Judul: Pengaruh eksploitasi air tanah terhadap sistem keseimbangan tata air di wilayah Jakarta
Abstrak: Tujuan penelitian ini adalah untuk mengetahui pengarunpengaruh, ataupun dampak yang disebabkan oleh pengambilan/penyedotan air tanah di wilayah DKI Jaya dan sekitarnya. Pengamatan cl i l akukan terhadap sumur-sumur pantau, sumur penduduk, uji pemompaan ( pumping test ), pengukuran daya hantar listrik (DHL atau electric conductivity ), serta menganalisis data reKaman sumursumur yang terpantau dengan balk dari tahun ke tahun. Atas dasar basil penelitian ini, maka aKan dihasil kan beberapa saran dan rekomendasi penanganan, agar tidak terjadi gangguan keseimbangan lingkungan yang parah. Daerah penelitian meliputi luas sekitar 650 km2 yang mencakup seluruh kawasan DKI Jaya dan sekitarnya r.Jii mana sistem cekungan akuifer (lapisan pembawa air) Jakarta berada. Mengingat sistem cekungan air tanah Jakarta mempunyai Kaitan erat dengan lingkungan di luarnya, maka dalam penelitian ini dibahas pula pengaruh DAS (daerah aliran sungai) Ciliwung dan Cisadane sebagai input (masukan) air tanah bagi wilayah DKI Jaya. ...
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Judul: Pengaruh penyusupan air laut terhadap kualitas air tanah di Wilayah DKI Jakarta
Abstrak: Peningkatan kadar garam air tanah oleh penyusupan air laut dapat mengakibatkan terganggunya pemanfaatan air untuk berbagai keperluan terutama air minum. Studi ini bertujuan untuk menelusuri terjadinya penyusupan air laut di wilayah DKI Jakarta dan mempelajari pengaruhnya terhadap kualitas air tanah berdasarkan parameter-parameter tertentu. Studi dilakukan di wilayah DKI Jakarta yang meli- puti Jakarta Selatan, Jakarta Pusat, Jakarta Barat, Ja- karta Utara dan Jakarta Timur. Data-data yang diperlu- kan diperoleh dari Direktorat Geologi Tata Lingkungan dan Perusahaan Air Minum Jaya. Data kualitas air tanah dangkal dan dalam dianalisa berdasarkan kriteria Revelle. Analisa data untuk mendapatkan sebaran zona air tanah payau/asin digunakan klasifikasi PAHIAA Jakarta, yaitu ditetapkan dengan angka DHL 1500 mikromhos/cm dan ka- = dar Cl = 500 mg/l jika nilai DHL dan Cl melebihi angka tersebut rasa air tanah sudah payau. Data fluktuasi muka air tanah yang diperoleh dari sumur-sumur pantau dievaluasi berdasarkan zona pengambilan air tanah DKI Jakarta yang terbagi dalam 7 zona (Soefner, 1985)…dst
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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