Judul: Formulasi Masalah Puzzle Sudoku Menggunakan Binary Integer Linear Programming (BILP) serta Implementasinya pada Julia, Python dan Minizinc
Abstrak: Sudoku merupakan permainan teka-teki angka yang populer di berbagai kalangan. Dalam matematika, Sudoku dapat dimodelkan sebagai masalah pemrograman linear khususnya masalah Binary Integer Linear Programming (BILP). Penyelesaian Sudoku menggunakan BILP cukup sulit karena membutuhkan banyak iterasi untuk itu perlu bantuan software. Penelitian ini bertujuan untuk menganalisis permasalahan Sudoku menggunakan formulasi pemrograman linear integer 0-1 dan mengimplementasikan permasalahan tersebut menggunakan package JuMP pada Julia serta membandingkan efisiensinya berdasarkan waktu komputasi pada Python dan MiniZinc. Hasil implementasi Sudoku pada Julia, Python dan MiniZinc menunjukkan bahwa bahasa pemrograman Julia memiliki performa yang lebih baik dibandingkan Python dan MiniZinc berdasarkan waktu komputasi., Sudoku is a number puzzle game that is popular in various circles. In mathematics, Sudoku can be modeled as a linear programming problem, especially the Binary Integer Linear Programming (BILP) problem. Solving Sudoku using BILP is quite difficult because it requires many iterations for that it requires software assistance. This study aims to analyze the Sudoku problem using the 0-1 integer linear programming formulation and implement the problem using the JUMP package on Julia and compare its efficiency based on computational time in Python and MiniZinc. The results of implementing Sudoku on Julia, Python and MiniZinc show that the implement on Julia programming language has less computational time than Python and MiniZinc.
Keyword: Julia, MiniZinc, Linear Programming, Python, Sudoku

Judul: Penyelesaian Permainan Sudoku, Challenger Puzzle, dan N-Queens Problem Menggunakan Integer Programming
Abstrak: Many people think that mathematics is complicated so they are not interested to learn it. Presenting mathematics in the form of a puzzle is one way to attract people to study mathematics. The puzzle will attract curiosity of someone to solve problems. When someone can solve the puzzle, then it implies that he in fact has studied mathematics. In this paper, some mathematical puzzles are formulated, such as Sudoku, Puzzle Challenger, and the N-Queens Problem using integer programming and are solved by using LINGO 11.0
Keyword: Sudoku, N-Queens Problem, Integer Programming, Challenger Puzzle

Judul: Thermal Characteristics and Dynamics of Tropical Cyclone over Western North Pacific Ocean: A Case Study of Typhoon Songda (Chedeng) 2011
Abstrak: The frequent occasion of Tropical Cyclone (TC) over Western North Pacific (WNP) Ocean lies from 10˚N to 26˚N and 121˚E to 170˚E. Sources of TC development come from warm ocean temperature where latent heat is released during condensation processes and subsequently concentrated in the boundary layer. Relative humidity at 850-700 hPa is responsible to produce the most intense storm. Meanwhile, weak vertical wind shear between 850-200 hPa is one of the dynamical factors that lead to the development of TC. Pressure level of 850-200 hPa is chosen to minimize the thermodynamic effect in the lower troposphere. Typhoon Songda (Chedeng in the Philippines) or TSC lasted from May 18th to 30th, 2011 and strengthened into powerful Super Typhoon stage between May 24th and 27th. Long curving track and the exhibition of all sequences of TC life cycle, TSC is then considered as an ideal case of TC. The objective of the study with case of TSC is to investigate the role of thermal characteristics and dynamics on TC intensity. The research is carried out by using Advanced Research of Weather Research and Forecasting model (WRF ARW model) version 3.3. Two domains are employed in the model. The first domain situate from 02˚N to 40˚N and 118˚E to 149˚E and cover spatial resolution () of 33.1 km. The second domain situate from 09˚N to 27˚N and 119˚E to 132˚E with of 11 km. Timestep of the model () is 120 seconds. The model is supported by the following physical parameterization, i.e., Yonsei University Scheme (YSU) in the boundary layer, Kain-Fritsch scheme (KF) in the cumulus, and WRF Single-Moment 3-class scheme in the microphysics. Initial meteorological condition prior to the formation of the cyclone is generated using WRF ARW standard-release model. Sensitivity of the model output is obtained from a selected single-parameter change scenarios, namely, 10 % to 20 % decrease and increase of wind shear initial data at 850-200 hPa, and by 10 % to 20 % decrease of relative humidity initial data at 850-700 hPa. The result showed that the negative correlations between wind shear and intensity are found in wind shear scenarios. Wind shears of 10 ms-1 which lead to strengthening of the wind intensity in the early period of Typhoon development are found in wind shear scenarios. The effect of wind shear changes on wind intensity is statistically significant in the 20 % wind shear scenarios. During mature stage, weak wind intensity occurred when wind shear increase as given in the WRF standard-release and the 20 % decreasing scenario. Different situation is found in the 20 % increasing scenario where wind shear tend to weak and lead to strong wind intensity at this stage. Meanwhile, the reduction of moisture supply at 850-700 hPa resulting from 20 % decreasing relative humidity play a major role in the weakening of wind intensity and reduces mechanical energy of the cycle process as much as 300 J kg-1.
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