Judul: Sifat operasi dan eksistensi invers suatu matriks dalam aljabar max-plus
Abstrak: Karya ilmiah ini membahas sifat-sifat operasi dalam aljabar max-plus dan sifat-sifat yang diaplikasikan pada matriks serta eksistensi invers matriks dalam aljabar max-plus. Operasi-operasi matriks yang dapat diaplikasikan dalam aljabar max-plus meliputi operasi penjumlahan dan perkalian antar matriks, matriks transpose, matriks identitas, matriks segi pangkat ke-k, serta perkalian matriks dengan skalar. Sifat- sifat yang berlaku untuk matriks dalam aljabar max-plus yaitu sifat asosiatif (untuk operasi penjumlahan dan perkalian), komutatif (hanya untuk operasi penjumlahan), dan distributif. Eksistensi invers suatu matriks a ∈ dalam aljabar max-plus dapat dipastikan ada jika dan hanya jika a merupakan perkalian matriks permutasi dan matriks diagonal . Max nxn p ( ) i d 
Keyword: matriks, aljabar max-plus

Judul: Sistem Persamaan Linear Pada Aljabar Max-Plus Dan Solusinya
Abstrak: Aljabar max-plus adalah himpunan bilangan real ℝmax = ℝ ∪ {ϵ} yang memenuhi operasi penjumlahan ⊕ dan operasi perkalian ⊗. Aljabar max-plus dapat digunakan untuk menyelesaikan masalah sistem persamaan linear. Sistem persamaan linear pada aljabar max-plus dapat diselesaikan dengan metode matriks diskrepansi. Matriks diskrepansi adalah matriks dengan semua batas atas dari xi dan xi dapat ditemukan dengan cara mengambil minimum kolom ke-j dari matriks tersebut. Metode matriks diskrepansi pada aljabar max-plus digunakan untuk menyelesaikan sistem persamaan linear dengan matriks ukuran n × n dan m × n dimana m < n dan m > n dalam (ℝmax, ⊕, ⊗) sehingga didapatkan sistem persamaan linear pada aljabar max-plus ada yang memiliki satu penyelesaian, penyelesaian tak hingga, ataupun tanpa penyelesaian. Di dalam karya tulis ini ditunjukan bahwa Sistem Pesamaan Linear pada aljabar max-plus dengan matriks ukuran n × n dan m × n, dengan m > n yaitu ada yang memiliki satu penyelesaian, tak hingga penyelesaian ataupun tanpa penyelesaian. Namun Sistem Pesamaan Linear pada aljabar max-plus dengan ukuran matiks m × n, dengan m < n hanya memiliki tak hingga penyelesaian atau tanpa penyelesaian., The max-plus algebra is real numbers of the set ℝmax = ℝ ∪ {ϵ} which is the equipped of additional operation (⊕) and multiplication operation (⊗). Max-plus algebra can be used to solve a problem of system of linear equations. The system of linear equations in max-plus algebra can be solved by the discrepancy matrix method. The discrepancy matrix is a matrix with all the upper bounds of the xi's and that each xi can be found by taking the minimum of the jth column of the matrix. Discrepancy matrix method of the max-plus algebra is used to solve a problem of system of linear equations with matrix n × n and m × m where m < n dan m > n in (ℝmax, ⊕, ⊗) so that there are system of linear equations in max-plus algebra that have one solution, infinite solution, or no solution. In this article is shown that system of linear equations in max-plus algebra with matrix n × n and m × n where m > n that have one solution, infinite solution, or no solution. However the system of linear equations in max-plus algebra with matrix m × n where m < n only have infinite solution or no solution.
Keyword: max-plus algebra, system of linear equations, discrepancy matrix  method

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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