Judul: Penerapan Metode Carathéodory untuk Menentukan Solusi Periodik Persamaan Diferensial Takotonom Orde Dua
Abstrak: Persamaan diferensial takotonom merupakan persamaan diferensial yang secara eksplisit memuat variabel bebas. Persamaan diferensial ini jika diberikan kondisi batas periodik akan menghasilkan suatu solusi periodik. Pada karya ilmiah ini akan dipelajari penggunaan metode Carathéodory untuk mencari solusi periodik dari persamaan diferensial takotonom orde dua yang memiliki syarat batas periodik. Berdasarkan penggunaan metode Carathéodory didapatkan hasil bahwa solusi periodik persamaan diferensial takotonom orde dua adalah solusi dari minimizer persamaan variasional. Untuk menggambarkan solusi periodik dari persamaan diferensial takotonom orde dua digunakan bantuan software Mathematica 6.
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Judul: Metode Beda Hingga untuk Persamaan Diferensial Biasa Orde Dua Linear dengan Syarat Batas Dirichlet
Abstrak: Persamaan diferensial dapat digunakan untuk memodelkan suatu fenomena dinamis. Seringkali model tersebut sangat kompleks yang mengakibatkan penyelesaian persamaan diferensial secara analitik sulit dilakukan sehingga dibutuhkan suatu pendekatan numerik untuk mencari solusi persamaan. Secara umum pendekatan numerik menggunakan prinsip hampiran sehingga hasil solusi numerik akan memiliki selisih nilai dengan hasil solusi analitik. Karya ilmiah ini berfokus pada penyelesaian persamaan diferensial biasa orde dua linear secara numerik menggunakan metode beda hingga. Solusi khusus dalam penelitian ini diperoleh dengan menggunakan syarat batas Dirichlet yang menspesifikasi nilai solusi fungsi pada nilai variabel bebas tertentu. Metode beda hingga bekerja dengan mengganti suatu persamaan diferensial dengan syarat batas menjadi sebuah sistem persamaan linear yang dilakukan dengan mendiskretisasi daerah asal dan mengubah turunan pada persamaan dengan hampiran beda hingga pusat. Hasil penelitian menunjukkan bahwa pendekatan secara numerik menggunakan metode beda hingga hasilnya tidak berbeda jauh dengan metode analitik, hal ini terlihat dari nilai MAPE yang memiliki kisaran kurang dari 10% pada setiap kasus.
Keyword: persamaan diferensial biasa orde dua linear, syarat batas Dirichlet, metode beda hingga

Judul: Penilaian Risiko Kualitatif Pemasukan Virus Avian Influenza (H5N1) ke Pasar Burung Pramuka Jakarta Melalui Unggas
Abstrak: Traditional market or poultry/live birds market was identified as one of avian influenza (AI) virus spot circulation and very potential to contribute on virus spreading to human. Virus infection at the market could not be defined, but the risk value for virus infection can be estimated due to understand well its likelihood and risk factors need to be managed. Qualitative risk assessment had been known as a way to estimate its risk value. Qualitative risk assessment was conducted at Pramuka Birds Market with the purpose to identify biological risk pathways of the entering of Avian Influenza virus (H5N1) and to estimate its risk level through birds. Risk assessment had been done based on the qualitative risk assessment method published by Organization of Internationale Epizootica (OIE) on 2009. The research was conducted on February-June 2012 with primary and secondary data support. Primary data were collected through field observation and questionnaire for 30 sellers and 30 consumers respondents, and through indepth interview with 17 expert respondents, three middlemans and three intstitutions who concern with bird trading. The result of this study identified that there were six pathways of birds supplies to the market defined as risk biological pathways, which are entering of (1) domestic waterfowl, (2) chickens (kampoong, ornamental, or hobbies/pet chickens, (3) wetland birds, (4) “bridges species” birds, (5) songs birds, and (6) exotic birds. Critical control points had been identified in each birds supplies chain are birds collecting fascilities in catcher or collector level, kiosks or sale fascilities, farms, and entry/exit point. Source of birds for the market were (1) nature (capturing from nature), (2) farm, and (3) other country (through importation process). Generally, all groups of birds were important for bringing risk of AI virus entering to PB Pramuka, but both domestic waterfowl and chickens had identified as very import group to bring the risk. Risk estimation value of entering of AI virus (H5N1) to PB Pramuka Jakarta through six groups of poultry/birds originally come from nature, farm and other country was moderate, with the moderate uncertainty. Moderate risk estimation means that before some commodities to be approved for entering the area, it was mandatory to do assessment on risk management implementation, included on its visibility, effectivity, and mechanism of its verification. Based on risk management point of view, moderate risk estimation needed an efforts for risk management implementation to achieve the appropiate level of protection (ALOP) at “negligible” level. This ALOP’s level determined based on characteristic of AI which were zoonotic and had big risk included death both for animal and human. With AI endemic status for Indonesia, still known that AI virus potentially active for mutation, and the findings of high number on entering or selling birds at the market, implementation of applicable risk management must be applied on the birds supplies chain, from the origin until entry the market. Continous surveillance program, development and implementation of operational standard procedures and diseases early warning system, providing appropiate biosecurity fascilities at the market, and better implementation of biosecurity practices with law enforcement support are recommended as risk management actions that
Keyword: assessment, birds, Pramuka Bird Market, qualitative, risk