Judul: Sampo antiketombe alami dengan komponen aktif ekstrak etanol daun bakau hitam (Rhizophora mucronata) dan karaginan
Abstrak: Ekstrak etanol daun bakau hitam memiliki aktivitas antimikroba. Karaginan berfungsi sebagai penstabil dan pengental produk. Tujuan dari penelitian ini adalah untuk menentukan aktivitas antifungi dari ekstrak etanol daun bakau hitam terhadap fungi penyebab ketombe dan menentukan formulasi sampo antiketombe yang tepat dengan penambahan karaginan. Hasil penelitian menunjukkan bahwa ekstrak etanol daun bakau hitam memiliki aktivitas antifungi terhadap fungi penyebab ketombe. Ekstrak etanol daun bakau hitam sebesar 2 mg/sumur menghasilkan zona hambat sebesar 16,50 mm untuk fungi P. ovale dan 14,50 mm untuk fungi C. albicans. Konsentrasi hambat minimum ekstrak etanol daun bakau hitam terhadap fungi penyebab ketombe yaitu konsentrasi ekstrak 0,05 mg/mL. Formulasi sampo antiketombe yang tepat yaitu formulasi dengan penambahan karaginan sebanyak 0,01%. Sampo antiketombe memiliki nilai pH yang stabil pada suhu 4 oC, suhu ruang (± 25 oC) dan suhu 40 oC selama penyimpanan 4 minggu (28 hari). Viskositas sampo antiketombe mengalami perubahan pada setiap perlakuan suhu selama penyimpanan 4 minggu, tetapi viskositas sediaan masih dalam standar.
Keyword: antidandruff, shampoo formulations, antifungal, black mangrove, carrageenan

Judul: Gel antijerawat alami dengan komponen aktif ekstrak etanol Daun Bakau Hitam (R. mucronata) dan karaginan
Abstrak: Ekstrak etanol daun bakau hitam memiliki aktivitas antibakteri yang berasal dari komponen aktif yang dimilikinya. Karaginan merupakan bahan alami yang dapat berfungsi sebagai penstabil dan pengental produk. Tujuan dari penelitian ini adalah untuk menentukan aktivitas antibakteri dari ekstrak etanol daun bakau hitam terhadap bakteri penyebab jerawat dan menentukan formulasi gel antijerawat yang terpilih dengan penambahan karaginan. Hasil penelitian menunjukkan bahwa ekstrak etanol daun bakau hitam memiliki aktivitas antibakteri terhadap bakteri penyebab jerawat. Ekstrak etanol daun bakau hitam dengan konsentrasi 2 mg/20 µL menghasilkan zona hambat terbesar yaitu 13 mm untuk bakteri Staphylococcus aureus dan 11,5 mm untuk Staphylococcus epidermidis. Nilai konsentrasi hambat minimum (KHM) ekstrak etanol daun bakau hitam terhadap bakteri penyebab jerawat yaitu 0,05 mg/mL. Formulasi gel yang terpilih yaitu gel dengan penambahan karaginan 0,25%. Gel antijerawat mengalami perubahan fisik dan kimia selama penyimpanan 28 hari (4 minggu), tetapi pH dan viskositas sediaan masih dalam standar.
Keyword: antiacne gel formulation, antibacterial, black mangrove leaves

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