Judul: The Determinant Formulation of Circulant Matrix with entry of the 2nd Order Recurrence Relation Number Formasi Jangkar
Abstrak: Matriks circulant merupakan matriks segi yang entri-entri pada setiap barisnya sama dengan entri-entri pada baris sebelumnya dan bergeser posisi ke kanan. Entri-entri dari matriks circulant dapat diisi dengan berbagai entri, salah satunya adalah bilangan-bilangan yang membentuk suatu barisan bilangan. Barisan bilangan dapat dibuat dengan menggunakan relasi rekurensi orde-2. Pada karya ilmiah ini, relasi rekurensi tersebut didefinisikan sebagai \[J_{n}=2J_{n−1}+3J_{n−2}\] dengan syarat awal \[J_0=3,J_1=1,n≥2,\] dan membentuk barisan bilangan yang dinamakan Formasi Jangkar. Kemudian, determinan matriks circulant dengan entri barisan bilangan Formasi Jangkar dapat dirumuskan secara eksplisit menggunakan sifat-sifat determinan sederhana yang berkaitan dengan operasi baris dasar., The circulant matrix is a faceted matrix where the entries in each row are the same as the entries in the previous row and shift position to the right. The entries of the circulant matrix can be filled with various entries, one of which is the numbers that form a sequence of numbers. Sequences of numbers can be constructed by a recurrence relation of order-2. In this scientific work, the recurrence relation is defined as \[J_{n}=2J_{n−1}+3J_{n−2}\] with initial condition \[J_0=3,J_1=1,n≥2,\] and form a sequence of numbers called Formasi Jangkar. Then, the determinant of the circulant matrix with entry the Formasi Jangkar can be formulated eksplicitly using the properties of determinants based on elementary row operations.
Keyword: bilangan Formasi Jangkar, determinan, matriks circulant, operasi baris  dasar, Relasi rekurensi, circulant matrix, elementary row operation, Formasi  Jangkar number, recurrence relation, determinant

Judul: Perhitungan Determinan dan Invers Matriks Circulant dengan Entri Jacobsthal Numbers Menggunakan Operasi Baris atau Kolom Dasar
Abstrak: Matriks circulant merupakan matriks segi berukuran n × n dengan setiap diagonal mempunyai elemen yang sama serta elemen matriks pada baris sebelumnya digeser satu posisi ke kanan pada baris berikutnya. Salah satu sifat yang dimiliki matriks circulant, yaitu inversnya juga berupa circulant. Entri-entri dari matriks circulant dapat menggunakan entri dengan berbagai bilangan, salah satunya adalah Jacobsthal Number. Pada karya ilmiah ini ditentukan perhitungan determinan dan invers matriks circulant dengan entri Jacobsthal Numbers. Pembuktian formulasi determinan matriks circulant dengan entri Jacobsthal Numbers didapatkan dari serangkaian operasi baris dasar sehingga terbentuk matriks segitiga atas, sedangkan formulasi invers matriks didapatkan berdasarkan sifat-sifat ekuivalensi matriks dari hasil serangkaian operasi baris dan kolom dasar sehingga terbentuk matriks diagonal. Matrix circulant is a n × n triangular matrix with the identical elements on each diagonal and the elements from the previous row relocated one place to the right in the next row. The circulant's entries can contain a variety of numbers, one of which is the Jacobsthal numbers. In this scientific work, it is determined the calculation of the determinant and the inverse of the circulant with the entry of Jacobsthal Numbers. The determinant formulation is obtained from a series of elementary row operations to get an upper triangular matrix, and the inverse formulation is based on the matrix equivalence properties of a series of elementary row and column operations to get a diagonal matrix.
Keyword: elementary row or column operation, circulant matrices, determinant, invers, jacobsthal numbers

Judul: Antioxidant activity of Pluchea indica Less leaves methanolic extract and its fraction and their capacity to inhibit cooked duck meat warmed over flavor
Abstrak: Pluchea indica Less is a herb commonly used as food and traditional medicine. Its leaves have antioxidant activity due to its various phytochemical compounds. The antioxidant activity of methanolic extract of Pluchea leaves to prevent cooked duck meat warmed over flavor (WOF) is still under explored. The objective of this study was to investigate the antioxidant activity of methanolic extract of Pluchea leaves and its fraction (ethyl acetate, water, and n-butanol) by using different analysis approaches test systems (2,2-phenyl-1-picrylhydrazyl (DPPH), superoxide and hydroxyl radical-scavenging activities, hydrogen peroxide scavenging activity, ferric reducing power, iron chelating capacity, and -carotene-linoleic acid bleaching assay). Furthermore, their application as inhibitor to cooked duck meat WOF has also been conducted. Antioxidant activity of Pluchea leaves was obtained by dividing its leaves into 3 groups, i.e 1-3, 4-6 and >6. The methanolic extract of those groups contained phytochemical compounds, such as tannin, sterol, phenol hydroquinone, and flavonoid. The methanolic extract of 1-6 Pluchea leaves (EMB) had more potential source of DPPH free radical scavenging activity. In addition, this extract was fractionated by various solvents with different polarity, such as ethyl acetate, n-butanol, and water. The result showed that ethyl acetate fraction (FEA) had higher antioxidant activity than EMB and the other fraction, but its activity was lower than methanolic extract of green tea (EMT). The antioxidant activity assay of EMB and FEA was compared to BHT and -tocopherol by using different analysis approaches test systems. It showed that FEA had superoxide radical-scavenging activity, iron chelating capacity and ferric reducing power, while EMB had superoxide radical-scavenging activity, ferric reducing power and -carotene–linoleic acid bleaching assay. FEA at 250 ppm concentration was more effective to prevent the formation of cooked duck meat WOF than FEA at 600 ppm concentration and EMB. This fraction significantly inhibited the oxidation of PUFA (linoleic and arachidonic acids) and the formation of malondialdehide (MDA) and hexanal content. In comparison with FEA, EMB showed less potent antioxidant activity. However, the volatile compounds in EMB extract had an effect in improving sensory properties of duck meat, mainly by increased hedonic-preference scores on acceptance sensory test and also suppressed green and grassy aromatic intensities of duck meat during cooking and storage.
Keyword: Asteraceae