Judul: On Determinant, Inverse, and Eigenvalues of  Circulant Matrix with Geometric Progression
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 dari matriks circulant dapat diisi dengan barisan bilangan apapun, salah satunya barisan bilangan geometri yang mana digunakan sebagai objek utama dari penelitian ini. Karya ilmiah ini bertujuan menurunkan formulasi sederhana dari nilai eigen, determinan, dan invers. Formulasi determinan diperoleh sebagai hasil kali semua elemen dari diagonal utama matriks diagonal setelah melakukan serangkaian operasi baris dasar dan kolom dasar. Sementara itu, formulasi invers diperoleh dari mengadaptasi langkah pada metode sebelumnya, dan kita peroleh C_(a,r,n)^(-1)=QD^(-1) P dengan P dan Q berturut-turut merupakan matriks yang diperoleh dari serangkaian operasi baris dasar dan kolom dasar tersebut yang dikenakan pada matriks indentitas I_n. Formulasi nilai eigen diperoleh dengan pendekatan konsep subgrup siklik dan geometri dari akar kesatuan ke-n., Circulant matrix is a square matrix composed by a right circular 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 in any sequence of numbers, such as a geometric progression sequence which we use as the main object of this research. The goal of this research is to derive simple formulations for the eigenvalues, determinant, and inverse. The determinant formulation obtained as the product of all elements in the main diagonal matrix after applying a series of elementary row operations and elementary column operations. Meanwhile, the inverse formulation is obtained from adapted the previous method, and we get C_(a,r,n)^(-1)=QD^(-1) P where P and Q are matrices of a series of elementary row and column operations performed previously applied to identity matrix I_n, respectively. Formulation of eigenvalues is obtained from approaching the concept of cyclic subgroup and geometry representation of n^throot of unity.
Keyword: circulant matrix, eigenvalues, determinant, inverse, geometric progression

Judul: Determinan dan Invers Matriks Circulant dengan Entri Barisan Aritmetika
Abstrak: Matriks circulant adalah matriks segi yang entrinya bergeser satu kolom ke kanan secara berurutan. Sehingga entri matriks circulant dapat dilihat dari satu kolom atau satu baris matriks tersebut. Salah satu sifat yang dimiliki matriks circulant, adalah bahwa inversnya juga bersifat circulant. Entri baris pertama suatu matriks circulant dapat diisi dengan berbagai bentuk barisan bilangan yang salah satunya adalah barisan aritmetika. Pada karya ilmiah ini diformulasikan secara eksplisit determinan dan invers matriks ... dst, Circulant matrix is a square matrix whose entry are shifted one column to the right sequentially. So the entry of a circulant matrix can be seen as one column or one row of the matrix. One of the property of a circulant matrix is the inverse also in the form of circulant. The first row of a circulant matrix can be filled in various type of sequence of numbers such as arithmetic sequence. In this research, the determinant and the inverse of a circulant matrix ... dst
Keyword: arithmetic sequence, circulant matrix, determinant, inverse

Judul: Amfibi sebagai satwa peliharaan: Ekspor, Impor dan Perdagangan Domestik
Abstrak: Indonesia has exported amphibian as frozen frog legs (listed since 1969 under fishery product) for consumption and live amphibian (listed since 1983 under reptilian class in forestry product) for pets. There are also live amphibian trading in local level i.e in markets and malls. This research aims to identify amphibian species exported and imported by investigating document from related administration and to identify amphibian species traded in domestic market by observation at Jakarta. Research is primarily conducted by processing quota data taken from Department of Forestry Republic of Indonesia database in Jakarta. Market observation was carried out in 18 locations (3 markets and 15 malls) in Jakarta. I carried out interview with trader and export business, which related to net trading live amphibians for pets. Respondent was choosen using snowball sampling manner. Name of species is written according to Iskandar & Coljin (2000). If there is no such record in the checklist (for example species are from outside Indonesia), then the species name is written according to Frost (2004). There are 56 species from eight families of wild amphibians that have pets quota between 1998-2008. Nineteen species was traded since 1983. The highest export quota is Litoria caerulea (21,37%). Allocation of highest catching quota is for BKSDA Jayapura (20,40%) and BKSDA Papua Barat (18,96%). Four species are included in IUCN Red List categories as vulnerable, among others are Limnonectes macrodon, Meristogenys jerboa, Nyctixalus margaritifer and Rhacophorus margaritifer. The number of amphibians that have export realization are 39 species. Two species of amphibian, Leptobrachium hasseltii and Rhacophorus margaritifer are amphibian species whose been known infected by chytrid fungus in the wild. The biggest species exported is Litoria caerulea (54,34%). Between 1983-1991, the biggest import amphibian for pets from Indonesia (66,13%) is Netherlands. Number of quota was relative stable in the last eight years, where as the number of export realization is more fluctuates. Amphibian species imported and re-exported between 1983-2008 come from Africa, South Asia, Malaysian, Archipelago Oceania, North America, Central America and South America. The number of pet amphibian species traded at domestic market is less than exported. Data showed that Indonesia imports 15 amphibian species between 1983-2008, However I found different species in the market that was unrecorded in the Ministry of Forestry data, which is the Fire Belly Salamander.
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