Judul: Analisis Karakteristik Angin Wilayah Pantai Menggunakan Model Meteorologi Skala Meso (MM5) sebagai Dasar Pendugaan Potensi Penyebaran Pencemar (Studi Kasus: DKI Jakarta).
Abstrak: DKI Jakarta is faced with the problem of air pollution. The location of Jakarta, in the bay-shaped beach, makes the formation of daily wind circulation. It makes the air pollution dispersion caused by daily circulation need to be assessed. The purposes of this study are to determine the wind patterns of the study area and to analyse the estimation pollution dispersion. Wind patterns are obtained by using Mesoscale Model Version 5 (MM5) then be analyzed visually. The study area is divided into mother domain and sub-domain. The modelling results of dominant wind in the both domains are generally the easterly. The wind patterns twist around the bay when the onset of sea-land breeze (at 10.00 and 04.00). Sea breeze can penetrate about 40 km inland and land breeze can penetrate about 16.65 km to the sea. When the land breeze occurs, contaminants moving toward the sea, but the twisting wind makes the pollutant only twist around the bay. While sea breezes occur, pollutants will be heading to west Jakarta. At the day, pollutants will be mixing with low concentration compared to the night and early morning.
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Judul: Keterkaitan perubahan arah dan kecepatan angin dengan pola hujan harian di DKI Jakarta dan sekitarnya: Studi kasus tahun 1994
Abstrak: DKI Jakarta terletak di pantai Utara P. Jawa dengan garis pantai membentuk teluk menunjukkan adanya pola konvergen saat terjadi angin darat dan pola divergen saat terjadi angin laut. Pola konvergen saat terjadi angin darat menyebabkan curah hujan harian tertinggi di daerah ini biasanya pada malam atau menjelang pagi hari. Selain angin laut dan darat, sistem angin yang berpengaruh di DKI Jakarta dan sekitarnya adalah monsun. Dampak angin monsun adalah adanya angin Baratan (Oktober - Maret) yang cenderung membawa massa udara dingin yang lembab sehingga menimbulkan banyak hujan dan angin Timuran yang membawa massa udara kering sehingga tidak mendatangkan hujan. Penelitian ini menganalisa hubungan angin pada beberapa level pengamatan (permukaan, 330 m, 660 m, 990 m dan 1650 m) di Stasiun pengamatan angin Cengkareng dan Curug dengan curah hujan harian di Stasiun Klimatologi Halim PK, Ciledug dan Serpong. Komponen angin dipisahkan menjadi dua yaitu; angin Zonal (Barat-Timur) dan Meridional (Utara- Selatan). Hubungan angin Zonal maupun Meridional dengan curah hujan harian antar stasiun dibagi atas dua waktu yaitu; siang dan malam hari. Analisa hubungan angin Zonal maupun Meridional dengan curah hujan barian antar stasiun pengamatan menggunakan korelasi linear yang dibantu oleh perangkat pengolah data Statistika (Statistica Ver. 5) dan menghitung nilai peluang berdasarkan nilai koefisien korelasi untuk uji taraf nyata. Hasil analisis tersebut menunjukkan sebagian besar memiliki hubungan yang tidak nyata. Namun ada yang menunjukkan hubungan nyata (± 20 %), sebagian besar terjadi pada level pengamatan angin 330 m, 660 m, dan 990 m saat angin Zonal pada kedua Stasiun pengamatan angin dengan curah hujan harian di Stasiun Halim PK dan Ciledug. Sehingga dapat dikatakan bahwa besarnya curah hujan harian (mm) di DKI Jakarta dan sekitarnya lebih ditentukan oleh angin pada level 330 m, 660 m dan 990 m.
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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