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: Uji kinerja promoter gen LEAFY dan AGAMOUS tanaman kakao (Theobroma cacao L.) pada tanaman tembakau (Nicotiana tabacum L.)
Abstrak: Performance of cocoa’s (Theobroma cacao L.) gene promoters, TcLFY and TcAG, in a tobacco plant (Nicotiana tabacum L.) used as a plant model has been tested. The two promoters were introduced into the tobacco plant cells using a modified leaf discs method employing Agrobacterium tumifaciens AGL0. The transformed tobacco plant cells were then regenerated and their morphology were observed periodically. The tobacco plants harbouring the gene promoter TcLFY, during regeneration, showed a leaf morphology similar to that of the positive control. However, the growth rate of tobacco plants inserted with promoter TcLFY was faster compared to that of the positive control. Tobacco plants harbouring gene promoter TcAG, during regeneration, showed imperfect leaf morphology. The growth rate of these tobacco plants was slower than that of the positive control and of the tobacco plants inserted harbouring gene promoter TcLFY. These results indicated that the introduced promoters affect the morphology of the tobacco plants. In order to further confirm the presence of the GFP gene and activation of TcLFY: GFP and TcAG: GFP, a molecular verification test was carried out. Variation of sucrose concentration in the media was made to examine the effect of sucrose on the activity promoters TcAG and TcLFY in tobacco plants. The sucrose concentration tested were 0%, 0,5% and 4% followed by observation on the 3rd and 7th day of cultivation. At 0% sucrose concentration the tobacco plants harbouring promoter TcLFY showed yellowish leaf, while those cultivated in the media with sucrose concentration of 0.5% and 4% grew well and normal. This indicated that sucrose affects the activity of the promoter TcLFY in tobacco plants. Tobacco plants inserted with promoter TcAG did not show significant morphological changes when grown in a medium of 0%, 0,5% or 4% sucrose concentration. This indicated that addition of sucrose does not significantly affect the induction of expression of the AG gene and the activation of the promoter TcAG.
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