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: Kajian Keberadaan Virus Avian Influenza pada Unggas di Pasar Burung Pramuka, Jakarta
Abstrak: Avian Influenza (AI) which is caused by influenzavirus A of the family Orthomyxoviridae cause an important impact, including in health, social and economic sectors. AI viruses (AIV) can infect various birds and mammals, therefore bird market as a meeting place for human and poultry can potentially transmit AI virus among birds or from birds to human. Indonesia is a habitat of various bird species; therefore research about AIV on bird, especially which are sold in the Pramuka Bird Market, as the biggest bird market in Jakarta, is urgently needed. In general, the aim of this study was to examine the presence of AIV in various bird species sold in Pramuka Bird Market, Jakarta. Specifically, the aims of this study were: (1) to assess the presence of H5 AI virus in oropharyngeal swab, cloacal swab, and fecal samples of various bird species using real time Reverse Transcriptase-Polymerase Chain Reaction (rRT-PCR); (2) to detect the presence of antibodies against AIV (H5) in various bird species using hemagglutination inhibition (HI) test, and (3) to determine the relationship among weather and geographic origin of birds to the prevalence of AIV. During April until September 2011, a number of 862 field samples from 28 families and 96 bird species were collected in Pramuka Bird Market, Jakarta. These field samples consisted of 649 fecal samples, 114 cloacal swab samples, and 99 oropharyngeal swab samples. As many as 7 of 649 faecal samples (1.08%) were positive AI. However, none cloacal or oropharyngel swab were positive AI. Positive fecal samples were detected in four bird species, which are three magpie-robins (Copsychus saularis, family Turdidae), two white-eyes (Zosterops palpebrosus, family Zostropidae), a yellow-vented bulbul (Pycnonotus goiavier, family Pycnotidae), and a robin (Leiothrix lutea, family Sylviidae). In addition to field samples, during April until September 2011, 178 birds from 21 families and 47 species were purchased from the same bird market. From 178 birds, two birds (1.12%), which were two white-eyes (Zosterops palpebrosus, family Zostropidae), were positive AI. The whole positive samples were from Passeriformis order. However, based on rRT-PCR result, there were no H5 positive samples. A number of 163 serum samples were collected from 178 purchased birds from Pramuka Bird Market. Based on HI test using antigen A/Legok/IPB-SGT/1/2004 (H5N1) and A/Ck/West Java/PWT-Wij/2006 (H5N1), seven of 163 birds (4.29%) had positive antibodies to AI. There were differences in HI titers between the two antigens. By using A/Legok/IPB-SGT/1/2004 (H5N1) antigen, two sample were strongly positive (titers ≥ 24), while the other five samples were weakly positive (titers <24). Strongly positive results were obtained from two scooty-headed bulbul (Pycnonotus aurigaster, family Pycnotidae). While the weakly positive results were obtained from a swan (Cygnus sp., family Anatidae), a duck (Anas sp., family Anatidae), a munia (Lonchura maja, family Ploceidae), a spotted-dove (Streptopelia chinensis, family Columbidae), and a black-crowned iv night heron (Nyctorax nyctorax, family Ardeidae). By using A/Ck/West Java/PWT-Wij/2006 (H5N1) antigen, the average HI titer obtained was higher. Five samples were strongly positive (Lonchura maja, Cygnus sp., Nyctorax nyctorax, and two Pycnonotus aurigaster), while samples from Anas sp. and Streptopelia chinensis were weakly positive.
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