Judul: Sifat Fisikokimia dan Antioksidan Film Kitosan dengan Penambahan β-Karotena dan Hidroksitoluena Berbutil
Abstrak: Sifat mekanis film kitosan dapat dimanfaatkan sebagai kemasan makanan biodegradabel, namun memiliki aktivitas antioksidan yang rendah. Pada penelitian ini, pengaruh penambahan β-karotena dan hidroksitoluena berbutil (BHT) pada film kitosan diteliti. Pembuatan film kitosan- -karotena memerlukan lebih banyak gliserol sebagai pemlastis, yang berpengaruh pada ketebalan dan kadar air yang lebih tinggi. Penambahan kedua antioksidan sangat menurunkan kuat tarik dan persen pemanjangan film. Hal ini diperkuat oleh penurunan titik leleh film dengan penambahan antioksidan pada analisis termal. Penambahan BHT menurunkan permeabilitas uap air, sedangkan  -karotena menaikkannya. Analisis spektrum inframerah menunjukkan interaksi non-kovalen antara kitosan dan antioksidan. Aktivitas antioksidan film pada radikal 2,2-difenil-1-pikrilhidrazil lebih tinggi pada film dengan penambahan antioksidan. Berdasarkan hasil ini, antioksidan dapat ditambahkan ke dalam film kitosan, namun memerlukan bahan lain untuk memulihkan sifat mekanis.
Keyword: analisis termal, BHT, β-karotena, kitosan, sifat mekanis

Judul: Pengaruh Penambahan Nanopartikel ZnO dan Asam Stearat Terhadap Sifat Fungsional Kemasan Film Nanokomposit Berbasis Kitosan
Abstrak: Kitosan merupakan bahan pembuatan kemasan film yang baik. Film dari kitosan memiliki sifat mekanis dan antimikroba yang unggul dibandingkan biopolimer lain. Kelemahan film kitosan adalah sensitif terhadap kelembaban dan elongasi yang terbatas. Penambahan nanopartikel ZnO (NPZ) dapat meningkatkan kuat tarik, ketahanan terhadap kelembaban dan kemampuan antimikroba dari kitosan film. Sementara penambahan asam stearat berguna untuk menurunkan tingkat permeabilitas uap air pada film. Penelitian ini bertujuan mempelajari karakter sifat fungsional kemasan film kitosan yang dikomposisikan dengan penambahan NPZ dan juga asam lemak stearat. Hasil penelitian sementara menunjukkan aktivitas antimikroba dari film mampu mencegah pertumbuhan pada bakteri pathogen Gram positif maupun Gram negatif. Selain itu, performa kuat tarik dan elongasi dari film memiliki korelasi positif dengan penambahan NPZ hingga kadar 1%. Penambahan NPZ hingga 1% dan asam lemak stearate juga mampu menurunkan laju permeabilitas uap air sehingga meningkatkan kualitas film sebagai bahan pengemas. Namun keberadaan asam lemak stearat pada film bionanokomposit kitosan-NPZ mengurangi tingkat aktivitas antimikroba film, kuat tarik film, dan elongasi. Sehingga didapatlah formula dengan penambahan NPZ sebanyak 1% tanpa penambahan asam stearat sebagai formulasi paling optimum.
Keyword: Sifat Fungsional, Kitosan, Nanopartikel ZnO (NPZ), Asam stearat, Aktivitas antimikroba

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