Judul: Isolasi, Karakterisasi, dan Penentuan Konsentrasi Hambatan Minimum Senyawa Antibakteri dari Fraksi Heksana Bawang Putih
Abstrak: Timbulnya masalah resistensi beberapa mikrob patogen terhadap antibiotik menyebabkan tnntutan ditemukannya senyawa antimikrob bam yang dapat menghamhat atau membunuh mikroorganisme dan aman penggunaannya hagi penderita. Banyak tanaman yang berguna sebagai obat -obatan yang telah digunakan oleh orang secara empiris. Beberapa ekstrak tanaman menunjukkan adanya senyawa antimikroba di dalam jaringarmya. Dalam penelitian ini digunakan tanaman uji hawang pntih yang berfungsi sebagai antibakteri.
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Judul: Isolasi Senyawa Antibakteri Da1u Biji Mahoni (Swietenin innhngoni Jacq)
Abstrak: Mahoni mempakan salah satu tuinbuhan yang banyak dikenal di Indonesia dan banyak dibudidayakan. Kayu mahoni dipergunakan untuk venir dekoratif, kayu lapis, mebel, panil, perkapalan, balok percetakan, barang kerajinan, barang bubutan, dan komponen musik, sedangkan kulit dan biji mahoni banyak digunakan sebagai obat secara tradisional. Secara tradisional, biji mahoni daun kecil (Swietenia mahagoni Jacq) berkhasiat sebagai obat tekanan darah tinggi, encok, eksim, masuk angin, malaria, demam, anemia, diare, dan disentri. Dalam penelitian ini dilakukan isolasi senyawa antibakteri dari biji mahoni. Dilakukan uji aktivitas antibakteri dari ekslrak heksana, metanol, etil asetat, dan fraksi etil asetat hasil kromatografi kolom biji mahoni untuk menghambat aktivitas bakteri dengan memperhatikan atail mengamati zona bening yang terbentuk pada media agar. Hasil uji aktivitas antibakteri ekslrak heksana terhadap bakteri Esclterichia coli mempunyai zona hambat yang lebih kecil dibandingkan pada bakteri st16stilis, sedangkan ekstrak metanol terhadap bakteri E. coli mempunyai zona hambat yang lebih besar dibandingkan pada bakteri substilis. Uji aktivitas antibakteri ekstrak etil asetat terhadap bakteri E. coli mempunyai zona hambat yang lebih besar dibandingkan pada bakteri substilis pada konsentrasi 1 %, 2 %, dan 3 %. Hasil uji aktivitas antibakteri menunjukkan ekslrak heksana, metanol, dan etil asetat mempu~~yaaik tivitas antibakteri mulai konsentrasi 1 % terhadap bakteri E. coli dan bakteri substilis. Fraksinasi eksttak etil asetat dengan kromatografi kolom menghasilkan 13 fraksi. Berdasarkan uji aktivitas antibakteri terhadap bakteri E, coli dan bakteri substilis, fraksi 4 mempakan fraksi paling aktif yang berpotensi sebagai senyawa antibakteri dan mengandung steroidltriterpenoid, alkaloid, dan flavonoid.
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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