Judul: Pengaruh nisbah metanol, suhu, dan waktu reaksi pada rendemen biodiesel dalam transesterifikasi in situ biji bintaro
Abstrak: Cerbera odollam, known as bintaro, is potentially use for raw material in production of biodiesel because it has oil content until 68% dry basis. The purpose of research is to determine the best condition in producing biodiesel that made from bintaro seed through in situ transesterification of bintaro seed. It uses factorial experimental design and it determines the quality of biodiesel that has produced. The parameters of research are methanol ratio influence of the material, time, and reaction temperature toward the biodiesel yield that has produced. The ratio factor and time reaction are dominantly influence toward biodiesel yield that has produced and toward test result variety. Those two factors are significantly influence the yield. Meanwhile the temperature factor doesn’t give significant influence toward the yield. The optimum conditions that has acquired are 7:1 methanol: materials, 4 hours of time reaction, and 40 oC temperature reaction. Also the highest yield is 36.97%. The quality of biodiesel that acquired indicates the qualified biodiesel that regulated by SNI 04-7182-2006.
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Judul: Optimasi Proses Pembuatan Biodiesel Dari Minyak Bintaro Dengan Metode Respon Permukaan
Abstrak: Biodiesel dapat dijadikan alternatif dalam mengatasi masalah ketersediaan bahan bakar. Namun terdapat faktor penghambat seperti ketersediaan bahan baku dan harga produksi biodiesel yang cenderung mahal. Oleh karena itu diperlukan proses optimasi produksi biodiesel. Penelitian ini bertujuan untuk mengoptimasi kondisi proses produksi biodiesel dari biji bintaro melalui transesterifikasi menggunakan metode respon permukaan, serta mengetahui pengaruh kondisikondisi proses tersebut terhadap kualitas biodiesel yang dihasilkan. Variabel proses yang dioptimasi adalah rasio molar metanol terhadap minyak terhadap minyak (A) dan konsentrasi katalis NaOH (B) dengan repon rendemen, bilangan asam, bilangan penyabunan, bilangan iod, viskositas, densitas, titik nyala dan angka setana. Model polinomial yang sesuai untuk respon rendemen, bilangan asam, dan bilangan penyabunan adalah model polinomial orde kedua atau kuadratik, sedangkan model polinomial untuk respon bilangan iod, viskositas dan densitas adalah model polinomial orde satu atau linier. Kondisi proses yang optimum untuk respon rendemen, bilangan iod dan densitas serta titik nyala dan angka setana diperoleh pada rasio molar metanol terhadap minyak terhadap minyak 9 : 1 dan konsentrasi NaOH 0.5% (w/w). Kondisi proses yang optimum untuk respon bilangan asam, bilangan penyabunan dan viskositas diperoleh pada rasio molar metanol terhadap minyak terhadap minyak 9 : 1 dan konsentrasi NaOH 1.5% (w/w). Variabel yang berpengaruh untuk respon rendemen, bilangan asam, bilangan penyabunan, bilangan iod adalah rasio molar metanol terhadap minyak dan konsentrasi NaOH. Sedangkan varibel yang berpengaruh untuk respon viskositas dan densitas adalah rasio molar metanol terhadap minyak. Hasil prediksi optimasi pada kondisi optimum masing-masing respon adalah 95.38% untuk rendemen, 0.41 mg KOH/g untuk bilangan asam, 196.683 mg KOH/g untuk bilangan penyabunan, 35.87 g I2/100g untuk bilangan iod, 3.62 mm2/s untuk viskositas dan 0.85 g/cm3 untuk densitas. Nilai titik nyala biodiesel dari biji bintaro adalah sebesar 181.5 oC. Sedangkan untuk nilai angka setana biodiesel bintaro adalah 52.
Keyword: biodiesel, minyak bintaro, optimasi, metode respon permukaan

Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm