Judul: Desinfeksi Escherichia coli Melalui Fotokatalisis Titanium Dioksida (Ti02) Bubuk Faserutile
Abstrak: Penelitian ini bertujuan membuktikan kernampuan destruksi polutan organik Escherichia coli (E. coli) melalui fotokatalisis pada titanium dioksida (TiDl ) yang mengabsorbsi cahaya ultra violet (UV). Pemanasan Ti~ bubuk hingga mencapai suhu 500 "C selama 45 menit akan menghaSilkan rase rutile. Metalui citra kristaJografi difraksi sinar-x menunjukkan bahwa sejumlah kristaJ telah tumbuh padaprefe"ed orientation rase rutile dengan indeks (I 10), (211), (101), (220) dan (JOl). Efek desinfeksi diujicobak:an pada E. col; menggunakan 3 metode perlakuan yaitu fotokatalisis, fotolisis dan penambaha I TiOl . Dosis TiQ, yang digunakan yaitu O.01wt% (0, I gil). SeteJah 4 jam perlakuan, fotokatalisis diketahui teJah mampu menurunkan jumlah populasi E. coli hingga 52.4%, 2.43 kati lebih banyak dibandingkan daya desinfeksi fotolisis atau 4.03 kati lebih besac dibandingkan daya bunuh Ti(h saja. Hal ini dikarenakan aktivasi TiOz oleh sinar UV pada proses fotokata1isis sehingga menambah k
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Judul: Disinfeksi Escherichia coli Pengaruh Variasi Intensitas Sinar UV dan Konsentrasi TiO2
Abstrak: Kemampuan fotokatalisis dengan menggunakan bubuk TiO2 fase anatase sebagai katalis untuk menurunkan populasi bakteri Escherichia coli dipengaruhi oleh intensitas sinar UV dan konsentrasi katalis TiO2. Dalam penelitian ini dilakukan variasi intensitas melalui pengaturan jarak lampu UV ke bibir reaktor sebesar 0 cm, 5 cm, dan 10 cm masing-masing untuk konsentrasi TiO2 0.01 %,0.05%, dan 0.1%. Bubuk TiO2 yang dipakai memiliki parameter kisi a = 9.462 A, c = 3.751 A, ukuran kristal sebesar 3.313 A. Secara umum, fotokatalisis berlangsung sangat cepat pada 15 menit awal reaksi daripada 30 menit dan 45 menit. Nilai tetapan disinfeksi untuk masing-masing variasi perlakuan pada 15 menit pertama lebih tinggi daripada nilai tetapan setelah 30 menit dan 45 menit berlangsungnya reaksi. Dari hasil penelitian ini, untuk pemberian TiO2 0.01%, jarak lampu UV ke reaktor yang paling efektif ialah 10 cm, dengan waktu reaksi efektif sebesar 45 menit. Dengan menggunakan TiO2 0.050%, jarak lampu ke reaktor paling efektif yaitu 5 cm, dengan waktu reaksi efektif antara 15-30 menit. Sedangkan pemberian TiO2 sebesar 0.1% paling efektif dilakukan dengan memberikan penyinaran dengan intensitas maksimum, dengan waktu reaksi efektif 30 menit.
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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