Judul: Pengaruh Penambahan Titanium Dioksida Terhadap Karakteristik Membran Selulosa Asetat Filter Rokok
Abstrak: Membran dengan memanfaatkan selulosa asetat pada filter rokok yang dibuat dengan metode casting dengan penambahan TiO2 menjadi salah satu upaya dalam penyaringan air. Penelitian ini bertujuan menganalisis karakteristik membran selulosa asetat dengan penambahan variasi konsentrasi TiO2 sebesar 0,5, 1, 2, 3, dan 5% berupa fluks air, porositas, kuat tarik, regangan, modulus Young, gugus fungsi dan morfologi permukaan membran. ...
Keyword: fluks air, porositas, selulosa asetat, sifat mekanik, titanium dioksida

Judul: Sintesa dan Karakterisasi Sifat Mekanik Membran Polisulfon yang Didadah Titanium Dioksida
Abstrak: Penerapan teknologi membran masih mengalami kendala terutama pada sifat mekaniknya. Tujuan penelitian ini adalah untuk mengetahui dan mempelajari pengaruh penambahan TiO2 terhadap sifat mekanik dan kinerja membran polisulfon. Pembuatan membran dilakukan dengan metode inversi fasa dengan komposisi polisulfon 12% (b/b), DMAc dan TiO2 dengan variasi komposisi 0.5% (b/b), 1% (b/b), 3% (b/b), 5% (b/b) dan 7% (b/b). Karakterisasi yang dilakukan meliputi: pengukuran fluks air, sifat mekanik (kuat tekan (compressive strength), kuat tarik (tensile strength) dan kuat getar (strong vibration)) dan analisis morfologi membran dengan SEM. Membran yang memiliki sifat mekanik baik diperoleh pada membran dengan variasi konsentrasi TiO2 5% (b/b). Nilai kuat tekan, kuat tarik dan kuat getar yang didapat adalah 0.047 N/mm2, 2.20 N/mm2 dan 4080 getaran selama 108 sekon. Fluks air terbaik diperoleh pada membran dengan variasi konsentrasi TiO2 3% (b/b). Nilai fluks air yang diperoleh dengan metode cross-flow lebih stabil dibandingkan dengan metode dead-end selama 15 menit. Bentuk morfologi penampang melintang membran yang diamati menggunakan SEM memperlihatkan pori-pori yang asimetri dan menjari.
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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