Judul: Validasi metode analisis krom heksavalen dan krom total secara spektrofotometri serta aplikasinya pada air Sungai Cisadane di Bogor dan Tangerang
Abstrak: Di dalam air sungai, krom stabil dalam keadaan heksavalen dan trivalen. Krom heksavalen jauh lebih toksik dibandingkan dengan trivalen sehingga keberadaannya di dalam air sungai perlu dipantau secara berkala. Untuk itu, diperlukan metode yang baik, sederhana, dan cepat dalam menganalisanya. Validasi metode analisis krom heksavalen meliputi uji linearitas, penentuan nilai absorpitivitas molar, serta pengujian pengaruh matriks. Vaksinasi metode analisis krom total meliputi pemilihan oksidator dan penentuan persen recovery metode terpilih.
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Judul: Dynamic of River Water Quality in a Various Landuse at The Upper Watershed Cisadane
Abstrak: Sungai Cisadane yang mengalir dari Kabupaten Bogor ke Jakarta melalui Kota Bogor banyak dimanfaatkan untuk berbagai macam kegiatan manusia seperti pertanian, perikanan, industri, pariwisata dan juga keperluan rumah tangga. Akibat pemanfaatan sumberdaya air tersebut maka muncul berbagai permasalahan lingkungan diantaranya adalah menurunnya kualitas air. Penurunan kualitas air terutama terjadi pada sungai/alur sungai dengan tingkat kegiatan yang intensif seperti pemukiman kota. Sehubungan dengan hal-hal tersebut, maka perlu diadakan pengkajian dan penelaahan terhadap kualitas air Sungai Cisadane. Penelitian ini bertujuan untuk mengetahui kualitas air sungai Cisadane Bogor. Pengambilan contoh air dilakukan di lima lokasi yang mewakili komposisi penggunaan lahan. Parameter yang diamati meliputi parameter fisika, yaitu suhu dan total padatan tersuspensi (TSS) dan parameter kimia yang meliputi pH, kebutuhan oksigen biokimiawi (BOD), serta kandungan nitrat, fosfat dan timbal. Data yang diperoleh dianalisis secara deskriptif dengan membandingkan data hasil analisis terhadap data standar baku mutu air menurut PP No. 82 Tahun 2001 tentang pengelolaan kualitas air dan pengendalian pencemaran air. Hasil penelitian menunjukkan bahwa kualitas air Cisadane di sekitar hulu cenderung lebih baik dibandingkan di tengah-hilir. Aliran sungai di hulu memiliki kandungan BOD (5.04-7.87 mg/l) dan fosfat (0.01-0.02 mg/l) lebih rendah dibandingkan daerah hilir dengan kandungan BOD (10.17-23.61 mg/l) dan fosfat (0.03-0.07 mg/l). Selain itu, kualitas air sesaat sesudah hujan (debit tinggi) lebih baik yang ditunjukkan dengan nilai suhu dan BOD lebih rendah dibandingkan dengan saat tidak ada hujan (debit rendah). Parameter kualitas air yang memenuhi baku mutu air menurut PPRI No. 82 Tahun 2001 disemua kelas diantaranya parameter suhu, pH dan fosfat. Parameter TSS dan BOD hanya memenuhi baku mutu air kelas tiga dan empat, sedangkan nitrat dan timbal memenuhi semua kelas baku mutu air hanya di beberapa lokasi penelitian.
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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