Judul: Pemanfaatan Arang Aktif Cangkang Buah Bintaro (Cerbera manghas) sebagai Adsorben pada Peningkatan Kualitas Air
Abstrak: Biji buah bintaro banyak digunakan sebagai bahan baku alternatif dalam pembuatan biodiesel sehingga akan menghasilkan limbah berupa cangkang buah bintaro. Pada penelitian ini, limbah tersebut akan dijadikan bahan baku alternatif untuk pembuatan arang aktif. Pengaktifan dilakukan dengan 2 faktor yaitu aktivasi kimia (konsentrasi H3PO4) dan fisika (lama steam uap air). Sebagai indikator kualitas arang aktif dilakukan karakterisasi berdasarkan Standar Nasional Indonesia (SNI 06-3730-1995). Dari berbagai perlakuan tersebut akan dipilih arang aktif terbaik. Hasil penelitian menunjukkan arang aktif yang sesuai SNI adalah arang aktif yang diaktivasi menggunakan H3PO4 15% dan steam uap air selama 90 menit dengan kadar air 9.98%, kadar zat terbang 9.16%, kadar abu 12.45%, kadar karbon terikat 78.4%, daya jerap iodin 784.498 mg/g, daya jerap benzena 17.73 %, dan daya jerap biru metilena 127.705 mg/g. Mekanisme adsorpsi mengikuti isoterm adsorpsi Langmuir dengan linearitas 0.9691. Arang aktif terbaik mampu menurunkan logam besi dan mangan berturut-turut sampai 100% dan 86.94%.
Keyword: Arang aktif, Cerbera manghas, Isoterm Adsorpsi

Judul: Arang Aktif Cangkang Buah Bintaro (Cerbera manghas) sebagai Adsorben Logam Merkuri (Hg).
Abstrak: Buah bintaro (Cerbera manghas) sebagai limbah yang belum banyak dimanfaatkan dapat diubah menjadi arang aktif yang bermanfaat untuk menjerap logam berat merkuri. Tujuan penelitian ini adalah membuat arang aktif dari cangkang buah tersebut dan menentukan kapasitas adsorpsinya terhadap logam merkuri. Arang diaktivasi secara kimia dan fisik (uap) dengan beberapa ragam kondisi yaitu (1) aktivasi fisik, (2) aktivasi kimia dengan konsentrasi H3PO4 (10%, 15%, dan 20%), serta (3) aktivasi kombinasi aktivasi kimia konsentrasi H3PO4 (10%, 15%, dan 20%) dan dilanjutkan dengan aktivasi fisik dengan lama uap 60 menit. Kualitas produk didasarkan pada Standar Nasional Indonesia (SNI 06-3730-1995). Hasilnya menunjukkan bahwa arang aktif terbaik diperoleh pada kombinasi H3PO4 15%–uap 60 menit dengan ciri kadar air 4.48%, kadar zat terbang 6.8%, kadar abu 8.58%, kadar karbon terikat 84.62%, dan daya jerap iodin 780.96 mg/g. Berdasarkan hasil percobaan dan studi literatur, arang aktif terbaik cangkang buah bintaro diprediksi memiliki nilai kapasitas adsorpsi cukup baik terhadap logam merkuri.
Keyword: adsorpsi, arang aktif, buah bintaro, merkuri

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