Judul: Critical Points and Eigenvalues of Massive Particle Dynamics in Kerr 4+1 Dimensional Geometry
Abstrak: Pada penelitian sebelumnya telah dibentuk persamaan metrik dari geometri Kerr 4+1 dimensi. Penelitian ini memaparkan karakteristik dari geometri tersebut dengan menggunakan persamaan geodesik dan nilai eigen pada komponen dan . Persamaan geodesik memberikan suatu persamaan gerak yang menggambarkan kondisi partikel bermassa di sekitar geometri Kerr 4+1 dimensi pada kondisi karena objek bergerak pada bidang ekuator. Titik kritis didapatkan dengan saling mensubstitusi ekspresi komponen dan dengan bantuan software Wolfram Mathematica 9.0. Hasil nilai eigen yang didapat terdiri dari bilangan real dan imajiner yang berupa positif maupun negatif. Sehingga karakteristik titik kritis tersebut berupa unstable point dan unstable sadle tergantung dengan nilai parameter m, M, a, p, dan q yang disubstitusi., In previous research, only the metric equation of the 4+1 dimensional Kerr geometry has been established. So in this paper describes the characteristics of the geometry using geodesic equation and the eigenvalues of and components. The geodesic equation provides an motion equation that describes condition of the massive particle around the 4+1 dimensional Kerr geometry under the condition because the object moves on the equatorial plane. Critical points are obtained by substituting the expressions of of and components with the help of Wolfram Mathematica 9.0 software. The eigenvalue results obtained consists of real and imaginary numbers that are both positive and negative. So that the characteristics of the critical point are unstable point and unstable saddle depending on the substituted parameter values of m, M, a, p, and q.
Keyword: Nilai Eigen, Titik Kritis, Geometri Kerr 4+1 Dimensi, Partikel Bermassa

Judul: Gerak Partikel Bermassa dan Tidak Bermassa di Sekitar Black Hole dalam Ruang-waktu Kerr 4+1 Dimensi
Abstrak: Metrik dari ruang-waktu Kerr 4+1 dimensi telah dikonstruksi di dalam penelitian sebelumnya, namun karakteristik dari ruang-waktu tersebut belum diuraikan lebih lanjut. Penelitian ini menguraikan karakteristik tersebut dengan merumuskan radius singularitas dan persamaan geodesiknya agar dapat memvisualisasikan gerak partikel bermassa dan tidak bermassa di sekitar black hole. Radius singularitas dari metrik Kerr 4+1 dimensi dapat dihitung dari komponen dr^2 dan didapatkan hasil r=√(2M-a^2). Radius ini menggambarkan batas dari black hole atau dikenal sebagai event horizon. Radius event horizon lain juga ditemukan sebagai kasus khusus untuk partikel tidak bermassa dan didapatkan hasil r=√((ah/k)-a^2). Dari persamaan geodesik, hasil yang didapatkan berupa grafik-grafik potensial efektif dan visualisasi lintasan gerak partikel bermassa dan tidak bermassa yang berupa lintasan orbit tak terikat. Perbedaan bentuk setiap orbit lintasan partikel bermassa dan tidak bermassa ini diindikasikan sebagai konsekuensi dari dimensi ruang ekstra yang direpresentasikan dengan koordinat α., The metric of the 4+1 dimensional Kerr spacetime has been constructed in the previous research, however, the characteristics of this spacetime have not been elaborated furthermore. This research elaborates the characteristics by formulating the radius of singularity and geodesic equation for visualizing the massive and massless particle motion near the black hole. The radius of the singularity of the 4+1 dimensional Kerr metric can be obtained by dr^2-component and its result is r=√(2M-a^2). This radius describes the boundary of the black hole recognized as the event horizon. The other radius of event horizon also has been found as a special case for massless particle and its result is r=√((ah/k)-a^2). From the geodesic equation, the obtained results are in the form of graphs of the effective potential and visualization of the trajectories of massive and massless particle motion in the unbounded orbit. The difference between each trajectory of massive and massless particle motion is indicated as a consequence of the extra dimension represented by the α-coordinate.
Keyword: extra dimension, geodesic equation, Kerr spacetime, massive and massless particle, radius of singularity

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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