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: Nanokomposit kaolin-TiO2 dengan dopan urea untuk adsorpsi dan fotodegradasi zat warna biru metilena
Abstrak: Methylene blue is one type of dyes found as pollutant in Indonesia water system. Kaolin-TiO2 nanocomposite was synthesized and used to overcome this problem by utilizing its adsorption-photodegradation mechanism. Kaolin-TiO2 nanocomposite was made by mixing kaolin powder and TiO2 powder physically using ball milling and paste methods. The ball milling method is found to be simpler than paste method, and also resulting in smaller particle size. Smaller particle size also found to increase both adsorption and photodegradation activities. It is believed that ball milling method also generated a homogenous mixture. From 2 different sample compositions and 3 milling times used, it was found that synthesis kaolin-TiO2 nanocomposite requiring calciumbased binder with an optimum milling time of 5 hours. Kaolin-TiO2 nanocomposite was doped with urea by manual physical mixing followed by calsination at 300 °C for 2 hours. Urea doped-nanocomposite has larger activity than undoped nanocomposite in visible light zone. It means that the photocatalytic activity of urea doped-nanocomposite was successfully shifted to the red zone area of the visible light. Therefore, incident sunlight can be used as energy source in the adsorption-photodegradation process using nanocomposite Kaolin-TiO2.
Keyword: adsorption, ball milling, kaolin, methylene blue, photodegradation

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