Judul: Adsorpsi Fenol Menggunakan Zeolit-Kitosan Termodifikasi N-Setil-N,N,N-trimetilamonium Bromida serta Kajian Kinetika dan Termodinamikanya.
Abstrak: Zeolit termodifikasi dapat digunakan sebagai adsorben untuk menjerap fenol. Zeolit dimodifikasi menggunakan kitosan dan N-setil-N,N,N-trimetilamonium bromida (CTAB) untuk meningkatkan kapasitas adsorpsinya. Pencirian menggunakan sinar-X difraktometer menunjukkan zeolit Cikalong mengandung mordenit dan klinoptilolit. Spektrum inframerah menunjukkan kitosan dan CTAB telah menempel pada zeolit dengan puncak serapan tambahan pada 2926 dan 2855 cm-1 (vibrasi ulur -CH2 dan CH3-R), 1464 cm-1 (vibrasi tekuk CH2) dan 1427 cm-1 (vibrasi ulur C-O) dibandingkan pada zeolit alam. Nilai kapasitas tukar kation Na-zeolit yang dihasilkan sebesar 117 cmol/kg. Adsorpsi metode lapik tetap dengan kondisi terbaik pada penelitian ini diperoleh saat konsentrasi CTAB 10 mM dengan waktu kontak 60 menit, dan konsentrasi 60 mg/L. Kajian kinetika adsorpsi mengikuti model Thomas dan model Yoon-Nelson dengan R2 sebesar 0.9948. Kajian termodinamika menunjukkan adsorpsi terjadi secara fisisorpsi, spontan, dan endotermik.
Keyword: adsorpsi, CTAB, fenol, kitosan, lapik tetap, zeolit

Judul: Adsorpsi Fenol Menggunakan Zeolit Termodifikasi N-Setil-N,N,N-Trimetilamonium Bromida Serta Kajian Kinetika Dan Termodinamika Adsorpsi
Abstrak: Zeolit dapat digunakan sebagai adsorben untuk menjerap polutan organik salah satunya adalah fenol. Namun zeolit memiliki kapasitas adsorpsi yang rendah. Modifikasi permukaan zeolit menggunakan N-Setil-N,N,N-trimetilamonium bromida (CTAB) diharapkan mampu meningkatkan kapasitas adsorpsi. Zeolit-CTAB diperoleh dari pencampuran zeolit dan CTAB dengan ragam konsentrasi CTAB 0.5, 1.8, dan 5 mmol/L kemudian diaduk selama 2 jam. Spektrum inframerah menunjukkan bahwa CTAB telah menempel pada zeolit dan pola difraksi sinar-X menunjukkan bahwa jenis zeolit adalah mordenit. Adsorpsi terbaik diperoleh pada formula zeolit-CTAB 5 mmol/L dengan waktu kontak 50 menit, dan konsentrasi tertinggi yang masih dapat dijerap adalah 60 mg/L. Pola kinetika adsorpsi mengikuti kinetika orde pertama semu, isoterm adsorpsi Freundlich, dan kajian termodinamika adsorpsi menunjukkan bahwa adsorpsi terjadi secara fisisorpsi, spontan, dan endotermik.
Keyword: Adsorpsi, mordenit, N-Setil-N,N,N-trimetilamonium bromida, zeolit

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