Judul: Tingkat peluruhan bahan organik pada musim kemarau di Muara Sungai Cisadane (bagian tawar dan payau) Tangerang, Banten
Abstrak: Dekomposisi menerangkan besarnya proses yang dialami oleh bahan-bahan organik. Dekomposisi sangat dipengaruhi oleh kondisi lingkungan terutama ketersediaan oksigen terlarut bagi dekomposer aerobik. Sebagai suatu proses yang dinamis, dekomposisi memiliki dimensi kecepatan yang mungkin berbeda dari waktu ke waktu tergantung faktor-faktor yang mempengaruhinya. Laju dekomposisi umumnya diukur secara tidak langsung melalui pendugaan konsumsi oksigen. Penelitian ini bertujuan untuk mengetahui tingkat peluruhan bahan organik melalui nilai k (laju reaksi). Penelitian dilaksanakan pada bulan Juni-Agustus 2008. Pengamatan dan pengambilan sampel air dilakukan pada musim kemarau dan bertempat di Muara Sungai Cisadane, Tangerang Banten. Analisis sampel air dilakukan di Laboratorium Produktivitas dan Lingkungan Perairan, Departemen Manajemen Sumberdaya Perairan, Fakultas Perikanan dan Ilmu Kelautan, Institut Pertanian Bogor
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Judul: Peluruhan Bahan Organik saat Musim Kemarau pada Bagian Payau dan Laut di Muara Sungai Cisadane Tangerang, Banten
Abstrak: Aktivitas manusia di sepanjang DAS Cisadane memberikan kontribusi baik secara langsung maupun tidak langsung terhadap peningkatan bahan organik. Bahan organik ini akan terbawa aliran air hingga menuju muara sungai. Kandungan bahan organik yang tinggi di muara sungai dapat meningkatkan BOD sehingga dapat menurunkan kadar oksigen terlarut pada daerah tersebut. Apabila laju pemanfaatan oksigen untuk proses dekomposisi tidak menyebabkan kadar oksigen turun di bawah batas minimum yang aman, maka kondisi perairan masih belum terganggu, namun apabila laju pemanfaatan oksigen tersebut telah menyebabkan kadar oksigen turun dibawah batas minimum, maka kondisi perairan akan terganggu dan perlu dilakukan pengendalian terhadap pencemaran bahan organik. Penelitian ini dilakukan untuk mengkaji laju peluruhan bahan organik saat musim kemarau pada bagian payau dan laut di muara Sungai Cisadane. Penelitian dilakukan pada bulan Juni-Agustus 2008. Lokasi penelitian berada di Muara Sungai Cisadane, Desa Tanjung Burung, Kecamatan Teluk Naga, Kabupaten Tangerang, Propinsi Banten. Dalam penelitian ini terdapat dua titik pengambilan sampel (stasiun), stasiun satu (ST.1) adalah daerah percampuran antara air tawar dan air laut yang masih berada di dalam daerah aliran sungai, sedangkan stasiun dua (ST.2) adalah daerah yang relatif sudah tidak terpengaruh oleh pengenceran dari air tawar dan berada di lepas pantai.
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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