Judul: Dinamika Kandungan Bahan Organik (BOD) di Kalimalang Bekasi
Abstrak: Kalimalang is downstream such as from the West Tarum Canal, crosses Karawang, Bekasi, and DKI Jakarta (East Jakarta) regional. Kalimalang has suffered from pollution, especially the organic pollution upstream. This study aims to determine the dynamic of organic matter (BOD) each season, and its related the supporting parameters such as temperature, DO, TSS, pH, coliform, and debit water. In addition, STORET index is also used to determine the status of water quality. Organic matter highest in the dry season with a BOD value of 15.6 mg / l and lowest in rainy season with a BOD value of 4.89 mg / l. The high BOD value indicates that the waters are polluted It is also supported by STORET index value that is worth more than -21, which means that these waters are heavily polluted so it is not suitable for class status B.
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Judul: Kandungan Bahan Organik (BOD) Di Sungai Cipining Kabupaten Sumedang, Jawa Barat
Abstrak: Penelitian mengenai Kandungan Bahan Organik (BOD) Di Sungai Cipining Kabupaten Sumedang, Jawa Barat ini dilakukan pada tanggal 3 - 8 Juni 2003. Penelitian ini bertujuan untuk mengetahui kandungan bahan organik pada musim kemarau dengan pengukuran BOD, serta pengukuran parameter fisika dan kimia yang menjadi pendukung dalam menganalisa kandungan bahan organik di sungai tersebut. Selain itu juga nilai parameter tersebut dibandingkan dengan nilai baku mutu air kelas 2 berdasarkan PPRI No. 82 tahun 2001. Berdasarkan hasil pengamatan didapatkan kondisi perairan Sungai Cipining dengan parameter suhu, DO, pH, amonia, nitrit, nitrat, BOD, dan TSS berkisar antara: 22-24 °C; 6-8 mg/L; 7-8; 0,024 -0.063 mg/L; 0,197 -0,357 mg/L; 0,005-0,041 mg/L; 0.740-3,910 mg/L; 187-270 mg/L. Menurut baku mutu air kelas 2 PPRI No.82 tahun 2001 nilai parameter fisika dan kimia yang di ukur masing-masing suhu, DO, pH, amonia, nitrat, perairan memiliki nilai yang masih berada pada kisaran nilai baku mutu kelas 2. Hanya nitrit yang memiliki nilai diatas nilai baku mutu. Hal ini diduga karena proses dekomposisi amaonia menjadi nitrat baru berjalan pada proses perombakan amonia menjadi nitrit. Sedangkan Nilai BOD dan TSS berdasarkan hasil pengamatan masih berada pada kisaran yang baik untuk kegiatan perikanan. Dari hasil penelitian dapat disimpulkan bahwa kandungan bahan organik Sungai Cipining masih dapat dikatakan dalam kondisi baik dan masih dapat dilakukan aktivitas perikanan di DAS sungai tersebut.
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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