Judul: Penurunan Bilangan Kappa Pulp Organocell dari Beberapa Jenis Kayu Hutan Tanaman Industri
Abstrak: Permintaan pasar akan pulp dan kertas dari waktu ke waktu cenderung meningkat. Hal ini seiring dengan pertumbuhan penduduk dan perkembangan teknologi. Pada tahun 1998/1999 diharapkan kapasitas produksi industri pulp national dapat mencapai 4.387.900 ton (ibnusantoso, 1995).
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Judul: Penurunan bilangan kappa pulp alcell kayu akasia (Acacia mangium Willd) melalui pencucian pulp secara bertahap
Abstrak: Sejalan dengan pertambahan penduduk yang terus meningkat, berdampak positif terhadap perkembangan industri pulp sebagai bahan baku industri kertas. Perubahan- perubahan yang menyangkut daya beli masyarakat, pendidikan, selera konsumen atau tingkat kemajuan sektor industri lainnya terutama pada sektor yang banyak memanfaatkan kertas mengakibatkan permintan kertas akan terus meningkat. Pengembangan Hutan Tanaman Industri (HTI) merupakan salah satu langkah ke arah pemenuhan kebutuhan kayu bagi industri-industri yang menggunakan kayu sebagai bahan baku utamanya. Salah satu jenis kayu yang dikembangkan adalah kayu Akasia (Acacia mangium Willd) karena jenis ini dipandang mempunyai keistimewaan seperti cepat tumbuh, produksi kayu tinggi, kurang menuntut persyaratan hidup yang tinggi serta mudah dalam penyediaan benihnya. Umumnya industri pulp dan kertas di Indonesia menggunakan proses pulping kimia terutama proses sulfat (kraft). Akan tetapi proses sulfat ini menimbulkan pencemaran lingkungan dengan ditimbulkannya gas hidrogen sulfida (H2S) dan metil merkaptan (CH3SH) serta membutuhkan biaya investasi awal dan kapasitas produksi minimal yang besar. Akhir-akhir ini, dikembangkan penelitian proses pulping yang bebas pencemaran lingkungan. Salah satu metode yang dikembangkan adalah proses Alcell. Selain pencemaran lingkungan yang ditimbulkannya rendah, proses ini juga memungkinkan pemanfaatan lignin dan hemiselulosa, sistem daur ulang bahan kimia mudah serta penggunaannya efisien. Tujuan penelitian ini adalah untuk mengetahui pengaruh pencucian pulp secara bertahap dengan menggunakan ethanol-air dan NaOH terhadap penurunan bilangan kappa pulp Alcell kayu Akasia (Acacia mangium Willd).
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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