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Mochamad Tito Julianto
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Milang Journal of Mathematics and Its Applications
Published by Institut Pertanian Bogor
ISSN : -     EISSN : 29635233     DOI : https://doi.org/10.29244/milang.18.1
Core Subject : Science, Education, Agriculture, Engineering,
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Mathematics
The name MILANG is a Sundanese word that means “to count”, and is also an acronym of the topics covered in the journal: Mathematics in Informatics, Life Sciences, Actuarial Science, Natural Sciences, and Graph Theory.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 216 Documents
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IDENTIFIABILITY OF HIDDEN MARKOV MODELS B. SETIAWATY
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 1 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (117.368 KB) | DOI: 10.29244/jmap.4.1.13-22

Abstract

This paper shows that the identifiability problem for hidden Markov models can be derived from the identifiability of finite mixtures.
PENDUGAAN PARAMETER MODEL HIDDEN MARKOV * B. SETIAWATY; L. KRISTINA
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 1 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (372.971 KB) | DOI: 10.29244/jmap.4.1.23-40

Abstract

Pendugaan parameter untuk model Hidden Markov Elliott et. al. (1995) dilakukan mengunakan Metode Maximum Likelihood dan pendugaan ulang menggunakan metode Expectation Maximization yang melibatkan perubahan ukuran. Dari metode tersebut diperoleh algoritma untuk menduga parameter model.
OPTIMAL TRACKING AND REGULATION ACCURACY OF FEEDBACK CONTROL SYSTEMS T. BAKHTIAR
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 1 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (180.795 KB) | DOI: 10.29244/jmap.4.1.41-50

Abstract

This paper deals with intrinsic performance limits achievable by feedback control. We give analytical expressions of the optimal tracking and regulation problems for linear shift- invariant single-input and multiple-output (SIMO) discrete-time systems. For the former, we modify the existing results by means of the delta operator and show that the continuous-time counter- part results can be properly recovered from this point. For the latter, we derive a discrete-time result first and show the conver- gence property.
ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS I W. MANGKU; I. WIDIYASTUTI; I G. P. PURNABA
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 1 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (93.899 KB) | DOI: 10.29244/jmap.4.1.51-57

Abstract

An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established.
A NOTE ON ESTIMATION OF THE GLOBAL INTENSITY OF A CYCLIC POISSON PROCESS IN THE PRESENCE OF LINEAR TREND I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 2 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (130.078 KB) | DOI: 10.29244/jmap.4.2.1-12

Abstract

We construct and investigate a consistent kernel-type nonparametric estimator of the global intensity of a cyclic Poisson process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias and variance of the proposed estimator are computed. Bias reduction of the estimator is also proposed.1991 Mathematics Subject Classification: 60
CELLULAR AUTOMATA SIMULATION OF TRAFFIC LIGHT STRATEGIES IN OPTIMIZING THE TRAFFIC FLOW E. H. NUGRAHANI; R. RAMDHANI
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 2 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (270.983 KB) | DOI: 10.29244/jmap.4.2.13-20

Abstract

The behavior of traffic system controlled by traffic lights is presented under assumptions of city traffic on a single lane based on the optimal velocity model.  The effect of differrent traffic light control strategies on the traffic flow is discussed using three different strategies, i.e. the synchronized, green wave, and random offset strategies. The flow-density diagrams are analyzed using these strategies.   The numerical investigation is carried out using cellular automata model to get a better understanding of the microscopic behavior of the system under the three different traffic light strategies.
PEMODELAN NILAI TUKAR RUPIAH TERHADAP $US MENGGUNAKAN HIDDEN MARKOV* B. SETIAWATY; D. N. SARI
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 2 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (306.056 KB) | DOI: 10.29244/jmap.4.2.21-28

