Judul: Kandungan bahan organik di dua ruas sungai Cisadane, Bogor
Abstrak: Penelitian ini bertujuan untuk membandingkan kandungan bahan organik dua ruas Sungai Cisadane, Bogro berdasarkan tata guna lahan di sekitarnya, serta melihat pengaruhnya terhadap kondisi kualitas air sungainya. Lokasi penelitian di dua ruas Sungai Cisadane, yaitu daerah Lengkong yang terletak di Kota Bogor. Jarak antar lokasi yaitu 39 km. Penelitian ini dilaksanakan pada bulan Juni - Juli 2006 (musim kemarau).
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Judul: Telaah beberapa parameter fisika kimia di sungai Cisarua, Kabupaten Bogor
Abstrak: Penelitian dilaksanakan pada Bulan Maret sampai April 1988, di Sungai Cisarua Kabupaten Bogor. Sungai Cisarua merupakan salah satu sumber air bagi penduduk disekitarnya, maupun bagi penduduk Bogor dan Jakarta. Sungai ini mendapat pengaruh dari kegiatan- kegiatan disekitarnya, yaitu berupa buangan dari Taman Safari Nasional (TSN), perkebunan, pemukiman dan persawahan. Untuk mengetahui pengaruh-pengaruh tersebut dilakukan pengamatan di tiga lokasi. Lokasi pertama (bagian hulu) menerima pengaruh dari perkebunan. Lokasi kedua (bagian tengah) berjarak 6 km dari lokasi pertama menerima pengaruh dari Taman Safari Nasional, perkebunan dan pemukiman. Lokasi ketiga (bagian hilir) berjarak 9 km dari lokasi kedua menerima pengaruh dari pemukiman dan persawahan. Parameter kualitas air yang diukur adalah : suhu air, debit air, muatan padatan tersuspensi, kekeruhan, Daya Hantar Listrik (DHL), nilai pH, oksigen terlarut, karbondioksida bebas, Biochemical Oxygen Demand" (BOD5), bahan organik total, fosfat, ammonia dan nitrat. Parameter-parameter tersebut diukur sebanyak 6 (enam) kali dengan interval waktu 5 (lima) hari. Berdasarkan pengamatan setiap parameter yang kualitas air Sungai Cisarua masih berada pada diukur kisaran yang baik. Indeks Kualitas Lingkungan (IKL) Sungai Cisarua berada pada kisaran yang tidak membahayakan kelangsungan hidup organisme air, yaitu berada pada kisaran yang cukup baik. Selama penelitian buangan dari Taman Safari Nasional (TSN), perkebunan, pemukiman dan persawahan belum menunjukkan pengaruh yang nyata terhadap Sungai Cisarua…
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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