Judul: Formulasi Eksplisit untuk Determinan, Invers, dan Nilai Eigen Matriks Skew Circulant dengan Entri Barisan Fibonacci Berganti Tanda
Abstrak: Matriks skew circulant memiliki banyak terapan di berbagai bidang, seperti rekayasa jaringan. Determinan, invers, dan nilai eigennya sering dimanfaatkan dalam penerapannya. Tujuan penelitian ini adalah merumuskan determinan, invers, dan nilai eigen matriks skew circulant dengan entri barisan Fibonacci berganti tanda, mengonstruksi algoritmenya, dan menunjukkan efisiensi waktu komputasinya. Dalam penelitian ini, determinan dan invers dirumuskan secara sederhana menggunakan operasi baris dan kolom dasar dengan mengubah matriksnya menjadi matriks segitiga bawah dan diagonal yang ekuivalen, dan hasilnya dapat dituliskan hanya dalam satu teorema. Sedangkan, nilai eigen dirumuskan dengan menyederhanakan rumus umum nilai eigen matriks skew circulant yang memanfaatkan keistimewaan barisan Fibonacci berganti tanda dan sifat-sifat grup siklik. Kemudian, algoritme untuk semua formulasi tersebut dibuat. Secara komputasi, semua algoritme tersebut dapat bekerja dengan sangat cepat dan efisien., The skew circulant matrix is a type of matrix that has many applications in various fields, such as networks engineering. The determinant, inverse, and eigenvalues are often used in the application. The purpose of this research is to formulate the determinant, inverse, and eigenvalues of the skew circulant matrix with alternating Fibonacci sequence entries, construct the algorithms, and show the efficiency of computing time. In this research, the determinant and inverse are formulated simply using elementary row and column operations by changing the matrix into equivalent lower triangular and diagonal matrix, and the results can be written in just one theorem. Meanwhile, the eigenvalues are formulated by simplifying the general formula for the eigenvalues of the skew circulant matrix which exploits the specialty of the alternating Fibonacci sequence and the properties of cyclic groups. Then, algorithms for all these formulations are constructed. Computationally, all of these algorithms can work very fast and efficent.
Keyword: alternating Fibonacci numbers, determinant, eigenvalues, inverse, skew circulant matrix

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: 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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