Judul: Pengaruh kerapatan pertanaman terhadap pemamfaatan radiasi surya dan produksi tanaman jehe gajah (Zingiber officinale Rosc.)
Abstrak: Tujuan Penelitian ini ialah untuk mengetahui pemanfaatan radiasi surya pada berbagai jarak tanam dan produksi biomas tanaman jahe. Penelitian ini dilakukan di kebun percobaan stasiun Meteorologi dan Geofisika di Cikarawang, Bogor yang ber- langsung dari bulan November 1990 sampai Maret 1991. Dalam penelitian ini perlakuan yang digunakan adalah jarak tanam yaitu: 60cm x 50cm (32 407 tanaman/ha), 60cm X 40 cm (41 667 tanaman/ha), 60cm X 30cm (50 926 tanaman/ha), 50cm x 60cm (37 809 tanaman/ha), 40cm x40 cm (62 500 tanaman/ha), 30cm x 30cm (93 364 tanaman/ha), 30cm x 25cm (110 340 tanaman/ha), 30cm x 20 cm (144 290 tanaman/ha), 25cm x 25cm (130 401 tanaman/ha). Penanaman dengan arah baris Utara Selatan. Rancangan yang digunakan adalah rancangan acak kelompok dengan 3 ulangan.
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Judul: Radiasi, Pertumbuhan Dan Produksi Bahan Kering Pada Berbagai Populasi Tanaman Jagung (Zea mays L.)
Abstrak: Penelitian ini dilaksanakan di Kebun Percobaan IPB Darmaga, Bogor dari 19 Desember 1981 hingga 30 April 1982 dengan menggunakan jagung varietas Harapan Baru (Hg). Tujuan penelitian ini adalah untuk mengetahui: (1) berapa besar radiasi surya yang dapat digunakan oleh suatu komu- nitas jagung dalam berbagai populasi, (2) hubungan absorbsi Radiasi Aktif Fotosintesa (PAR) oleh tanaman dengan Laju Pertumbuhan Tanaman (CGR) dan produksi bahan kering, hubungan Indeks Luas Daun (LAI) dengan CGR, absorbsi PAR dan intersepsi radiasi surya (Is), (3) albedo jagung dan hubungannya dengan populasi dan (4) berapa besar CGR, Efisiensi Pertumbuhan Tanaman (Eg) dan Indeks Panen (HI). Percobaan menggunakan perlakuan berupa populasi yaitu populasi 25 000 tanaman per ha (A), 50 000 tanaman per ha (B) dan 75 000 tanaman per ha (C). Penentuan CGR, Eg, absorbsi PAR dan Is dilakukan dengan menggunakan beberapa persamaan. Penentuan hubungan absorbsi PAR dengan CGR, produksi bahan kering dan enersi radiasi yang dibutuhkan untuk produksi dilakukan dengan pendekatan regresi/korelasi. Unsur iklim yang diukur langsung di lapang adalah intensi- tas radiasi surya total harian dan albedo tanaman sedang unsur agronomis meliputi luas daun dan produksi. ...
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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