Judul: Penggunaan Metode Perturbasi Homotopi pada Masalah Gelombang Rossby yang Melibatkan Gaya Coriolis
Abstrak: Masalah gelombang Rossby yang melibatkan gaya coriolis merupakan salah satu masalah gelombang yang sering muncul di daerah khatulistiwa dan model matematikanya berbentuk persamaan diferensial tak linear. Salah satu model matematika yang menjelaskan masalah gelombang Rossby adalah persamaan Zakharov-Kuznetsov(ZK)-Burgers. Persamaan ZK-Burgers diselesaikan dengan metode perturbasi homotopi. Penyelesaian menggunakan metode perturbasi homotopi dinyatakan dalam bentuk deret pangkat. Hasil penelitian menunjukkan bahwa galat relatif antara penyelesaian menggunakan metode perturbasi homotopi dan penyelesaian eksak dari model masalah gelombang Rossby relatif kecil. Selain itu, diperoleh bahwa amplitudo gelombang mengalami penurunan pada saat perambatan.
Keyword: gelombang Rossby, persamaan Zakharov-Kuznetsov-Burgers, metode perturbasi homotopi

Judul: Penggunaan Metode Perturbasi Homotopi untuk Menyelesaikan Persamaan Burgers dan Penerapannya pada Masalah Arus Lalu Lintas
Abstrak: Traffic flow problems are frequently referred as problems of congestion, accidents and traffic violations. Traffic accidents often occur because the vehicle drivers can not control the speed of their vehicle. One of the efforts that must be made by the vehicle drivers to control the speed of their vehicle is driving under the road speed limit. On this traffic flow problems, the road speed limit will be assessed based on the Burgers equation. The Burgers equation can be solved by the homotopy perturbation methods. The results of the homotopy perturbation method will be compared to the results of numerical methods.
Keyword: traffic flow problems, homotopy perturbation method, Burgers equation

Judul: Synthesis of Apatite - Chitosan Composite Using Duck Eggshell and Chitosan with Temperature and pH Control
Abstrak: Composite of apatite-chitosan was prepared by using chitosan as polymer matrix. Calcium phosphate was prepared from CaO and (NH4)2HPO4, which the ratio Ca : P had to be 1.67. Chitosan is produced by deacetilase from biopolymer chitin. Duck eggshell (95% CaCO3) as starting material was converted to be calcium oxide (CaO) through calcinations with temperature 1000oC for 5 hours. In-situ and ex-situ methods were prepared from apatite and chitosan (dissolved with acetate acid 2%). Calcium phosphate prepared for bone implantation, but it is too fragile and brittle to be implant into the body. So addition of chitosan can decrease crystalinity and increase mechanic characteristic (tougher). Composite apatite-chitosan was resulted by fast precipitation. Fast precipitation was held in a breaker glass with nitrogen atmosphere, under controlled temperature at 37oC and pH 7, in order to increase amount of hydroxyapatite. Precipitation with CaO which was dropped by (NH4)2HPO4. Hydroxyapatite and chitosan were appearing at samples with in-situ and ex-situ methods which indicating by peak matching of XRD (closed lattice parameter, crystal size), overlapping at FTIR spectra and supporting by SEM picture (homogenous and agglomerated particle). However, it still needs further research to examine biocompatibility osteoconductive degree of sample by in-vivo and in-vitro test.
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