Judul: Analysis of Efficiency and Income of The Pamelo Orange Farming (Case Study: Bageng Village, Gembong District, Pati Regency
Abstrak: Jeruk pamelo merupakan buah unggulan di Kabupaten Pati dengan sentra produksi berada di Desa Bageng. Penurunan hasil produksi jeruk pamelo berdampak pada produktivitas yang mengalami penurunan. Penelitian ini bertujuan untuk menganalisis efisiensi teknis, faktor-faktor yang memengaruhi produktivitas, dan pendapatan usahatani jeruk pamelo. Metode yang digunakan adalah analisis fungsi produksi stochastic frontier, analisis pendapatan dan R/C rasio. Hasil penelitian menunjukkan rata-rata efisiensi teknis sebesar 0,73 yang artinya usahatani jeruk pamelo sudah efisien secara teknis. Pendidikan dan pengalaman usahatani secara signifikan memengaruhi inefisiensi teknis. Penggunaan pupuk kandang, pupuk NPK, pupuk urea, dan jumlah pohon secara signifikan meningkatkan produktivitas. Rata-rata pendapatan petani jeruk pamelo sebesar Rp12.587.903,76 per tahun per hektar dengan R/C rasio 1,48 yang artinya usahatani jeruk pamelo menguntungkan dan layak diusahakan., Pamelo orange is a superior fruit in Pati Regency with the production center located in Bageng Village. The decrease in yield of pamelo oranges has an impact on the productivity which has decreased. This research aims to analyze the technical efficiency, the factors that affect the productivity, and the income of the pamelo orange farm. The method used is stochastic frontier production function analysis, income analysis and R/C ratio. The result of the research shows that the average technical efficiency is 0.73 which means that the pamelo orange farming is technically efficient. Farming education and experience significantly influence technical inefficiency. The use of manure, NPK fertilizer, urea fertilizer, and the number of trees significantly increased productivity. The average income of pomelo orange farmer is Rp12,587,903.76 per year per hectare with an R/C ratio of 1.48, which means that the pamelo oranges farming is profitable and feasible.
Keyword: cobb-douglas, produktivitas, R/C rasio, regresi, stochastic frontier

Judul: Income Analysis and Factors Affecting Pummelo Production in Pati District
Abstrak: Jeruk pamelo sebagai buah unggulan Kabupaten Pati memiliki produksi yang cenderung meningkat sementara luas lahan panen cenderung menurun. Artinya ada faktor lain yang memengaruhi produksi selain luas lahan. Namun, produksi tinggi belum tentu mencerminkan pendapatan petani juga tinggi. Penelitian ini dilakukan untuk menganalisis faktor-faktor yang memengaruhi produksi dan menganalisis pendapatan petani jeruk pamelo di Kabupaten Pati. Metode analisis yang digunakan yaitu analisis deskriptif, analisis fungsi produksi Cobb-Douglass, serta analisis pendapatan usahatani dan R/C ratio. Hasil regresi menunjukkan bahwa hanya 2 dari 6 faktor yang berpengaruh nyata. Faktor jumlah pohon dan penggunaan tenaga kerja berpengaruh positif signifikan terhadap produksi. Hasil analisis pendapatan usahatani menunjukkan bahwa usahatani tidak menguntungkan jika memperhitungkan seluruh biaya (total biaya) dan tidak mampu memberikan imbalan terhadap seluruh sumber daya yang digunakan. Kerugian bersih yang diterima petani sebesar Rp 132.967,00 per pohon per tahun dengan R/C atas total biaya sebesar 0,8918. Namun, jika hanya memperhitungkan biaya tunai, usahatani masih memberikan keuntungan Rp 297.194,00 per pohon per tahun dengan R/C sebesar 2,3297., Pummelo as a superior fruit in Pati Regency has a production that trends to increase while the area of harvested land trends to decrease. It mean that there are other factors that influence production besides land area. However, high production does not necessarily reflect high farmers income. This research was conducted to analyze the factors that influence production and to analyze the income of pummelo farmers in Pati Regency. The analytical method used is descriptive analysis, Cobb-Douglass production function analysis, and farm income analysis and R/C ratio. The regression results show that only 2 of 6 factors have a real effect. The number of trees and the use of labor had a significant positive effect on production. The results of the analysis of farm income show that farming is not profitable if it takes into account all costs (total costs) and it unable to provide rewards for all the resources used. The net loss received by farmers was IDR 132.967,00 per tree per year and R/C for the total cost of 0,8918. However, if only consider cash costs, farming still provides a profit of IDR 297.194,00 per tree per year and R/C of 2,3297.
Keyword: income, production, production factor, R/C ratio

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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