Judul: Kesuburan Tanah pada Berbagai Tingkat Kerapatan Tajuk di Gunung Cibodas Ciampea, Bogor
Abstrak: Perubahan vegetasi di kawasan karst menyebabkan berkurangnya sumber hara dalam kesuburan tanah. Penelitian ini bertujuan menganalisis pengaruh kerapatan tajuk terhadap tingkat kesuburan tanah di ekosistem karst Gunung Cibodas Ciampea berdasarkan sifat fisika dan sifat kimia tanah. Kerapatan tajuk diukur menggunakan spherical densiometer (SD) kemudian contoh tanah terusik diambil di lima titik dengan kedalaman 0 - 60 cm. Contoh tanah kemudian dianalisis tekstur, pH, kandungan C-organik, kapasitas tukar kation (KTK), kejenuhan basa (KB), kandungan unsur P2O5 dan K2O, serta status kesuburan tanah ditentukan berdasarkan kriteria penilaian sifat tanah menurut Pusat Penelitian Tanah tahun 1995. Berdasarkan hasil analisis, status kesuburan tanah di Gunung Cibodas Ciampea tergolong dalam kategori sedang pada seluruh tingkat kerapatan tajuk. Hubungan antara tingkat kerapatan tajuk dan kesuburan tanah memiliki korelasi positif signifikan pada KTK dan korelasi negatif signifikan pada pH tanah.
Keyword: karst, kerapatan tajuk, kesuburan tanah, kimia tanah, spherical densiometer

Judul: Kesuburan Tanah dan Potensi Tegakan Mahoni di Gunung Kapur, Ciampea, Bogor.
Abstrak: Kesuburan tanah adalah kualitas tanah dalam hal kemampuannya untuk berbagi faktor unsur hara yang memadai dalam jumlah yang cukup dengan jumlah unsur hara yang tepat di medan yang cocok untuk pengembangan spesies tanaman. Status kesuburan tanah pun menjadi penting menjamin pertumbuhan dan produksi tanaman yang optimum. Untuk mendapatkan status kesuburan tanah, maka dilakukan analisis tanah dan analisis tegakan. Analisis tanah yang diukur adalah pH, kandungan Fosfor, C-Organik, kandungan Kalium, kapastias tukar kation (KTK), dan kejenuhan basa (KB). Analisis tegakan dilakukan dengan pengamatan dan pengukuran terhadap pohon/tegakan dengan jumlah plot yaitu 3 plot dengan jari–jari lingkaran 17.8 m (0.1 ha)/plot. Status kesuburan tanah pada Tegakan Mahoni di Gunung Kapur, Ciampea, Bogor berkisar sedang hingga tinggi. Potensi tegakan pada Tegakan Mahoni di Gunung Kapur, Ciampea, Bogor yaitu berkisar dari 8.84 m3/ha sampai 10.73 m3/ha.
Keyword: Analisis tanah, kejenuhan basa, kesuburan tanah, pH tanah, status kesuburan tanah.

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