Let is H a disconnected graph and c is the locating k-coloring of H. The locating-chromatic number of H, denoted by XL
'
(H), is the smallest k such that H admits a locating-coloring with k colors. In this paper, we study the locating-chromatic number of disconnected graph with path P
4 and double stars Sm,n
graph as its components.
In this study, mathematical modeling will be discussed to determine the probabilityof goods purchase based on other goods. Research on this topic is considered to be important and interesting to study because it describes the implementation of applied mathematics by constructing a mathematical model and solving it using an apriori algorithm related to the application of the probability concept. In this case, the apriori algorithm is used to determine the pattern of dependency relationships between goods and other goods so that the probabilityof goods purchase based on other goods can be found. To get the output of this research which is in the form of the mathematical modeling for determining the probability of goods being purchased depended on the purchase of other goods, then selecting and classifying the types of goods based on the sales, using the apriori algorithm, constructing models, finding a solution of models and interpreting of the model are conducted.
Abstrak. Opsi Asia adalah opsi yang mempunyai nilai payo bergantung pada ratarataharga saham selama masa opsi berlangsung. Penentuan harga opsi Asia dapatdilakukan dengan pendekatan terhadap rata-rata aritmatik. Karakterisik pendekatanterhadap rata-rata aritmatik adalah ketika harga saham berdistribusi lognormal, ini berartirata-rata aritmatik harga saham tidak berdistribusi normal. Oleh karena itu, hargaopsi Asia dapat ditentukan secara numerik diantaranya dengan simulasi Monte Carlo.Simulasi Monte Carlo memanfaatkan strong law of large dalam perhitungan. Semakinbanyak jumlah simulasi yang dilakukan maka semakin baik pendekatan harga opsi Asiayang diperoleh. Berdasarkan hasil penelitian harga opsi Asia dengan berbagai simulasidiperoleh bahwa harga opsi Asia yang konvergen pada suatu nilai.Kata Kunci: Opsi, Opsi Asia, Rata-rata Aritmatik, Monte Carlo
Abstrak. Dalam makalah ini akan dibahas opsi call tipe Eropa menggunakan metodetrinomial. Metode trinomial memiliki perubahan harga saham yang dipengaruhi olehkoesien naik turun yang relatif sama dengan suku bunga. Permasalahan yang timbuldalam metode ini adalah persamaan linier yang digunakan overdetermined. Persamaanyang overdetermined diselesaikan dengan menggunakan invers semu (pseudoinverse).
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