Judul: Adsorpsi biru metilena pada kaolin dan nanokomposit kaolin/TiO2 serta uji sifat fotokatalisis
Abstrak: Kaolin is rarely used as an adsorbent due to its small adsorption capacity. Therefore, kaolin was modified into a nanocomposite by physically mixing TiO2 powder with binder. Diffractometer X-ray characterization of Bangka Belitung kaolin (BNK) was done for comparison with Japan Clay Science Society (JCSS). The investigation showed the Bangka Belitung kaolin to have the same peaks as JCSS (2θ=12,36 and 24,88). Both kaolin and nanocomposite were tested for adsorption with methylene blue solution at concentrations of 25, 50, 75, 100, 150, 200, and 300 mg/L. Maximum adsorption capacity in both kaolins occurred at a concentration of 150 mg/L with a capacity of adsorption by Bangka Belitung kaolin of 28,93 mg/g, while that of the JCSS was lower (24,27 mg/g). The maximum concentration decreased for the nanocomposites as compared to the kaolin to 100 mg/L with the adsorption capacity for the BNK/TiO2 nanocomposite at 12,65 mg/g and JCSS/TiO2 nanocomposite at 8,58 mg/g. The photocatalytic properties of the nanocomposite was then tested using ultraviolet light (UV) at a wavelength of 254 nm. The test results with UV light showed that the nanocomposite could degrade methylene blue 12,5 mg/L, as indicated by the colorless filtrate and pale precipitate when compared with controls in the dark treatment. This result showed that nanocomposite can be used for adsorption-photodegradation of methylene blue.
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Judul: Adsorpsi biru metilena pada metakaolin dan nanokomposit metakaolin-TiO2 serta uji fotokatalisis
Abstrak: One method used for handling organic dyes in wastewater is adsorption-photodegradation. This method is based on adsorption of the organic compound by the surface of a solid material that subsequently degrades the organic compound. Clay materials such as kaolin are commonly used as the adsorbent. High temperature heating of kaolin damages its structure and forms amorphous metakaolin. However, metakaolin is rarely used as adsorbent due to its low adsorption capacity. Therefore, modification was done on metakaolin to obtain a nanocomposite by physically mixing metakaolin with TiO2 anatase. In this study metakaolin was formed from Bangka Belitung kaolin by calcinations at temperatures of 550 and 700 ˚C for 3 and 6 hours for a total of four treatments. The study showed that the adsorption capacity decreased with increasing calcination temperature. Metakaolin calcined at 550 ˚C for 3 hours was used to create metakaolin-TiO2 nanocomposite using TB3 as binder with a metakaolin:binder:TiO2 mixing ratio of 6:3:1. The adsorption capacity of the nanocomposite was slightly lower than that of the metakaolin at 13.26 and 14.76 mg/g, respectively. This nanocomposite successfully photodegraded the methylene blue compound.
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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