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: Hubungan Variasi Waktu Distilasi Kukus Rimpang Temu Hitam (Curcuma aeruginosa) dan Aktivitas Antibakteri Minyak Atsiri
Abstrak: Waktu distilasi dapat mempengaruhi ekstraksi minyak atsiri seperti pada rimpang temu hitam (Curcuma aeruginosa) yang telah dibuktikan memiliki aktivitas antibakteri. Oleh karena itu, penelitian ini bertujuan menentukan waktu distilasi yang optimum dalam menghasilkan minyak rimpang temu hitam dengan aktivitas antibakteri terkuat. Rimpang temu hitam didistilasi kukus dengan perbedaan lama waktu setiap 30 menit selama 4 jam untuk mendapatkan minyak atsiri dan ditentukan senyawa yang terdapat di dalamnya menggunakan gas chromatography-mass spectrometry. Aktivitas antibakteri ditentukan dengan difusi cakram terhadap bakteri Streptococcus mutans, Escherichia coli, dan Staphylococcus aureus. Senyawa yang terdapat pada minyak atsiri yang paling dominan adalah eukaliptol (34,89%), epikurzerenon (20,58%), dan kamfor (16,90%) berdasarkan rerata luas puncak pada total waktu distilasi. Potensi antibakteri terkuat didapatkan pada waktu distilasi 30 menit pertama untuk bakteri S. mutans dan E. coli, serta waktu distilasi 30 menit ketujuh untuk bakteri S. aureus., Distillation time can affect the extraction of essential oils such as the rhizome of temu hitam (Curcuma aeruginosa) which has been shown to have antibacterial activity. Therefore, this study aims to determine the optimum distillation time to produce temu hitam rhizome oil with the strongest antibacterial activity. The rhizomes of temu hitam were steam distilled with different lengths of time every 30 minutes for 4 hours to obtain essential oil and determined the compounds contained in them using gas chromatography-mass spectrometry. Antibacterial activity was determined by disc diffusion against Streptococcus mutans, Escherichia coli, and Staphylococcus aureus. The most dominant compounds present in essential oils are eucalyptol (34,89%), epicurzerenone (20,58%), and camphor (16,90%) based on the average peak of the total distillation time. The strongest antibacterial potency was obtained in the first 30 minutes of distillation for S. mutans and E. coli, and in the seventh 30 minutes of distillation for Staphylococcus aureus.
Keyword: antibacterial, essential oil, GC-MS, steam distillation

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