Judul: Stabilitas antosianin manggis (Garcinia mangostana) dalam minuman berkarbonat
Abstrak: Antosianin merupakan pigmen yang memiliki kemampuan sebagai bahan pewarna makanan: Salah satu masalah dari pigmen ini adalah stabilitasnya yang relatif rendah. Maka dalam penelitian ini dipelajari mengenai stabilitas antosianin, khusus dalam minuman berkarbonat, dalam berbagai kondisi penyimpanan dan jenis asam yang digunakan Minuman berkarbonat dibuat dengan komposisi: 1.4% bubuk antontanin, 0.1 % asam, 13.6 % sukrosa dan 0.05% batrium benzoat. Jenis asam yang digunakan adalah asam sitrat, acam fosfat dan asam malat. Kondini penyimpanan yang dipakai adalah penyimpanan dalam lemari es, penyimpanan dalam ruangan tertutup, penyimpanan dalam ruangan terbuka, dan penyimpanan dalam inkubator.
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Judul: Ekstraksi, Purifikasi dan Karakterisasi Antosianin dari Kulit Manggis (Garcinia mangostana L.)
Abstrak: Antosianin merupakan zat warna alam yang banyak terdapat pada buah, bunga dan sayur-sayuran. Senyawa ini berperan sebagai pemberi warna merah, biru dan ungu. Istilah antosianin berasal dari kata anto = bunga dan sianos = biru, yang digunakan untuk menamai zat warna biru dari suatu bunga. Dalam tanaman. antosianin terdapat dalam bentuk glikosida yaitu yaitu bentuk ester dengan monosakarida seperti : glukosa, ramnosa dannkadang-kadang pentosa, xilosa serta arabinosa.
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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