Judul: Pemisahan Torium dan Uranium dari Pasir Monazit Pulau Bangka dengan Metode Destruksi dan Pengendapan
Abstrak: Thorium and uranium can be separated from monazite sand by destruction and precipitation method. Destruction was carried out using NaOH by wet and dry destruction method. Solids as the destruction result were diluted in concentrated HCl, followed by precipitation using NH4OH at pH 4 and 7. The precipitates were characterized by x-ray fluorescence. Thorium and uranium content from dry destruction were 2.40% and 0.137%, while those from wet destruction were 3.52% and 0.161%, respectively. Thorium and uranium from wet destruction had higher solubility than those from dry destruction method. By wet destruction methods the precipitates could not be obtained at pH 4, while at pH 7 the precipitates showed higher thorium content but lower uranium content than those by dry destruction. Based on thorium and uranium contents, the two methods did not give satification as separation output.
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Judul: Pengayaan Unsur Tanah Jarang Secara Destruksi dan Pengendapan dari Pasir Monasit Bangka
Abstrak: Rare earth elements (REEs) are lanthanide elements widely used in high-tech electronic equipment. In this study, REEs from earth minerals were enriched through several stages, namely destruction, extraction by microwave oven, and precipitation. The dry and wet destruction phases by using NaOH produced a total of 25.56% and 44.30% REEs, respectively. At the extraction by microwaves stage with HCl 37% as solvent, REEs were successfully dissolved in 30 minutes at high energy. Total amount of REEs which contained in the liquid phase from wet and dry destruction were 35.72% and 29.97%, respectively. Precipitation of REEs started when the pH value was higher than 7, reached by using NH4OH 2 N. Total precipitated REEs in wet and dry feed destruction at pH 10 was 2.76% and 1.18%, respectively. Precipitation at pH 10 gave the highest total REEs. Dry feed destruction produced precipitate that effectively enrich REEs by decreasing impurity elements, such as Si and P, and there was no Th element found. It is also contained low U element which was only 12 ppm. This is consistent with the value of percent recovery and the non-radioactive REEs which was smaller than the wet feed destruction, but contains elements of U in the amount of not less than 0.00006 g and without Th element.
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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