Judul: Aliran permukaan dan erosi pada tanah yang tertutup tanaman teh dan hutan alam di Gambung, Bandung
Abstrak: Tajuk yang rapat dan adanya serasah pada tanaman teh umur enam tahun memberikan pengaruh yang tidak berbeda nyata terhadap aliran permukaan dan erosi bila dibandingkan dengan tipe vegetasi hutan alam yang mempunyai struktur tajuk berlapis serta tumbuhan bawah dan serasah yang relatif tidak terganggu. Unsur hara yang hilang melalui erosi pada tanaman teh umur satu tahun, tanaman teh umur enam tahun dan hutan alam secara berturut-turut adalah 236.7, 11.4 34.5 kg/ha Nitrogen, 8.2, 1.5 dan 1.3 kg/ha Fosfor 13.6, 1.1 dan 2.9 kg/ha Kalium. Dengan anggapan dan serta sedimen sebagai faktor pelarut ternyata konsentrasi hara (Y) dan konsentrasi sedimen (X) mempunyai hubungan yang erat
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Judul: Mempelajari pengaruh pengelolaan tanah dan tanaman serta sifat-sifat hujan terhadap erosi tanah dan aliran permukaan
Abstrak: Untuk mempelajari pengaruh pengelolaan tanah dan tanaman serta sifat-sifat curah hujan terhadap erosi tanah dan aliran permukaan, suatu penelitian telah dilakukan dari bulan Nopember 1975 sampai bulan April 1976 di desa Jegu kabupaten Blitar, Jawa Timur. Percobaan dilakukan pada tanah Grumusel dengan kemiringan 7 persen dan terdiri dari 6 perlakuan, (1) tanah ter buka (kontrol), (2) tanaman ketela pohon digulud searah lereng, (3) tanaman ketela pohon, (4) tanaman ketela pohon distrip dengan kacang tanah, kemudian pada rotasi kedua kacang tanah diganti dengan kedele, (5) campuran tanaman ketela pohon dengan kacang tanah, kemudian pada rotasi kedua kacang tanah diganti dengan kedele, dan (6) ketela pohon digulud memotong lereng. Dalam penelitian ini untuk mengukur erosi tanah digunakan dengan metoda petak kecil, dengan pengamatan setiap satu hari kejadian hujan. Pengamatan dilakukan terhadap sifat- sifat curah hujan harian, tanah yang ter-erosi, jumlah aliran permukaan dan persentase penutupan tanah oleh tanaman. Kancangan percobaan yang digunakan adalah Rancangan Acak Kelompok yang terairi dari 4 kelompok pada kemiringan lereng tanah yang sama. Erosi tanah dan aliran permukaan semakin besar apabila laju aliran permukaan dan pukulan langsung butir-butir hujan pada tanan semakin sedikit mengalami rintangan. Rata-rata erosi dan aliran permukaan terbesar terdapat pada, (a) tanan terbuka mempunyai erosi sebesar 152,79 ton/ha/6 bulan dan jumlan aliran permukaan sebesar 6704,46 m m³/ha/6 bulan, dan (b) tanaman ketela pohon digulug searah lereng mempunyai aliran permukaan sebesar 6727,19 m³/ha/6 bulan. ...
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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