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: Penanganan Ketidakhomogenan Ragam Akibat Keberadaan Data Ekstrim Melalui Pendekatan EM-AMMI
Abstrak: Multilocation trial is applied to identify adaptation of genotypes from various locations. Additive Main Effect Multiplicative Interaction (AMMI) can identify genotypes that able to adapt in some locations (stable genotype) or genotype that adapt in specific location (specific genotype). Multilocation trial with homogeneity error variance sometimes is not required. So it causes the violation of homogeneity of variance that is part of AMMI analysis. This research uses multilocation trial data from PAIR-BATAN that are consists of 12 genotypes at 5 trial locations. Measurement of responses is dried unhusked rice production (ton ha-1). The exploration of the presence of extreme data shows there are 6 observations of combination genotype by location that have too high variance. The Expectation Maximization-AMMI (EM-AMMI) will solve the violation of homogeneity error variance by eliminating extreme data initially so, AMMI analysis will be used appropriately. AMMI analysis shows that genotype G9 is stable and has a higher average of dried unhusked rice production than both total average and control genotype average.
Keyword: homogeneous, EM-AMMI, extreme data

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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