Judul: Kajian Proses Pembuatan Tepung Mangga (Mangifera indica L) Menggunakan Pengering Drum
Abstrak: Buab mangga (Mangifera indica L) merupakan salah satu buah tropis Indonesia dengan tingkat produktivitas yang cukup tinggi. Buah mangga bersifat musiman dan mudah rusak sehingga banyak dikonsumsi segar, namun kini telah banyak dikembangkan pengolahan lebih lanjut untuk meningkatkan nilai tambahnya. Salah satu diversifikasi produk olahan yang menarik untuk dikembangkan adalah tepung daging buah mangga (mango powder) yang telah dikembangkan di India. Tepung mangga dapat digunakan sebagai penambah cita rasa asam pada masakan dan campuran tambahan pada makanan olahan. baik sebagai baban campuran dalam makanan bayi dan anak, roti dan kue, jelly, pudding, juga sebagai penambah cita rasa es krim dan yoghurt. Perubahan karakteristik dari buah mangga menjadi tepung yang memiliki kadar air yang rendah akan memperpanjang umur simpan produk. Mangga yang tersedia melimpah dan bersifat mudah rusak dapat segera diolah dan keberadaannya dapat dipertahankan meskipun musim telah berlalu.
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Judul: Proses Produksi dan Karakteristik Tepung Biji Mangga (Mangifera indica L.)
Abstrak: Buah mangga termasuk buah-buahan penting yang ekonomis di Indonesia, yaitu terdapat sekitar tujuh juta pahon mangga yang meliputi lahan seluas 80.000 ha. Namun luasan lahan yang ditumbuhi varietas mangga yang dapat diekspor relatif kecil (Quane, 2002). Tahun 2002 Indonesia mengekspor mangga sebesar 63.742 kg atau senilai dengan $ 32,320 (BPS, 2003). Produksi mangga di Indonesia pada tahun 2002 mencapai 1.375.939 ton (Departemen Pertanian, 2003). Untuk menambah kegunaan dad buah mangga, maka biji mangga memungkinkan untuk dimanfaatkan. Sampai saat ini biji mangga belum dimanfaatkan secara optimal, namun memiliki kandungan nutrisi yang cukup tinggi, seperti karbohidrat, protein, lemak, dan sebagainya (Morales et al., 2002).
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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