Judul: Membran Cangkang Telur sebagai Adsorben Zat Warna Biru Metilena dalam Air.
Abstrak: Cangkang telur dikenal sebagai limbah rumah tangga, restoran, dan industri makanan dalam jumlah besar setiap harinya. Beberapa penelitian telah membuktikan bahwa membran cangkang telur (eggshell membrane, ESM) merupakan adsorben potensial untuk berbagai zat termasuk logam, fenol, dan zat warna. ESM dimodifikasi melalui esterifikasi menjadi modified eggshell membrane (MESM). Spektrum inframerah menunjukkan bahwa ESM tidak teresterifikasi sehingga pita serapan ESM mirip dengan pita MESM; dengan demikian kinerja adsorpsinya tidak berbeda nyata. Struktur MESM pada SEM berubah dengan timbulnya benjolan yang terjadi karena terdekomposisinya protein akibat pemanasan pada proses esterifikasi. Kondisi optimum ESM dan MESM dicapai pada pH 12,74 dan konsentrasi 23,40 ppm. Lamanya esterifikasi tidak termasuk faktor yang berpengaruh pada respons. Isoterm adsorpsi ESM dan MESM mengikuti tipe Isoterm Freundlich dengan nilai R2 masing-masing 0,998 dan 0.986 sehingga adsorpsi berlangsung pada banyak lapisan (multilayer).
Keyword: biru metilena, eggshell membrane, ESM, MESM, Isoterm

Judul: Adsorpsi Asam Lemak Bebas dan Zat Warna Biru Metilena Menggunakan Campuran Selulosa Kayu Sengon-Zeolit
Abstrak: Limbah minyak goreng bekas dan zat warna dari berbagai macam industri merupakan penyebab pencemaran di Indonesia. Tujuan penelitian ini adalah melakukan adsorpsi asam lemak bebas dari minyak goreng bekas dan zat warna biru metilena menggunakan selulosa hasil isolasi kayu sengon dan zeolit yang diaktivasi secara asam, menentukan kondisi optimum adsorpsi, serta menentukan isoterm adsorpsi dan kinetika adsorpsi. Percobaan yang digunakan adalah metode tumpak. Kondisi yang dioptimisasi meliputi bobot, waktu, dan nisbah dari kedua adsorben. Kondisi optimum adsorpsi asam lemak bebas didapatkan pada bobot 1 gram, dengan nisbah adsorben 3:1 pada selulosa:zeolit, dan waktu adsorpsi selama 60 menit. Kondisi optimum zat warna biru metilena didapatkan pada nisbah adsorben 1:3 untuk selulosa:zeolit pada waktu 10 menit. Adsorpsi asam lemak bebas dan biru metilena mengikuti isoterm Freundlich. Adsorpsi asam lemak bebas dan biru metilena mengikuti kinetika reaksi orde dua semu.
Keyword: adsorption, adsorption kinetics, cellulose, free fatty acid, methylene blue, zeolite

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