Judul: Hubungan Perubahan Kandungan Air Tanah dengan Unsur-unsur Klimatologi di Perkebunan Tebu Cinta Manis Sumatra Selatan
Abstrak: Tujuan dari penelitian ini adalah untuk mencari atau menentukan persanaan matematika kandungan air tanah dan hubungan perubahan kandungan air tanah dengan unsur-unsur kli- matologi pada beberapa kondisi dan kedalaman yang berbeda. Penerapan dari hasil penelitian ini adalah untuk-mengetahui: kondisi-kandungan air tanah,penggunaan air tanah untuk kebutuhan tanaman, pemberian air irigasi, dan mempelajari karakteristik tempat penyimpanan air tanah.
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Judul: Pengaruh Pemberian Kompos Terhadap Perubahan Kadar Air Tanah dan selang Pemberian Air Dengan Sistem Irigasi Curah di Perkebunan Tebu Cinta Manis PTP XXI - XXII
Abstrak: Tujuan dari penelitian ini adalah untuk mengetahui peng aruh pemberian kompos terhadap perubahan kadar air tanah dan selang pemberian air dengan sistem irigasi curah di lokasi Perkebunan Tebu PG Cinta Manis PTP XXI-XXII. Pemberian kompos dengan cara menebar kompos secara manual dan dengan dosis 10 ton/Ha, secara umum berpenga- ruh terhadap sifat fisik tanah. Perbaikan sifat fisik tanah akibat pemberian kompos ternyata hanya terlihat pa- da kedalaman pengukuran 10, 20 dan 30 cm. Pada kedalaman 40 cm pengaruh tersebut sudah tidak terlihat. Perbedaan kadar air tanah antara petak kompos dan tanpa kompos terlihat nyata secara statistik pada kedala- man pengukuran 10,20 dan 30 cm. Untuk kedalaman 40 cm perbedaan kadar air tanah antara petak kompos dan tanpa kompos tidak berbeda nyata secara statistik. Penurunan kadar air tanah per hari ternyata lebih besar pada petak kompos relatif terhadap petak tanpa kom- pos. Perbaikan sifat fisik tanah akibat pemberian kompos ...
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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