Judul: Invers dan Sifat Similaritas pada Matriks Pascal
Abstrak: Penelitian ini mengkaji invers dan sifat similaritas pada tiga bentuk matriks Pascal antara lain matriks Pascal segitiga bawah, matriks Pascal segitiga atas, dan matriks Pascal simetrik yang diselesaikan menggunakan metode perkalian matriks. Matriks Pascal yang didefinisikan sebagai matriks dengan elemen-elemen yang merupakan koefisien dari ekspansi binomial menjadi objek utama kajian. Matriks Pascal dikenal memiliki sifat unik yaitu hasil perkalian matriks Pascal segitiga bawah B_n dengan matriks Pascal segitiga atas A_n menghasilkan matriks Pascal simetrik S_n. Dengan demikian, invers dari matriks Pascal simetrik dapat ditemukan menggunakan hubungan invers dari matriks Pascal segitiga atas dan segitiga bawah, yaitu {S_n}^{-1} = {(B_nA_n)}^{-1} = {A_n}^{-1} {B_n}^{-1}. Sifat similaritas antara matriks Pascal simetrik dengan inversnya dapat ditunjukkan dengan menerapkan konsep kesimilaran pada matriks Pascal segitiga atas dan matriks Pascal segitiga bawah. Penelitian ini memberikan kontribusi dalam pemahaman lebih lanjut tentang sifat-sifat matriks Pascal dalam kajian teori matriks.
Keyword: direct multiplication, invers, matriks Pascal, similar

Judul: Matriks Pascal dan Sifat-Sifatnya
Abstrak: Pascal matrices are matrices that their elements contain binomial coefficients. Pascal matrices can be built into three different types: symmetric Pascal matrix lower triangular Pascal matrix and upper triangular Pascal matrix This study aims to determine the characteristics of the Pascal matrices. The proof of characteristics shows that multiplication of a lower triangular Pascal matrix with an upper triangular Pascal matrix always yields symmetric Pascal matrix through three methods: matrix multiplication, Gaussian elimination, and equality of functions. In this study, matrix multiplication is the most effective method of proof. The proof of also shows that each of and has the same determinant value, that is one . Another characteristics of the Pascal matrix is that transpose of a lower triangular Pascal matrix is an upper triangular Pascal matrix and vice versa
Keyword: upper triangular Pascal matrix., lower triangular Pascal matrix, Pascal matrix

Judul: Growth, Concentration Chlorophyll-a, and Structure of Macroalgae Gracilaria edulis in the Culture Media Containing Copper
Abstrak: The physiological responses (specific growth rate, concentration of chlorophyll-a, morphological and anatomical structure of the vegetative cells) of the marine macroalga Gracilaria edulis at the different concentrations of copper (0.01 as control, 0.04, 0.06 and 0,5 ppm) delivered continuously for 28 days under controlled laboratory conditions were investigated. Result showed that the degree of copper toxicity depends on both factor the concentration and exposure time. Copper concentration and day of exposure decreased significantly the specific growth rate (SGR) of the Gracilaria edulis but only 0,5 ppm Cu decreased the chlorophyll-a content when compared to control. Of the various physiological end points measured, growth proved to be the most sensitive response than chlorophyll-a with reductions in specific growth rate (SGR). The reason for this could be related to a greater sensitivity of the enzymes involved in growth than those related to chlorophyll-a or a greater energy needs to maintain cellular integrity and metabolic processes under sublethal Cu stress. In all cases, the main effect on vegetative cells were structure changes in cortex and subcortex cells, compared to control, macroalgae exposed to copper showed depigmentation and blending in the lateral branches, heavy staining of the cell wall and severe damage of cell membrane, while the mucilage and the cell walls was densely fibrillar, thick and heavily stained, the cortex cell was clearly vacuolated, the presence of endophytic on the cell wall and endophytic spores in the mucilage. The presence vacuoles should be related to a metal immobilization mechanism, minimizing the Cu toxicity for cells. The epiphytic bacteria can act as a biofilter diminishing the availability of Cu for macroalgae accumulation.
Keyword: