Judul: Uji daya absorbsi khitosan terhadap pigmen klorofil
Abstrak: Udang merupakan produk perikanan yang sudah diusahakan secara intensif di Indonesia. Pada urnumnya udang dimanfaatkan tanpa kepala atau tanpa kepala dan kulit. Limbah padat yang berasal dari pengolahan udang berkisar antara 65-85 %. Limbah tersebut berupa kulit, kepala, ekor maupun kaki udang. Limbah tersebut dapat diolah menjadi produk khitosan yang lebih menguntungkan secara ekonotnis.
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Judul: Studi ekstraksi khitosan dari kulit Udang Windu (Penaeus monodon) dan aplikasinya sebagai koagulan protein limbah cair pengolahan ebi
Abstrak: milik Perairan Indonesia memiliki potensi perikanan yang cukup besar dengan berbagai jenis ikan dan kelimpahannya. Udang merupakan salah satu komoditas yang penting bagi hasil perikanan Indonesia. Untuk tujuan ekspor umumnya udang dibekukan dalam bentuk tanpa kepala atau tanpa kepala dan kulit sehingga hal ini dapat menghasilkan limbah yang cukup besar dan belum diiringi dengan usaha-usaha peman- faatan secara maksimal. Oleh karena itu perlu adanya usaha kearah pemanfaatan limbah. Limbah yang berasal dari indus- tri pembekuan udang yang berupa kepala dan kulit dapat dimanfaatkan menjadi khitosan sedangkan limbah cair yang berasal dari pengolahan ebi dapat diolah menjadi produk protein terkoagulasi. Khitosan merupakan suatu polimer dan dapat berperan sebagai amino pengganti karena mengandung gugus amino dan gugus hidroksil yang bertindak sebagai donor elektron se- hingga dapat berinteraksi dengan zat-zat organik seperti protein. Karena sifat-sifat tersebut khitosan memiliki potensi untuk digunakan dalam bidang industri dan kesehat- an. Limbah cair pengolahan ebi selain sebagai sumber pro- tein yang terbuang atau belum dimanfaatkan secara maksimal ...
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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