Judul: Productivity Analysis of Potatoes (Solanum tuberosum L.) using Crop Simulation Model in Pasuruan Regency
Abstrak: Kabupaten Pasuruan memiliki ketinggian 1000 m di atas permukaan laut sehingga memiliki potensi untuk budidaya tanaman kentang. Kabupaten Pasuruan menyumbang produksi kentang di Jawa Timur sebesar 60%. Produktivitas kentang dipengaruhi oleh faktor iklim dan kebutuhan air tanaman kentang. Produktivitas kentang dapat diprediksi menggunakan model simulasi pertanian menggunakan masukan data iklim harian. Model simulasi pertanian menggunakan tiga submodel yaitu, pertumbuhan, perkembangan, dan neraca air. Perbandingan antara hasil model dengan data observasi lapang menunjukkan akurasi model (R2) sebesar 0,99 untuk wilayah Kabupaten Pasuruan. Estimasi nilai kebutuhan air tanaman kentang sekitar 13,3–36,5 mm/minggu. Selama fase pertumbuhan, tanaman kentang membutuhkan air terbanyak pada fase pematangan umbi sebesar 47%. Hasil model simulasi pertanian menunjukkan bahwa produktivitas rata-rata sebesar 28 ton/ha, dengan produktivitas tertinggi sebesar 30 ton/ha apabila penanaman dilakukan pada bulan Desember, dan terendah sebesar 5 ton/ha apabila penanaman dilakukan pada Agustus. Selain itu, kenaikan suhu sebesar 1 °C dapat menyebabkan penurunan produktivitas kentang sebesar 15,2–17,6%., Pasuruan Regency with an altitude of 1000 m above sea level so is potential for potato cultivation. Pasuruan Regency contributes 60% of potato production in East Java. Productivity of potato is influenced by climatic factors and potato water requirement. It can be predicted using crop simulation models with daily climate data as the input. The model contains three sub-models, that are growth, development, and water balance. The comparison between the model results and the field observation data demonstrate the accuracy (R2) of 0.99 for the Pasuruan Regency. Estimated value of water requirement for potato plant is around 13.3–36.5 mm week-1. During the growth phase, potato plant require the most water in the tuber bulking phase by 47%. Model show that the average productivity is 28 tonnes ha-1, with the highest productivity of 30 tonnes ha-1 when planting is done in December, and the lowest is 5 tonnes ha-1 when planting is done in August. An increase in temperature of 1 °C can cause a decrease in potato productivity by 15.2–17.6%.
Keyword: Biomassa, kebutuhan air, model simulasi, produktivitas kentang, Biomass, potato productivity, simulation model, water requirement

Judul: Aplikasi model simulasi untuk prediksi dampak perubahan iklim terhadap produktivitas tanaman kentang (Solanum tuberosum L.) di Indonesia
Abstrak: Potato is an important horticulture crop in Indonesia in terms of planted area more than 55.000 ha and its production 864.000 ton. The crop is commonly grown in upland areas above 800 m where runoff and erosion often cause environmental problem whereas the yield is relatively low due to various reasons. The crop growth depends on climatic variables particularly rainfall, solar radiation and temperature. Climate change, particularly temperature increase and rainfall decrease, is expected to adversely impact potato growth with the results of even lower yield of the crop compared to the current yield. In order to develop potato crop simulation model, field experiment at Pacet and Galudra (West Java Province) and Kerinci (Jambi Province) were conducted to derive parameters that are required for model building and validation. The experiments were conducted from December 2009 to September 2011. The model being constructed consists of (1) crop-development submodel, (2) crop-growth submodel, and (3) water-balance submodel. Model was calibrated using data collected from three field experiments. The application includes determining potential yield of potato crop under different climates, both under current condition and under different climate change scenarios. The model was also run at different planting dates to find the maximum yield from which optimum planting date was determined. Result showed that in general validation results using paired t-test suggest that model predictions are not significantly different (P > 0,05) with field measurements at Galudra and Kerinci for variables of periods of developmental phases, biomass of root, stem, leaf and tuber, leaf area index, and soil water content (Granola cultivar) and biomass of stem, tuber and soil water content (Atlantic cultivar). However, graphical test of the relationships between model predictions and field measurements have coefficients of determination (R2) higher than 0,80 for all of variables being tested. The simulation model of development, growth and waterbalance of potato crop could predict climate change impact on potato productivity in several potato production centers in Indonesia (Minahasa, Alahan Panjang, Pangalengan, Pasuruan, Wonosobo, and Deli Serdang). Predicted potato yields in the six potato production centers using three scenarios of increasing temperature and decreasing rainfall for the year 2020, 2050, and 2080 based on climate change projection in Indonesia for the future (SRES A1) were in the range of 13% – 31%, 25% – 47% and 37% – 63%, respectively. Potato production center in Pangalengan was predicted to experience the biggest decline in yield for all scenarios. Predicted yield of Atlantic variety was 25 ton ha-1, which was higher than Granola variety of 16 ton ha-1. Climate change adaptation options based on simulation of the model are: optimal planting time, use of superior potato varieties that have higher value of RUE, and select application of suitable potato varieties that are more tolerant to high temperatures.
Keyword: 

Judul: Invers Drazin dari Matriks Toeplitz Singular
Abstrak: Matriks Toeplitz adalah matriks yang setiap unsur pada diagonal utama bernilai sama dan setiap unsur pada subdiagonal yang bersesuaian dengan diagonal utama juga bernilai sama. Matriks singular adalah matriks yang tidak bisa ditentukan inversnya. Akan tetapi, dapat diupayakan untuk ditentukan inversnya menggunakan invers matriks yang diperumum. Invers Drazin merupakan salah satu jenis invers matriks yang diperumum. Pada karya ilmiah ini ditentukan invers Drazin dari matriks Toeplitz singular dengan menggunakan metode Leverrier Faddeev. Kemudian, ditentukan invers Drazin dari matriks Toeplitz singular yang direpresentasikan sebagai penjumlahan segitiga bawah dan segitiga atas matriks Toeplitz berdasar pada teorema Gohberg dan Semencul., Toeplitz matrix is a matrix in with element on the main diagonal has the same value and on the subdiagonal corresponding to the main diagonal also has the same value. Singular matrix is a matrix that has no inverse. However, it can be attempted to determine the inverse using a generalized inverse matrix. Inverse Drazin is a type of generalized matrix inverse. This paper discussed the inverse Drazin for a singular Toeplitz matrix using the Leverrier Faddeev method. Then, the Drazin inverse of the singular Toeplitz matrix which is represented as a sum of products of lower and upper triangular Toeplitz matrix based on Gohberg and Semencul theorem.
Keyword: inverse Drazine, singular Toeplitz matrix