Judul: Penyulingan dan Karakterisasi Minyak dari Serbuk Kulit Kayumanis (C. zeylanicum)
Abstrak: Serbuk kulit kayumanis (dust) merupakan hasil samping penggergajian kulit kayumanis. Hingga saat ini serbuk belum dimanfaatkan dengan baik, sehingga menimbulkan permasalahan bagi lingkungan. Penelitian ini bertujuan untuk mengekstrak dan mengetahui minyak kayumanis. Metode ekstraksi yang digunakan pada penelitian ini adalah penyulingan dengan uap dan air, pada suhu 100 sampai 105 derajat celcius selama 3 jam.
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Judul: Pengaruh Pengerokan Kulit Luar, Ukuran Bahan dan Lama Penyulingan terhadap Rendeman dan Mutu Minyak Kulit Kayu Manis (Cinnamomum zeylanicum Ness)
Abstrak: Minyak atsiri merupakan komoditi gang cukup potensial sebagai sumber devisa negara. Salah satu tanaman penghasil minyak atsiri yang cukup potensial untuk dikembangkan adalah kayu manis. Tetapi selana ini ekspor kulit kayu manis Indonesia hanya berbentuk gulungan kulit kering saja. Selain itu mutu kulit kayu manis Indonesia dinilai lebih rendah daripada mutu kulit kayu manis Ceylon. Oleh karena itu perlu pengembangsn produk hasil olahan kulit kayu manis, yaitu dengan cara penplingan kulit kayu manis. Selain itu perlu diteliti agar didapat minyak kulit kayu manis dengan rendemen yang tinggi dengan mutu yang baik. Penelitian ini bertujuzn untuk melihat pengaruh pengerokan kulit luar , ukuran bahan dan lama penyulingan dalam rangka menghasilkan rendemen yang tinggi dengan mutu yang baik. Analisa yzng dilakukan dalam penelitian i n i adalah rendemen, bobot jenis, indeks bias , putaran optik, kelarutan dalam etanol 70 persen, kadar sinamaldehid dan analisa komponen kirnia .rigyak dengan menggunakan kromatografi gas.
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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