Judul: Kemampuan Kangkung, Selada, Dan Genjer Untuk Menurunkan Ion Mn2+ Terlarut Dalam Air
Abstrak: Mangan mempakan salah satu logam berat yang berbahaya bagi kesehatan manusia. Keracunan Mn dap8.t mengakibatkan beberapa penyakit. yaitu kemsakan hati, secara almt menyebabkan pneumonitis dan secara kronis menyebabkan ensefalopati. Ambang Mn ulltuk pertanian sebesar 2 mgIL, Di dalam perairan. Mn dapat menyebabkan pakaian yang dicuci dan peralatan kamar mandi berkarat serta menyebabkan kerak di pipa-pipa pada konsentrasi melebihi 0,05 mgIL.
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Judul: Efisiensi Genjer, Kangkung Air, Dan Selada Air Dalam Menurunkan Konsentrasi Logam Resi (Fe) di Dalam Medium Air Tawar
Abstrak: Besi mcrupakan salah satu logam berat yang berbahaya bagi kesehatan manusia. Keracunan besi dapat mengakibatkan gangguan fungsi hati, ginjal, dan juga mcnyebabkan iritasi salman pencernaan. Di perairan, besi dapat menimbulkan berkas karat pada pakaian dan porselin serta mcnimbulkan rasa tidak enak pada air minum dengan konsentrasi standar maksimumnya 0,31 mg/l. Penelitian ini bertujuan mcngetahui efisiensi genjer, kangkung air, dan selada air dalam menurunkan logam besi di perairan tawar. Pengukuran sampel air dilakukan pada hari ke-O, 7, 14. 21, dan 28 dengan menggunakan spektrofiJtometer ultraviolet-sinal' latnpak patin panjang gelombang, 470 11m, Parameter utama yang diukul' aualah Fe terlarut sedangkan parameter pellunjangnya (ldalah suhu, pH, daya hantar listrik, kekeruhan, CO~ bebas, oksigen terlaruL dall kdHltUl1i11l oksigcn biologis. I-Iasil peneiitian menunjukkan bahwa semakin hari konscntrilsi bcsi yang diserap oleh ketiga tallaman semakin banyak. Pada hari ke-28 konsentrasi Fe eli perairan pild" tanHmtln selada air dengan kisaran 0,0002 s<lmpai 0,8025 ppm, sedangkan pada tanaman genjt.!1' (0,000." s<Jlllpai 6,0080 ppm) dan kangkung air (0,0005 sampai 6,0504 ppm). Bcrdasarkan anal isis stalislik11 diketahui babw<J pada hari kc-7, 14, 2!. dan 28 padi! tanalllan genjer, kangkung air, dan selada HiI' lllL'mberi respolls yang nyata dalam menurullkall logam Fe untuk perlakuan 0, 1,5,10, dan 15 ppm. Elisiensi absorbsi Fe paling tinggi teljacli pad a hari kc-28 perlakuan 15 ppm yaitu selada air (94,67%), genjcl' (59,991%)c1an kangkung air (59,66%). Parameter penunjang sepcrti daya hantar listrik, pi-I, oksigen tcrlarul, kebutuhan oksigen biologis bcrpengaruh paela turunnya jumlah Fe eli pcrairan scdangkan suilu. kckcl'uhan, CO:!: be bas tidak berpengaruh.
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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