Abstract

Perilaku nilai tukar Rupiah terhadap $US dari tahun 1998 sampai dengan 2005 dicoba dimodelkan dengan menggunakan Hidden Markov (Elliott, et. al. 1995) Pendugaan parameter model dilakukan mengunakan Metode Maximum Likelihood dan pendugaan ulang menggunakan metode Expectation Maximization yang melibatkan perubahan ukuran. Hasil yang diperoleh kurang baik karena galat antara nilai harapan dengan nilai sebenarnya cukup besar.
PENGGUNAAN ALGORITMA COLUMN GENERATION UNTUK MENENTUKAN RUTE OPTIMAL PENGANGKUTAN SAMPAH DI KOTA BOGOR F. HANUM
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 2 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2968.791 KB) | DOI: 10.29244/jmap.4.2.29-44

Abstract

Pengelolaan sampah di kota-kota besar pada saat ini telah menimbulkan persoalan lingkungan yang memerlukan penanganan segera. Jika tidak dikelola dengan baik, maka sampah akan menjadi sumber penyakit, menimbulkan bau busuk, mencemari air tanah, menimbulkan banjir, dan mengurangi keindahan lingkungan. Ada beberapa tahapan pengelolaan sampah yang selama ini dilakukan di beberapa kota di Indonesia yaitu (i) mengumpulkan sampah dari lokasi penghasil sampah (sumber sampah) kemudian diangkut ke TPS (Tempat Penampungan Sementara) sampah, (ii) mengangkut sampah dari TPS-TPS ke TPA (Tempat Pembuangan Akhir) sampah, dan (iii) memusnahkan sampah dengan lahan urug saniter, membakarnya di dalam incenerator, atau mengelola sampah menjadi barang yang dapat dipakai lagi, misalkan kompos, barang-barang keperluan rumah tangga dll. Di kota Bogor, biaya pengangkutan sampah ternyata lebih tinggi dibandingkan dengan biaya komponen lain dalam pengelolaan sampah. Pada penelitian ini, dilakukan pemodelan pengangkutan sampah di kota Bogor dengan capacitated node routing problem dan penentuan solusi optimalnya dengan menggunakan algoritma column generation. 
BIPLOT DAN IMPLEMENTASINYA DENGAN PEMROGRAMAN FUNGSIONAL MATHEMATICA N. K. K. ARDANA; S. SISWADI
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 2 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (5653.802 KB) | DOI: 10.29244/jmap.4.2.45-55

Abstract

Teknik pemrograman fungsional mathematica digunakan untuk mengimplementasikan metode (Gabriel) biplot. Hasil utarna yang diperoleh berupa suatu perintah/fungsi biplot[data, 0, opsi]. Argumen pertama: data berupa data mentah dalam bentuk matriks dan peubah ganda yang terdiri dari n obyek dan p peubah. Argumen a berupa koefisien a € [0,1] pada penguraian nilai singular rnatriks data X = VA V' = (U Aa)( A I-a V')=GH". Nilai a = 0 menghasilkan biplot korelasi, a = 1 menghasilkan biplot jarak Euclid, 0.= 0.5 menghasilkan biplot antara. Kombinasi a, = 1 untuk G dan 0.2 = 0 untuk H menghasilkan biplot kombinasi. Argumen opsi berupa tambahan untuk label titik-titik obyek dan vektor peubah. Perintah biplot akan menghasilkan sekaligus plot obyek yang dinyatakan dengan tebaran titik koordinatnya, dan plot vektor peubah yang dinyatakan dengan garis. Illustrasi kasus nyata berupa biplot pernanfaatan dan pengembangan Teknologi Informasi (TI) pada beberapa negara diberikan untuk melihat tampilan biplot yang dihasilkan beserta interpretasinya.
WEAK AND STRONG CONVERGENCE OF A KERNEL-TYPE ESTIMATOR FOR THE INTENSITY OF A PERIODIC POISSON PROCESSS I W. MANGKU
MILANG Journal of Mathematics and Its Applications Vol. 5 No. 1 (2006): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (132.697 KB) | DOI: 10.29244/jmap.5.1.1-12

Abstract

In this paper we survey some results on weak and strong convergence of kernel type estimators for the intensity of a periodic Poisson process. We consider the situation when the period is known in order to be able to present simple proofs of the results. For the more general results, which includes the case when the period is unknown, we refer to [15], [16].1991 Mathematics Subject Classification: 60G55, 62G05, 62G20.

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