Judul: On Determinant and Inverse of Circulant Matrix with Fibonacci Numbers
Abstrak: Matriks Circulant adalah matriks segi yang disusun oleh operasi pergeseran sirkular kanan, yaitu pergeseran entri terakhir ke posisi utama disertai pergeseran semua entri lainnya ke posisi berikutnya. Entri-entri dari matriks circulant dapat diisi dengan berbagai macam barisan bilangan, salah satunya bilangan Fibonacci. Pada karya ilmiah ini diformulasikan determinan dan invers matriks circulant dengan entri bilangan Fibonacci. Pembuktian formulasi determinan diperoleh dengan menggunakan operasi baris dasar sehingga ekuivalen ke matriks segitiga atas, dan nilai determinannya adalah hasil kali semua unsur diagonal matriks segitiga atas. Sedangkan formulasi invers diperoleh dengan mengadaptasi langkah pada metode sebelumnya, sehingga diperoleh A_(n)^(-1)=QD^(-1)P dengan P dan Q berturut-turut merupakan matriks yang diperoleh dari serangkaian operasi baris dasar dan operasi kolom dasar tersebut yang dikenakan pada matriks identitas I_(n)., Circulant matrix is a square matrix composed by a right circulant shift operation, namely the shift of the last entry to the first position followed by the shift of all other entries to the next position. The entry of a circulant matrix can be filled by any sequences of numbers, one of which is the Fibonacci numbers sequence. In this research, the determinants and the inverses of circulant matrix are formulated with Fibonacci numbers of entries. The proof of the determinant formulation is obtained using elementary row operation that it is equivalent to upper triangular matrix, and the determinant value is the product of all the diagonal. While the inverse formulation is obtained by adapting the previous method, then we obtain A_(n)^(-1)=QD^(-1)P where P and Q are matrices of a series of elementary row operation and elementary column operation performed previously applied to identity matrix I_(n).
Keyword: circulant matrix, determinant, inverse, fibonacci number

Judul: Determinan dan Invers Matriks Skew Left Circulant dengan Entri  Bilangan Fibonacci
Abstrak: Matriks skew left circulant adalah suatu matriks persegi dengan entri baris bergeser satu kolom secara berurutan ke kiri dan semua entri yang berada dibawah diagonal sekunder akan bernilai negatif, sehingga untuk mengetahui seluruh matriks skew left circulant dapat dilihat dari salah satu baris dari matriks tersebut. Entri-entri dari skew left circulant dapat menggunakan entri dengan berbagai barisan bilangan, salah satunya adalah dengan barisan bilangan Fibonacci. Pada karya ilmiah ini diformulasikan determinan dan invers matriks skew left circulant dengan entri bilangan Fibonacci. Pembuktian Formulasi determinan matriks skew left circulant diperoleh dari penerapan serangkaian operasi baris dasar pada matriks skew circulant sehingga diperoleh matriks segitiga atas, dilanjutkan mengalikan dengan determinan matriks Gamma. Sedangkan, formulasi inversnya diperoleh dengan membuat matriks-matriks dari matriks skew circulant representasi dari hasil serangkaian operasi baris dasar dan operasi kolom dasar, dilanjutkan dengan mengalikan dengan invers matriks Gamma., The left circulant skew matrix is a square matrix with row entries shifted one column sequentially to the left and all entries under the secondary diagonal will be negative, so to find out the entire circulant skew left matrix can be seen just from the first row of the matrix. Entries from the skew left circulant can be filled in various number sequences, one of which is the Fibonacci number sequence. In this scientific work, the determinants and inverses of the skew left circulant matrix are formulated with Fibonacci number entries. Proof The formulation of the skew left circulant matrix determinant is obtained from applying a series of basic row operations to the circulant skew matrix so that an upper triangular matrix is obtained, followed by multiplying it with the Gamma matrix determinant. Meanwhile, the inverse formulation is obtained by making matrices from a circulant skew matrix representing the results of a series of basic row or column operations, followed by multiplying by the inverse Gamma matrix.
Keyword: Fibonacci number, determinant, inverse, skew left circulant matrix

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