offered as single diet. These results indicate that dried macroalgae added to the artificial diets act as feeding stimulants and increasing the acceptability of artificial sea urchin diets. The third feeding trial used dried U. reticulata as feeding stimulant to artificial diet. Data suggest that artificial diet containing 10% dried U. reticulata boosting feed consumption and significantly increasing nutrient accumulation, gonad index, egg diameter and fix gonad color.
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