Judul: Adsorpsi Fenol Menggunakan Bentonit Termodifikasi N-Setil-N,N,N-trimetilammonium Bromida Serta Kajian Kinetika dan Termodinamikanya
Abstrak: Bentonit dimodifikasi menggunakan surfaktan N-setil-N,N,N-trimetilammonium bromida (CTAB) untuk membentuk organobentonit yang digunakan sebagai adsorben penjerap fenol. Organobentonit dicirikan menggunakan difraksi sinar X dan spektrometri inframerah Fourier. Penjerapan fenol menggunakan organobentonit ditinjau dengan mengubah beberapa parameter, seperti jenis organobentonit yang dibedakan berdasarkan tingkatan konsentrasi misel kritis, waktu kontak, dan konsentrasi fenol. Kapasitas adsorpsi meningkat seiring dengan lamanya waktu kontak antara adsorben dengan adsorbat dan mencapai titik stabil pada menit ke-40. Kapasitas adsorpsi diketahui meningkat seiring dengan meningkatnya konsentrasi adsorbat dengan Kapasitas adsorpsi maksimum sebesar 4,89 mg/g dan pola data adsorpsi fenol sesuai dengan isoterm adsorpsi Freundlich, serta data percobaan cocok dengan model kinetika orde kedua semu. Kajian termodinamik menunjukkan bahwa adsorpsi fenol menggunakan CTAB-bentonit berlangsung secara spontan dan eksotermik.
Keyword: adsorption, bentonite, CTAB, freundlich, phenol, thermodynamic

Judul: Adsorpsi Fenol Menggunakan Bentonit Termodifikasi NSetil- N,N,N-trimetilamonium Bromida dan Kitosan serta Kajian Kinetika dan Termodinamikanya.
Abstrak: Bentonit dapat digunakan dalam menjerap fenol. Bentonit dimodifikasi menggunakan N-setil-N,N,N-trimetilammonium bromida (CTAB) dan kitosan untuk meningkatkan kemampuan penjerapannya. Pencirian bentonit termodifikasi menggunakan difraksi sinar X menunjukkan keberadaan montmorilonit, kuarsa, dan kalsit. Spektrum inframerah memperlihatkan puncak tambahan pada serapan 2922, 2850, 1369, dan 1313 cm-1 yang menandakan CTAB dan kitosan berinteraksi dengan bentonit. Nilai kapasitas tukar kation Na-bentonit yang dihasilkan ialah 66.192 cmol/kg. Adsorpsi fenol yang paling tinggi terjadi pada konsentrasi awal fenol 60 mg/L dan pH 12 menggunakan konsentrasi CTAB 10 mmol/L selama 50 menit dengan nilai Ct/Co sebesar 0.43. Model matematika yang sesuai untuk adsorpsi fenol ialah model Adam-Bohart dengan nilai linearitas 0.9229 sehingga didapatkan konstanta kinetika sebesar 8.44  10-4 L mg-1 menit-1 dan konsentrasi jenuh fenol sebesar 465 mg/L. Proses penjerapan fenol oleh bentonit-CTAB-kitosan berlangsung secara fisisorpsi, spontan, dan endotermik.
Keyword: adsorpsi, bentonit, CTAB, kitosan, lapik tetap

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