Judul: Kajian Pemucatan Minyak Goreng Bekas dengan Metoda Adsorpsi dan Pengkelatan
Abstrak: Dalarn kehidupan sehari-hari, masyarakat menggunakan minyak goreng untuk mengolah bahan pangan dengan sistem deep frying (merendam). Pada kenyataannya minyak yang sudah digunakan untuk menggoreng ini tidak dibuang melainkan digunakan secara berulang-ulang dengan tujuan menghemat biaya. Tidak jarang minyak yang dipergunakan berwarna kehitaman dan berubah aromanya. Penggunaan kembali minyak goreng yang telah dipakai secara berulang-ulang diketahui dapat menurunkan mutu bahan makanan yang digoreng bahkan bersifat karsinogenik.
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Judul: Penentuan daya jerap dan pencirian parafin dalam perlakuan penjerapan minyak jelantah
Abstrak: Minyak goreng merupakan salah satu kebutuhan pokok rumah tangga di Indonesia, yang komponen utamanya berupa trigliserida dan mengandung asam lemak tidak jenuh. banyak Cara penyiapan makanan dengan metode menggoreng adalah sangat populer di negara kita. Pada proses menggoreng minyak goreng berfungsi sebagai medium penghantar panas, penambah rasa gurih, penambah nilai gizi dan kalori makanan serta turut memperbaiki tekstur makanan (Winarno 1997). Pada umumnya metode menggoreng bahan pangan ada dua macam yaitu sistem gangsa (pan frying) dan sistem menggoreng biasa (deep frying). Dalam proses gangsa bahan yang digoreng tidak sampai terendam dalam minyak. Sedangkan proses deep frying, bahan pangan yang digoreng terendam dalam minyak (Ketaren 1986). Penyiapan makanan dengan metode deep frying akan memberikan minyak sisa (minyak jelantah) hasil penggorengan yang cukup banyak. Biasanya minyak ini tidak dibuang tetapi digunakan kembali untuk proses penggorengan berikutnya sebagai usaha untuk menghemat. Proses ini dilakukan sampai beberapa kali bahkan kadang-kadang sampai minyak habis. Akibatnya minyak mengalami pemanasan berulang-ulang.
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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