Judul: Kapasitas jerapan kromat dari bahan tanah andisol dan oksisol serta bentonit dan organobentonit
Abstrak: Pencemaran krom (Cr) pada lingkungan terutama berasal dari proses- proses industri dan penggunaan produk-produk krom. Krom (Cr) dalam bentuk logam dan kromat diterapkan secara meluas sebagai pencegah karat yang banyak digunakan untuk alat-alat rumah tangga dan industri-industri dengan tujuan agar alat-alat yang diciptakan menjadi tahan lama. Krom dalam bentuk teroksidasi di dalam tanah merupakan masalah lingkungan yang penting, karena Cr (VI) bersifat lebih meracun dibanding dengan Cr (III). Cr (VI) biasanya muncul dalam bentuk anion seperti hidrokromat (HCrO4), dikromat (Cr2O72), kromat (CrO42) dan biasanya bersifat mobil dalam kondisi netral sampai alkalin. Karena kromat merupakan anion, maka jerapan kromat hanya mungkin dilakukan oleh bahan- bahan yang memiliki muatan positif. Penelitian ini bertujuan untuk mempelajari kapasitas bahan tanah andisol dan oksisol serta bentonit dan organobentonit dalam menjerap kromat. Bahan tanah Andisol dan oksisol merupakan tanah yang memiliki muatan tergantung pH, sedangkan bentonit merupakan bahan tambang yang memiliki kapasitas tukar kation tinggi dengan muatan berasal dari substitusi isomorfik. Sedangkan organobentonit adalah bentonit yang telah disisipi oleh senyawa alkil amonium untuk mengubah sifatnya dari hidrofilik menjadi organofilik. ...
Keyword: 

Judul: Adsorpsi dan desorpsi ion kromium(VI) pada bentonit yang dimodifikasi Heksadesiltrimetilamonium bromida
Abstrak: Bentonite is abundant mineral in Indonesia and potentially as adsorbent. Bentonite has negatively charge, so bentonite has high capability to adsorp cations, while the capability of bentonite to adsorp anion was very low. This research was modified bentonite from Leuwiliang with hexadecyltrimethylammonium bromide (HDTMABr). The result of bentonite modification was changes bentonite surface character from hidrofilic become hidrofobic or organofilic, so that can adsorp anion, like Cr(VI). This research made organobentonite 25, 50, and 100 % CEC. Some methodes were done in this research, they were determination of CEC, acidity, and adsorption optimum condition of Cr(VI) that covered determination of adsorption pH, contact time, isotherm, and desorption of Cr(VI) from organobentonite. Capacity Exchange Cation of bentonite, organobentonite 25 %, organobentonite 50 %, and organobentonite 100 % were 54.53, 45.14, 37.37, and 20.72 me/100 g, respectively. Acidity of bentonite, organobentonite 25 %, organobentonite 50 %, and organobentonite 100 % were 4.95, 3.62, 0.90, and 0.60 mmol/g, respectively. Optimum adsorption condition of Cr(VI) onto bentonite, organobentonite 25 %, organobentonite 50 %, and organobentonite 100 % were consist of pH 2 until 4, contact time 3 until 4 hours, on concentration 200 until 500 ppm. Adsorbtion capacity of bentonite, organobentonite 25 %, organobentonite 50 %, and organobentonite 100 %, respectively were 4.44, 11.96, 22.09, and 20.53 mg/g. Ability of HCl, aquadest, and CaCl2 to desorbed Cr(VI) from organobentonite was low, this matter showed that Cr(VI) was trapped strongly on organobentonite.
Keyword: 

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