Judul: Nilai Eigen, Determinan dan Norm Matriks Circulant dengan Entri Bilangan k-Fibonacci
Abstrak: Matriks circulant adalah matriks yang entrinya bergeser satu kolom ke kanan secara berurutan pada baris berikutnya. Entri–entri matriks circulant dapat diisi dengan berbagai barisan bilangan, salah satunya adalah bilangan k–Fibonacci. Berdasarkan definisinya, pada karya ilmiah ini, nilai eigen, determinan dan norm matriks circulant dengan entri bilangan k–Fibonacci diformulasikan secara eksplisit. Kemudian, contoh kalkulasi berdasarkan rumusan tersebut diberikan sebagai ilustrasi., A circulant matrix is a matrix whose entries are shifted one column to the right in succession in the next row. Circulant matrix entries can be filled in various sequence of numbers, one of which is k–Fibonacci number. In this scientific paper, based on the definition, the eigenvalues, determinants and norms of the circulant matrix with the entries of k–Fibonacci numbers are formulated explicitly. Then, examples of the calculation of the obtained formulas are given as illustrations.
Keyword: circulant matrix, determinants, eigen values, matrix norms, k-Fibonacci number

Judul: Determinants and Norm of Circulant and Left Circulant Matrix with Entries of Circulant Numbers
Abstrak: Matriks circulant adalah suatu matriks berukuran n×n yang dibentuk dari n vektor dan setiap entri dari baris sebelumnya bergeser satu posisi ke kanan pada baris berikutnya. Pada karya ilmiah ini ditentukan determinan dan norm dari matriks circulant dan circulant kiri dengan entri bilangan Tribonacci. Dari hasil pembuktian diperoleh bahwa determinan dari matriks circulant merupakan hasil perkalian dari semua nilai eigen pada matriks tersebut, norm jumlah kolom maksimum adalah jumlah maksimum dari jumlah kolom absolut, norm jumlah baris maksimum adalah jumlah maksimum dari jumlah baris absolut, dan Frobenius norm adalah akar kuadrat dari jumlah kuadrat absolut setiap elemen matriks circulant. Kemudian diberikan penghitungan determinan, norm jumlah kolom maksimum, norm jumlah baris maksimum, dan Frobenius norm dengan entri bilangan Tribonacci untuk matriks circulant berukuran 2×2 dan 3×3., Circulant matrix is an n × n matrix formed from n vectors and each row is a cyclic shift of the row above to the right. In this scientific work we determine the determinants and norms of the circulant and left circulant matrix involving Tribonacci numbers. From the results of the proof it is obtained that the determinant of the circulant matrix is product of all eigenvalue in the matrix, the maximum coloumn sum matrix norm is the maximum number of absolute column sums, the maximum row sum matrix norm is the maximum number of absolute row sums, and the Frobenius norm is the square root of the absolute squared number of each circulant matrix element. Then given the calculation from the determinant, the maximum coloumn sum matrix norm, the maximum row sum matrix norm, and the Frobenius norm involving Tribonacci numbers for 2×2 and 3×3 circulant matrix.
Keyword: Tribonacci numbers, Determinants, Circulant Matrices, Left Circulant Matrices, The Frobenius Norms

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