Judul: Kandungan Xanthorrizol temulawak (Curcuma xanthorriza Roxb) pada berbagai cara budidaya dan masa tanam
Abstrak: Ten~ulawak yang digunakan dalam penelitian ini ditanam di Desa Kelurahan, Kabupaten Ambarawa. Ada empat kelompok yang dilakukan perlakuan budidaya yaitu BPTO, PSB, BALITRO, dan lokal. Temulawak dipanen pada umur 6,7, 8, dan 9 bulan setelah tanam untuk dilakukan analisis kandungan xanthorrizol. Rimpang temulawak yang sudah dipanen dilakukan beberapa tahap preparasi meliputi: pencucian, penyotiran basah, perajangan, dan pengeringan. Untuk memperoleh ekstrak yang mengandung xanthorrizol diguakan teknik ekstraksi yaitu maserasi dengan menggunakan memo1 75% selama 2x24 jam. Kandungan xanthorrizol diuji dengan menggunalcan metode antibakteri difusi cakram.
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Judul: Pola akumulasi kurkuminoid rimpang induk temulawak, Curcuma xanthorriza Roxb) pada berbagai masa tanam dan perlakuan budidaya tanam
Abstrak: Temulawak (Curcuma xanthorriza Roxb) merupakan salah satu tumbuhan obat suku Zingiberaceae yang banyak tumbuh dan dipakai sebagai obat di Indonesia (Sidik et al 1992). Kurkuminoid merupakan hasil metabolit sekunder yang berkhasiat menetralkan racun, menghilangkan rasa nyeri sendi, menurunkan kadar kolesterol dan trigliserida darah, dan antibakteri. Penanaman temulawak dengan perlakuan budidaya dan masa tanam yang berbeda bertujuan untuk mengetahui pola akumulasi kurkuminiod rimpang induk temulawak. Tanaman temulawak berumur 6 bulan dipanen dan dianalisis kandungan kurkuminoid setiap bulannya sampai umur tanaman 10 bulan setelah penanaman. Perlakuan pemupukan dibedakan menjadi 4 jenis yaitu PSB, BALITRO, BPTO, dan LOKAL. Masing-masing perlakuan memiliki komposisi pupuk dan waktu pemberian pupuk yang berbeda. Hasil analisis menunjukkan kandungan kurkuminoid yang didapat pada pengukuran kandungan kurkuminoid adalah peningkatan kandungan kurkuminoid pada setiap bulannya. Kandungan kurkuminoid tertinggi dicapai oleh perlakuan budidaya PSB yang dipanen pada bulan kesembilan yaitu sebesar 0.23 gram/rumpun dan terendah pada perlakuan BALITRO pada bulan keenam sebesar 0.05 gram/rumpun. Waktu aplikasi dan komposisi pemupukan tidak dapat dicerminkan dengan kadar kurkumin. Hasil uji statistik kadar kurkumin pada berbagai komposisi pemupukan dan waktu penanaman tidak berbeda nyata dengan masa tanam sampai bulan kedelapan dan berbeda nyata pada bulan kesembilan. Sehingga kadar kurkumin tidak dapat dicerminkan oleh waktu aplikasi dan komposisi pemupukan.
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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