Judul: Pengelompokan Grid-Grid di propinsi jawa barat, banten, dan DKI Jakarta Berdasarkan Konsentrasi Zat Radioaktif (U, Th, k) dan Paparan Radiasi Total
Abstrak: Penelitian ini bertujuan untuk mengklasifikasikan grid-grid yang tersebar di Propinsi Jawa Barat, Banten dan OKI Jakarta berdasarkan konsentrasi zat radioaktif (uranium, thorium dan kalium) dan paparan radiasi totalnya serta menampilkan hasil pengelompokan tersebut secara visual dalam bentuk peta. Data yang digunakan merupakan data pengukuran konsentrasi zat radioaktif dan paparan radiasi Iingkungan di wilayah Propinsi Jawa Barat, Banten dan OKI Jakarta yang dilakukan oleh Pande Made Udiyani (2000) terhadap empat peubah yaitu paparan radiasi total, konsentrasi uranium, konsentrasi thorium dan konsentrasi kalium. Sebagai ukuran kedekatan antar peubah digunakan matrik korelasi.
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Judul: Pengukuran Konsentrasi Radioaktivitas Udara Lingkungan Di Kawasan Pusat Penelitian Tenaga Nuklir, Pasar Jumat, Jakarta
Abstrak: Konsentrasi radioaktivitas udara merupakan sa1ah sam komponen yang eliulrur daIam pemantauan radioaktivitas lingkungan. Udara adaIah bagian yang sangal penting bagi keIUdupan manusia. Udara yang tercemar oleh zat radioaktif akan mudah masuk Ire dalam tubuh manusia me1alui pemafusan. Karena itu elilakukan peogukumn Konsenttasi Radioaktivitas Udara (KRU) untuk menjaga agar tingkal radioaktivitasnya tidal< mdebihi baku motu yang diizinkan (menurut SK Kopala No.02lKa-Bapeten/V-99) seItingga tidal< menimbuIkan bahaya bagi kesehatan manusia kbususnya melalui pemapasan. Penclitian ini bertujuan nntuk mengctahui dan menctapkan data efisiensi alaI pencacah dan konsentrasi radioaktivilas udara eli kawasan sckitar Pusat Pene1itian Tenaga Nuklir. Pasar Iumat. Jakarta. Data konsentrasi radioaktivitas udara yang diperoleh djbandingkan dengan nilai baku mutu radioaktivitas lingkungan menurut SK Kopala Bapeten No.02lKa-Bapeten/V-99. Pencacaban diJakukan dcngan menggnnakan sistern pencacah Geiger-Mueller (G-M) Model TGS-136 buaIan Aloka. Efisiensi sitem pencacab ditenhdcan dengan mcncacah sumber standar dan dih;mdjogkan dengan aktivitas yang telah diketahui. Pengambilan sampel udara dilakukan dengan air sampler model NR 2030 buatan Negn:tti Automation yang se\anjumya elicacah dcngan sistem pcncacah G-M dcngan se\ang waktu tertentu nntuk me1ibat laju pelurulum zal radioaklifnya. Kemudian elitentukan ni\ai Konsentrasi Radioaktivitas Udara (KRU). Nilai KRU (Knnsentrasi Radioaktivitas Udara) yang elipcroleh eli setiap tempol daIam kawasan Pusal Pene1itian Tenaga Nuklir. Pasar lumat diharapkan berada eli bawah ni\ai baku motu lingkungan menurnl SK Kepa\a Bupcten No.02lKa-BapctenlV-99. Namun dari basil yang pcroleh tcrnyata ada beberapa tempat yang berada
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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