Judul: Determinant and Inverse Circulant Matrix with Pell Numbers Entries
Abstrak: Matriks circulant adalah matriks yang entrinya bergeser satu kolom ke kanan secara berurutan, sehingga untuk mengetahui seluruh entrinya dapat dilihat hanya dari kolom pertama. Salah satu sifat yang dimiliki matriks circulant adalah bahwa inversnya juga berupa circulant. Entri-entri matriks circulant dapat menggunakan entri berbagai bilangan, salah satunya adalah bilangan Pell. Pada karya ilmiah ini, determinan dan invers matriks circulant dengan entri bilangan Pell diformulasikan. Pembuktian formulasi determinan matriks circulant dengan entri bilangan Pell dilakukan berdasarkan serangkaian operasi baris dasar sehingga diperoleh mariks segitiga atas. Sedangkan pembuktian formulasi inversnya berlandaskan sifat-sifat ekuivalensi dari hasil kombinasi operasi baris dasar atau operasi kolom dasar., A circulant matrix is a matrix whose entries are shifted one column to the right in sequence, so to find out all the entries can be seen only from the first column. One of the properties of a circulant matrix is that its inverse is also a circulant. Circulant matrix entries can use entries of various numbers, one of which is Pell's number. In this scientific paper, the determinant and the inverse of the circulant matrix with Pell number entries formulated. Proof of the determinant formulation matrix circulant with Pell number entries performed based on a series of base row operations so that the upper triangular matrix is obtained. While the proof of the inverse formulation based on the equivalence properties of the result combination of base row operations or base column operations.
Keyword: circulant matrices, determinant, inverse,, Pell numbers

Judul: Determinan dan Invers Matriks Skew Circulant dengan Entri Bilangan Pell
Abstrak: Matriks skew circulant adalah matriks persegi yang entrinya bergeser satu kolom ke kanan secara berurutan dengan seluruh entri sebelum diagonal utama akan bernilai negatif. Entri-entri dari matriks skew circulant dapat diisi dengan entri berbagai bilangan, salah satunya yaitu bilangan Pell. Pada karya ilmiah ini, determinan dan invers matriks skew circulant dengan entri bilangan Pell diformulasikan. Pembuktian formulasi determinan matriks skew circulant dengan entri bilangan Pell dilakukan berdasarkan serangkaian operasi baris dasar sehingga diperoleh matriks segitiga atas. Sedangkan pembuktian formulasi pada inversnya berlandaskan sifat-sifat ekuivalensi dari hasil kombinasi operasi baris dasar dan operasi kolom dasar., Skew circulant matrix is a square matrix whose entries are shifted one column to the right and all entries before the main diagonal will be negative.The entries of the circulant skew matrix can be filled in various numbers, one of which is the Pell number. In this scientific work, the determinant and inverse of skew circulant matrices with the entry of the Pell number are formulated. The substantiation of the determinant formulation of the circulant skew matrix with the entry of the Pell numbers is carried out on the basis of a series of elementary row operations so that an upper triangular matrix is obtained. Meanwhile, the proof of the formulation in the inverse is based on the equivalence proprties of the results of a combination of elementary row and column operations.
Keyword: circulant matrix, circulant skew matrix, determinant, inverse, Pell numbers

Judul: Development of ready-to-drink white tea shot.
Abstrak: White tea leaf has been shown to possess physiological activities and has catechin which is the most abundant antioxidant compound found. This study was conducted to develop white tea shot formulated with white tea extract (WTE), ascorbic acid (AA), and sucrose (SC) in order to get high stability of catechin in the product. The first part of the study was conducted to choose best formula of white tea shot. The amount of water was set at 50 ml while WTE was set at 0.4% water basis. AA and SC amount were varied at 0.02, 0.05, 0.10% for AA and 3.0 and 6.0% for SC. The formula chosen was consists of 50 ml water, 0.4 % WTE, 0.10% AA, and 6.0% of SC. The decision was based on the rating hedonic test and short time storage catechin stability analysis of six formulation which the chosen formula revealed the least catechin lost and acceptable overall product likeness. The study also revealed that addition of AA is significant to lower catechin loss (P<0.05) while addition of SC did not reveal any effect (P>0.05). Physical, chemical, and microbiological characteristic was also observed in this study.
Keyword: Catechin, product development, white tea