Judul: Kesuburan alami dan homogenitas bahan induk tanah-tanah di Daerah Karangsambung, Kebumen, Jawa Tengah
Abstrak: Karangsarnbung region, Kebumen, Central Java was a region which formed by geological formation resulted interaction between Australia's Indian Ocean plates with Eurasia continental plates and has various rocks from several ages and forming process. The rocks were recording of earth process which will result different soil characteristic. This research was aimed to study natural fertility and homogeneity of soil parent materials which was developed fiom several rocks. Research was done in Natural Geological Laboratory Karangsarnbung, Kebumen. Soil samples were collected in 6 profiles. PI from diabas, P2 from phylite, P3 &om chert, P4 fi-om marble, P5 from basalt, and P6 from shale This research was done through analysis of clay fraction use DTAJTG and FTIIRS to determine type of clay mineral and analysis of soil parent material
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Judul: Distribusi Fe, Al, dan Si Oksida pada beberapa tanah di atas batuan induk berbeda di Karangsambung, Kebumen, Jawa Tengah
Abstrak: Karangsambung merupakan laboratorium alam geologi dimana berbagai jenis batuan dengan lingkungan permukaan yang berbeda-beda bisa dijumpai. Lokasi ini merupakan tempat pertemuan antara lempeng samudra Hindia Australia dengan lempeng benua Eurasia. Adanya berbagai macam batuan, tanah yang terbentuk kemungkinan akan berbeda-beda pula. Penelitian ini bertujuan untuk mengetahui distribusi Fe, Al, dan Si oksida pada berbagai tanah dari bahan induk yang berbeda-beda dan mengetahui tingkat pelapukan tanah. Pengambilan contoh tanah dilakukan di 6 lokasi yang mewakili 3 batuan induk : batuan beku, sedimen dan metamorf. Profil pertama sampai keenam (Pl, P2, P3, P4, P5, dan P6) merupakan profil tanah yang terbentuk dari batuan induk berturut-turut yaitu diabas, filit, rijang, manner, basalt, dan lempung. Kandungan Fe, Al, dan Si oksida di dalam tanah diekstraks dengan metode ditionit sitrat bikarbonat, ammonium oksalat dan pirofosfat.
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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