Judul: Penentuan Daerah Aman terhadap Tingkat Kerja (Working Level) dan Konsentrasi Gas Radon di Terowongan Tambang Bawah Tanah (Studi Kasus : Tambang Emas PT. Aneka Tambang Tbk, Cikotok)
Abstrak: The measurement of radon concentration (222 Rn) with decay were determined by working level in three (L-300 north, L-300 south and L-200 south) in Cikidang - Cikotok West Java.
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Judul: Pollutant Level of Natural Radionuclides 238U and 232Th in Waters Surrounding the Area of the Coal Fired Power Plant (Case Study Waters of Pulau Panjang and Coastal of Lada Bay, Banten).
Abstrak: This study had been carried out by collecting sample of the surficial sediments, sea water, seaweeds, fishs (Stolephorus) and mussels (Codakia) from 4 locations in waters of Pulau Panjang and coastal of Lada Bay (as control/comparison site), Banten in June-July 2010. Natural radionuclide (238U and 232Th) concentrations in samples were measured using neutron activation analysis (NAA) method. The results showed that total radionuclide concentrations in sediment (238U: 18,6160– 35,0013 Bq/kg; 232Th: 11,2020-35,6685 Bq/kg), seawater (238U: undetected; 232Th: 0,0790-0,1299 Bq/l), cultivation seaweeds (238U: undetected; 232Th: 3,6735- 4,8345 Bq/kg), natural seaweeds (238U: 3,6851-48,0430 Bq/kg; 232Th: 3,9941- 9,0788 Bq/kg), Stolephorus (238U: undetected; 232Th: 3,3078 Bq/kg) and Codakia (238U: 6,8903 Bq/kg; 232Th: 3,6023 Bq/kg) in Pulau Panjang, Banten around Suralaya coal fired power plant (PLTU) higher than control site that were around the Labuan coal fired power plant, namely in sediments (238U: 10,4253 Bq/kg; 232Th: 16,5952 Bq/kg), seawater (238U: undetected; 232Th: 0,0671 Bq/l), cultivation seaweeds (238U: undetected; 232Th: 2,3005 Bq/kg), natural seaweeds (238U:19,5367 Bq/kg; 232Th: 2,6729 Bq/kg) and Stolephorus (238U: undetected; 232Th: 2,0603 Bq/kg). This means the coal fired power plant has an impact on natural radionuclides pollution in the waters. The internal radiation exposured (via consumed of Codakia and Stolephorus) that received by inhabitant who live in Kampung Peres, Pulau Panjang, Banten are between range 0,00047-0,01984 mSv/year. This value was considered less than limitation of effective doses that recomended by IAEA for public (1 mSv/year).
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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