Judul: Fraksi Distilat pada Distilasi Rebus Minyak Atsiri Rimpang Temu Hitam (Curcuma aeruginosa) dan Aktivitas Antibakterinya
Abstrak: Minyak atsiri rimpang temu hitam memiliki potensi sebagai antibakteri. Penelitian ini bertujuan menentukan waktu distilasi rebus yang optimum untuk menghasilkan minyak atsiri rimpang temu hitam dengan aktivitas antibakteri terbaik. Senyawa yang terdapat di dalam minyak atsiri rimpang temu hitam diidentifikasi menggunakan gas chromatography-mass spectrometry (GC-MS). Kandungan senyawa dominan tertinggi dari semua waktu distilasi pada minyak atsiri rimpang temu hitam adalah epikurzerenon (45%), eukaliptol (70,14%), dan kamfor (15,27%). Aktivitas antibakteri minyak astiri rimpang temu hitam ditentukan dengan metode difusi cakram terhadap bakteri Streptococcus mutans, Escherichia coli, dan Staphylococcus aureus. Potensi antibakteri terbaik didapatkan pada lama waktu distilasi 30 menit pertama untuk bakteri S. mutans, 30 menit kedua untuk bakteri E. coli, dan 30 menit kelima untuk bakteri S. aureus., Temu hitam’s rhizome essential oil has potential as an antibacterial. This study aims to determine the optimum length of boiled distillation time to produce temu hitam’s rhizome essential oil with the best antibacterial activity. Compounds contained in the essential oil of temu hitam’s rhizome were identified using gas chromatography-mass spectrometry (GC-MS). The highest content of the dominant compounds from all times of distillation in temu hitam’s rhizome essential oil was epicurzerenone (45%), eucalyptol (70.14%), and camphor (15.27%). Antibacterial activity of temu hitam’s rhizome essential oil was determined by disc diffusion method against Streptococcus mutans, Escherichia coli, and Staphylococcus aureus. The best antibacterial potential was obtained in the first 30 minutes of distillation for S. mutans bacteria, the second 30 minutes for E. coli bacteria, and the fifth 30 minutes for S. aureus bacteria.
Keyword: Antibakteri, Distilasi Rebus, GC-MS, Minyak Atsiri

Judul: Essential oil of temu hitam (Curcuma aeruginosa Roxb.)„s rhizomes, stems, and leaves as antibacterial toward Streptococcus mutans and biofilm degradator on teeth
Abstrak: Rimpang temu hitam banyak digunakan sebagai antibakteri. Penelitian ini membandingkan kemampuan minyak atsiri rimpang, batang, dan daun temu hitam sebagai antibakteri Streptococcus mutans dan pendegradasi biofilm pada gigi menggunakan metode mikrodilusi. Minyak atsiri diisolasi dengan distilasi uap. Potensi antibakteri terbaik adalah minyak rimpang KHM=konsentrasi hambat minimum=15.63 μg/mL dan KBM=konsentrasi bunuh minimum=1000 μg/mL. KHM rimpang sama dengan tetrasiklin. Setelah difraksionasi dengan kolom maupun kromatografi lapis tipis preparatif, KHM dan KBMnya tidak lebih baik. Senyawa 2,2,5-trimetil-2‟(H)-5‟-6‟-dihidropirano[3‟,4‟,g]indan-1-on diduga paling berperan sebagai antibakteri S. mutans. Kemampuan degradasi biofilm minyak atsiri kasar temu hitam kurang kuat. Minyak atsiri batang lebih baik mendegradasi biofilm (IC50=1347 μg/mL) daripada rimpang dan daun. Setelah difraksionasi, beberapa fraksi minyak atsiri rimpang (F1, F2, dan F3) lebih baik kemampuan degradasinya tetapi IC50 lebih tinggi dari klorheksidin., Rhizomes of temu hitam are widely used as antibacterial. This research compare the potency of essential oil of rhizomes, stems, and leaves of temu hitam as antibacterial toward Streptococcus mutans and biofilm degradator on teeth. The essential oil was isolated by steam distillation. Rhizome‟s essential oil showed good potency as antibacterial with MIC=minimum inhibition concentration=15.63 μg/ml and MBC=minimum bactericidal concentration=1000 μg/ml. MIC of rhizome was same with tetracycline. MIC and MBC of rhizome‟s essential oil was smaller than fraction of column and preparative thin layer chromatography. The 2,2,5-trimethyl-2‟(H)-5‟-6‟-dihydropyrano[3‟,4‟,g]indan-1-one give better potency as antibacterial toward S. mutans. Essential oil of temu hitam was not stronger as biofilm degradator. Stem‟s essential oil was the better essential oil (IC50=1347 μg/mL) to degradate biofilm than rhizome and leave‟s essential oil, but some of fraction of rhizome‟s essential oil (F1, F2, and F3) have better potency than stem‟s essential oil but the IC50 was higher than chlorhexidine. Keywords: Antibacterial, biofilm degradator, essential oil, Streptococcus mutans
Keyword: antibakteri, minyak atsiri, pendegradasi biofilm, Streptococcus mutans

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