Judul: Analisis pencemaran udara O3 dan PM10 pada bulan terbasah dan bulan terkering (Studi kasus: DKI Jakarta)
Abstrak: Penelitian ini bertujuan unuk melihat pengaruh faktor meteorologi terhadap konsentrasi dan persebaran polutan pada bulan terbasah dan bulan terkering serta mengetahui kualitas udara di DKI Jakarta berdasarkan kategori ISPU. Penelitian ini dilaksanakan pada bulan November 2007 sampai Juni 2008 di BPLHD Jakarta dan Laboratorium Meteorologi dan Kualitas Udara Departemen Geofisika dan Meteorologi, FMIPA-IPB. Kualitas udara di kota besar seperti DKI Jakarta setiap tahun semakin menurun. Penurunan kualitas udara ini disebabkan oleh pencemaran udara yang disebabkan, diantaranya oleh polutan Ozon (O3) dan Particulate matter 10 (PM10) yang berdampak buruk bagi kesehatan manusia. O3 merupakan polutan berbentuk gas dan merupakan polutan sekunder yang terbentuk dari reaksi polutan primer, sedangkan PM10 berupa partikulat atau debu.
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Judul: Analisis Sebaran NO₂ dan O₃ menggunakan Weather Research and Forecasting Chemistry (WRF-Chem) di DKI Jakarta
Abstrak: DKI Jakarta sebagai ibukota negara sekaligus pusat aktivitas ekonomi memiliki kepadatan penduduk yang tinggi serta berimplikasi terhadap kepadatan transportasi. Hal tersebut menyebabkan emisi pencemar udara terutama NO₂ dan O₃ juga tinggi. NO₂ dan O₃ memiliki dampak serius terhadap kesehatan masyarakat dan perlu upaya untuk mengantisipasinya. Tujuan dari penelitian ini adalah untuk menduga sebaran pencemar NO₂ dan O₃ di permukaan wilayah DKI Jakarta. Metode dalam penelitian ini menggunakan model Weather Research and Forecasting Chemistry (WRF-Chem) dengan ukuran grid 4 km x 4 km, selama 7 hari (169 jam) masing-masing pada bulan Agustus dan Desember tahun 2014. Hasil model dibandingkan dengan data observasi konsentrasi pencemar dari lima Stasiun Pemantau Kualitas Udara (SPKU) di DKI Jakarta dengan analisis stastistik Root Mean Square Error (RMSE) dan analisis korelasi. Pola sebaran pencemar berdasar luaran model menunjukkan lokasi yang paling sering terpapar pencemar NO₂ maupun O₃ dengan konsentrasi maksimum adalah Jakarta Selatan dan Jakarta Timur. Pada siang hari konsentrasi maksimum cenderung sering terjadi di sekitar Jakarta Selatan. Nilai RMSE untuk NO₂ maupun O₃ tergolong tinggi dan koefisien korelasi konsentrasi NO₂ dan O₃ tergolong rendah, hal ini menunjukkan keluaran model belum cukup baik untuk memprediksi konsentrasi NO₂ dan O₃ di wilayah DKI Jakarta. Secara umum data hasil keluaran model underestimate terhadap data hasil observasi.
Keyword: Jakarta, Nitrogen oksida, Ozon, Sebaran pencemar, WRF-Chem

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