Judul: Improvement of mangosteen (Garcinia mangostana L.) seedling root system through agrobacterium rhizogeneses inoculation
Abstrak: Mangosteen is known as a slow growing plant, this is due to the root that is fragile, sensitive to the environmental condition and easly disturbed. Great care ia therefore required during the transplanting of seedling, which form a long taproot with few laterals. Many writers note an apparent absence of root hairs at all stage of growth. The use of Agrobacterium rhizogenes may improve root system of mangosteen.
Keyword: Hormone, Root hairs, Strain, Bacterium, T-DNA, Eksplan, In Vitro

Judul: Engineering technology of micrografting and microcutting in mangosteen (Garcinia mangostana).
Abstrak: The purpose of this study was to assemble propagation technology in mangosteen plant using micrografting and microcutting. This study consisted of four experimental steps, 1) in vitro bud induction technology development from bud explants of mangosteen seedling shoot, 2) physiology and anatomy studies of micrografting in mangosteen, 3) in vitro medium manipulation on mangosteen microcutting; 4) optimization of microcutting acclimatization on mangosteen with sterile porous medium technique (MSP) / in vitro soil-less propagation (IVS). The results of experiment I showed that the best medium for shoot induction phase was MS + BA 4,0 + TDZ 0,2 mg/l, MS + BA 8,0 BA + TDZ 0,2 or MS + BA 4,0 mg /l. Medium multiplication could not obtain shoot multiplication, only addition of nodes and elongation of shoots. The best medium for shoot elongation was medium MS + BA 1 mg/l + KIN 1 mg/l. Experiment II showed that the rootstock derived from a single intact seed germination was better success than other treatments in almost all the observed variables, such as flush shoot that was better success than dormant shoot. There are several factors that determine the success of micrografting, which is width of meristem encounter between the rootstock and scion, the equal cell growth rate between rootstock and scion cells, as well as the similarity in size and structural congeniality between rootstock and scion. The results of anatomical tissue observation (4 months after micrografting) indicated that there was a good graft union on micrografting. Roostsock and scion xylem tissue were fused perfectly. Experiment III results showed that the concentration of 25% MS medium concentration on various substrates with or without the addition of IBA might cause 50-80% of microcutting rooted with the root length between 1,8 to 4,38 cm. Experiment IV results showed that microcutting carried out using MSP technique could grow roots, even at the microcutting that were untreated with root growth stimulating substances. Microcutting that planted using a MSP technique with IBA and Rootone-F treatments at varied concentrations could cause mangosteen microcutting 100% rooted with the root length from 3,44 to 6,88 cm.
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Judul: Perbandingan Kekonvergenan Beberapa Model Binomial untuk Penentuan Harga Opsi Eropa
Abstrak: Kontrak opsi (selanjutnya disebut opsi) adalah suatu jenis kontrak antara dua pihak, satu pihak memberi hak kepada pihak lain untuk menjual atau membeli aset tertentu pada harga dan periode waktu tertentu. Terdapat dua jenis opsi yang paling mendasar, yaitu opsi call dan opsi put. Berdasarkan waktu eksekusi maka terdapat dua tipe opsi, yaitu opsi Eropa dan opsi Amerika. Untuk menentukan besarnya premi opsi maka dirumuskan dua cara yaitu dengan solusi analitik dan solusi numerik. Solusi analitik telah ditemukan oleh Black-Scholes pada tahun 1973. Metode numerik yang sering digunakan adalah metode beda hingga dan metode binomial dan trinomial. Beberapa model binomial hanya mendasarkan pada perbedaan faktor naik dan turun dari perkembangan harga saham. Metode binomial terutama digunakan untuk penentuan nilai opsi yang tidak dapat diturunkan secara analitik. Di antara modelmodel binomial tersebut adalah model CRR, JR, Tian, PP1, dan PP2. Model ini konvergen ke solusi Black-Scholes. Untuk melihat kevalidan masing-masing model perlu diketahui sifat-sifat kekonvergenannya, maka perlu melihat pendekatan numeriknya.
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