Judul: Klasifikasi Genotipe Pada Data Tidak Lengkap  Dengan Pendekatan Model Ammi
Abstrak: Multilocations trials play an important role in plant breeding and agronomic research. Study concerning genotype-environment interaction needed in selection of genotype to be released. AMMI (Additive Main effect and Multiplicative Interaction) is one of statistical technique to analyze data from multilocations trials. The analysis of AMMI is a combining analysis between additive main effect and principal component analysis. The main restriction of using AMMI analysis is balance data. However a multilocations trials give an opportunity of the occurrence of unbalance data become very big. It is intended for every combination of genotype and location have the same number of replication. Therefore, we must estimate the data which do not complete. Incomplete data case, it is needed some data estimation method analysis, at this research employed connected data method and EM-AMMI algorithm to estimate incomplete data. Data which used in this research is obtained from Indon Spices Medicinal Crops Research Institute (ISMECRI) Bogor. It is a secondary data of ginger essential content resulted from multilocations trials, sixteen of genotype ginger which tested at five location in West Java. Simulation result shows that estimation using connected data will obtain smaller MAPE if its followed by two times EM-AMMI algorithm, for the percentage of data lose 10% to 20%. Production of ginger essential content estimated with AMMI2 model can explain 76.09% interaction structure among location and genotype. Seen from stability of genotype, there are 2 stable genotype, that is genotype 3 and 7. Genotype 8, 12, 15 specific at location B; genotype 9, 11, 14, 16 specific at location D and E; and genotype 1, 2, 4, 5, 6, 10 and 13 specific at location A and C.
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Judul: Penerapan model ammi campuran pada interaksi genotipe-lingkungan spasial
Abstrak: Analisis AMMI (Additive Main Effect and Multiplicative Interactions) digunakan untuk analisis kestabilan dan kespesifikkan dalam percobaan multilokasi. Asumsi yang digunakan dalam suatu analisis statistika menjadi sesuatu yang penting dan harus ada. Akan tetapi, data yang berasal dari percobaan lapang sering mempunyai pola spasial yang dapat digambarkan dalam suatu fungsi, sehingga asumsi kebebasan ragam sisaan mungkin saja tidak terpenuhi. Oleh sebab itu diperlukan suatu cara yang dapat mengakomodir keragaman spasial sehingga asumsi kebebasan dapat terpenuhi. Dalam penelitian ini genotipe diasumsikan sebagai faktor tetap sedangkan lokasi diasumsikan sebagai faktor acak. Lokasi yang digunakan ada 12, sedangkan genotipe yang digunakan ada 14 genotipe. Sebagian besar lokasi tidak menunjukkan adanya pola spasial, kecuali daerah Ngawi1 (AR1xAR1), Deli Serdang1 (IDxAR1), dan Lebak2 (IDxAR1). Keragaman biplot AMMI2 yang mampu digambarkan oleh pengaruh interaksi genotipe dan lingkungan setelah mengakomodir pengaruh spasial lahan adalah sebesar 58.56%. Poligon dalam Biplot AMMI2 membagi lokasi-lokasi yang ada menjadi empat kelompok. Berdasarkan biplot tersebut genotipe yang spesifik adalah BP1932-3E-7-2-1, IPB97-F-13-1-1, IPB97-F-15-1-1, dan Padi Ciherang. Kemudian berdasarkan ellips yang terbentuk pada biplot AMMI2 ini genotipe yang stabil adalah BP3692-2E-8-2, B10531E-KN-15-2-0-LR-B378-2, OBS 1720/PSJ, BIO-110-BC-Pir 4, IPB98-F- 5-1-1, IPB102-F-46-2-1, dan Padi Gilirang.
Keyword: AMMI, interaksi genotipe x lingkungan (IGL), spasial, model campuran, uji multilokasi

Judul: Hamiltonian formulation for linear waves motion in two layers fluid
Abstrak: The surface wave could be considered as a wave that separates two fluids, namely water and air. Based on this assumption, it is introduced the interfacial wave, a wave between two layers of fluid with different density. The formulation of interfacial waves motion begins with deriving the base equation of irrotational ideal fluid. Furthermore, according to irrotational fluid assumption, the base equation can be stated in velocity potential. In this derivation, the fluids domain is assumed to be restricted by rigid lid boundary conditions, both at the upper and lower limit. Therefore, the interfacial waves motion can be explained in a hamiltonian formulation. In the hamiltonian formulation, total energy is defined as the sum of kinetic and potential energy. The hamiltonian system is obtained from reduction of kinetic energy by using the Dirichlet Neumann Operator. The resulted kinetic energy equation is nonlinear. Therefore, this form is linearized by first part of the Taylor expansion. This linearization gives a dispersion relation of linear wave. Based on this dispersion relation, the phase speed of the linear wave depends on the density ratio of the two layers fluid.
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