Judul: Pendugaan Tingkat Keasaman Air Hujan berdasar Konsentrasi Pencemar Udara Ambien (Studi Kasus: DKI Jakarta).
Abstrak: DKI Jakarta merupakan wilayah yang memiliki nilai pH air hujan di bawah 5.6. Dalam menganalisis hujan asam di suatu daerah diperlukan data pH air hujan yang lengkap. Kurangnya ketersediaan data pH air hujan di Indonesia, terutama di DKI Jakarta, menjadi masalah dalam menganalisis hujan asam. Pendekatan hukum Henry dapat dilakukan untuk menduga data pH air hujan berdasar data konsentrasi gas pencemar. Namun, data kualitas udara ambien kurang tersedia sehingga dibutuhkan pemodelan kualitas udara, salah satunya yaitu Weather Research Forecasting Chemistry (WRF-Chem). Penelitian ini bertujuan untuk menduga pH air hujan agar dapat digunakan dalam menganalisis hujan asam di DKI Jakarta dengan menggunakan pendekatan hukum Henry. Data konsentrasi gas SO2 dan NO2 yang digunakan berasal dari data kualitas udara ambien observasi stasiun pemantau dan output WRF-Chem. Hasil pH air hujan yang diduga dari perhitungan output WRF-Chem didapat nilai di bawah 5.6 serta memiliki variasi diurnal, yaitu pH air hujan rendah pada saat pagi dan malam hari serta tinggi di siang dan sore hari. Potensi keasaman air hujan pada saat musim hujan menunjukkan daerah Bundaran HI, Kebon Jeruk, dan Jagarkasa memiliki nilai yang tinggi, serta pada musim kemarau yang memiliki potensi keasaman air hujan yang tinggi adalah Bundaran HI dan Kelapa Gading. Sedangkan nilai pH dari data kualitas udara ambien didapat nilai di bawah 5.6 untuk semua Stasiun Pemantau Kualitas Udara (SPKU) pada saat musim hujan maupun musim kemarau.
Keyword: hujan asam, hukum Henry, NO2, SO2, WRF-Chem

Judul: Estimation of Rainwater Acidity Level based on CO2, SO2, and NO2 Concentration in Rural and Sub-Urban Area (Case Study: Bogor)
Abstrak: Hujan asam merupakan salah satu fenomena yang menunjukkan dampak pencemaran udara terhadap lingkungan. Tingkat keasaman air hujan dapat diketahui melalui pengukuran pH air hujan. Namun, observasi dan ketersediaan data tingkat keasaman air hujan masih sangat terbatas. Salah satu metode untuk mengetahui tingkat keasaman air hujan melalui pendugaan berdasarkan konsentrasi polutan. Penelitian ini bertujuan mengestimasi tingkat keasaman air hujan berdasarkan konsentrasi polutan CO2, SO2, dan NO2 di wilayah sub-urban dan rural. Titik sub-urban dalam penelitian ini adalah Baranangsiang, Kota Bogor, dan titik rural adalah Cibeureum, Puncak-Bogor. Metode yang digunakan adalah pendekatan hukum kimia Henry terkait kelarutan gas dalam air. Asumsi dalam penelitian ini bahwa CO2, SO2, dan NO2 diduga berpengaruh pada konsentrasi ion hidrogen (H+). Hasil penelitian menunjukkan wilayah sub-urban memiliki potensi tingkat keasaman air hujan yang lebih tinggi, yaitu berkisar dari 4 – 5, dibandingkan dengan wilayah rural, berkisar dari 4,5 – 5,5. Titik rural dan sub-urban menghasilkan nilai estimasi di bawah pH normal air hujan menunjukkan keduanya berpotensi untuk terjadi hujan asam, tetapi dengan tingkat keasaman yang berbeda. Perbandingan hasil estimasi dan data observasi tingkat keasaman air hujan di titik rural menunjukkan kesesuaian yang cukup baik dengan koefisien korelasi sebesar 0,49. Perbedaan hasil estimasi dan observasi pada periode Juni – September disebabkan kandungan kation yang dapat menetralkan air hujan, seperti Ca2+ dan NH4+. Perbedaan hasil estimasi dan observasi pada periode Februari – Mei disebabkan pengenceran akibat tingginya curah hujan., Acid rain is a phenomenon that shows the impact of air pollution on the environment. The acidity of rainwater can be determined by measuring the pH of rainwater. However, observation and availability of rainwater acidity data is still rare. One method to determine the acidity of rainwater is through estimation based on pollutant concentrations. This study aims to estimate the acidity of rainwater based on concentrations of CO2, SO2, and NO2 in sub-urban and rural areas. The sub-urban point in this study is Baranangsiang, Bogor City, and the rural point is Cibeureum, Puncak-Bogor. The method used is Henry's chemical law approach related to the solubility of gases in water. The assumption in this study is that CO2, SO2, and NO2 are thought to influence the concentration of hydrogen ions (H+). The results showed that sub-urban areas have a higher potential for acidity of rainwater, ranging from 4 to 5, compared to rural areas, ranging from 4.5 to 5.5. Rural and sub-urban points produce estimated values below the normal pH of rainwater indicating both have the potential for acid rain to occur, but with different acidity levels. Comparison of the estimation results and observation data on the acidity of rainwater at rural points shows a good match with a correlation coefficient of 0.49. The difference in the estimation and observation results in the June – September period is due to the content of cations that can neutralize rainwater, such as Ca2+ and NH4+. The difference in estimation and observation results in the February – May period is due to dilution due to high rainfall.
Keyword: acid rain, Henry's law, rural, sub-urban, wet deposition

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