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: Adsorption Studies of Fe(III) Ion on Glutaraldehyde Cross-linked Chitosan and Its Application to Vetiver Oil Purification.
Abstrak: Adsorption of Fe(III) ions by glutaraldehyde cross-linked chitosan (Chitosan-GA) was studied by the batch method. The objectives of this research are to know optimum adsorption condition of Fe(III) ions by Chitosan-GA, then to study about isothermal adsorption, kinetics, and influence of Cu(II) ion for adsorption of Fe(III) ion and its application to vetiver oil. Optimum conditions are finding out by response surface Box Behnken method. The adsorption isotherm models that were studied in this research are Langmuir and Freundlich model. Percent adsorption of Fe(III) ion by glutaraldehyde cross-linked chitosan (Chitosan-GA) is about 91,8439% in optimum conditions : adsorbent weight 0,75 gram, temperature 25 o The existence of Cu(II) ions can decrease percent adsorption of Fe(III) ion by chitosan-GA. Percent adsorption of Fe(III) ion by chitosan-GA is higher than adsorption of Cu(II) ion in all conditions. Percent adsorption of Fe(III) and Cu(II) ion by chitosan-GA in vetiver oil is lower than other condition (solution of FeC, time contact 360 minutes. Adsorption process of Fe(III) ion by chitosan-GA is fit to Freundlich and second-order models. Adsorption process is exothermic and not spontaneous. Percent desorption of chitosan-GA-Fe by 0.1 M HCl is about 9.0605% and achieved in 150 minutes. 3+ and Cu2+ ion with its concentration ratio 1:1). Vetiver oil color was changed from dark brown to red brown after adsorption by chitosan- GA.
Keyword: cross-linked chitosan, glutaraldehyde, adsorption, Fe(III) ion