Judul: Komposisi dan penyebaran Udang Penaieid Berdasarkan Salinitas di Muara Sungai Bondet  Kabupaten Cirebon, Jawa Barat
Abstrak: Penelitian ini dilakukan sejak tanggal 25 April sampai dengan tanggal 13 Juni 1984. Tujuan penelitian adalah untuk mengetahui komposisi jenis, komposisi carapak (carapace) dan penyebaran udah Penaeid berdasarkan penyebaran salinitas di Muara Sungan Bondet, Kabupaten Cirebon, Jawa Barat. Diloka penelitian ditetapkan lima buah stasiun pengambilan contoh yang dilakukan bersadarkan jarak dan posisi dari mulut sungai.
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Judul: Kelimpahan dan Penyebaran Udang Penaeid di Muara Sunagi Cidurian, Kabupaten Tanggerang dan Kabupaten Serang, Jawa Barat
Abstrak: Penelitian ini dilakukan sejak tanggal 2 Mei sampai dengan 25 Mei 1987, dengan tujuan untuk mengetahui komposisi jenis, kelimpahan dan penyebaran setempat udang penaeid di sekitar muara Sungai Cidurian yang terletak di antara Kabupaten Tangerang dan Kabupaten Serang, Propinsi Jawa Barat. Di lokasi penelitian ditetapkan lima buah stasiun pengambilan contoh, yang posisinya sesuai dengan keadaan muara sungai dan kondisi lingkungan. Pengukuran parameter perairan dan pengambilan udang contoh dilakukan sebanyak empat kali dengan selang waktu satu minggu. Udang contoh diambil dengan menggunakan alat tangkap sudu. Alat ini dioperasikan di setiap stasiun dengan cara mendorongnya ke depan sejauh 10 meter. Lebar mulut sudu 4,95 meter. Dari hasil penelitian didapatkan bahwa suhu perairan berkisar antara 32,0 - 34,0 °C, kedalaman 13,0 - 99,0 cm, kecerahan 8,0 - 55,8 cm, pH 6,0 -8,0 oksigen terlarut 4,2 - 16,6 ppm dan salinitas 7,0, - 35,0°/oo. Substrat dasar perairan terdiri dari empat macam tipe, yakni liat, pasir berlempung, lempung dan pasir. Selama penelitian didapatkan tiga jenis udang penaeid, dengan komposisi masing-masing adalah Penaeus merguiensis (de Man) sebesar 47,69%; Metapenaeus lysianassa (de Man) sebesar 28,46% dan Metapenaeus ensis (de Haan) sebesar 23,85%. Kelimpahan P. merguiensis dan M. ensis tidak berbeda di setiap stasiun, tetapi kelimpahan M. lysianassa berbeda. Kelimpahan rata-rata paling besar didapatkan bahwa P. merguiensis pada stasiun IV, M. ensis di stasiun I dan M. lysianassa pade stasiun II. Penyebaran udang terhadap salinitas rata-rata di setiap stasiun berdasarkan kelimpahan rata-rata, memperlihatkan bahwa jenis P. merguiensis kelimpahan rata-ratanya relatif besar pada salinitas relatif tinggi, yalmi stasiun III, IV dan V, sedangkan M. ensis dan M. lysianassa pada salinitas relatif rendah, yakni di stasiun I dan II…dst
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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