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Journal of Mathematical and Fundamental Sciences
Published by Institut Teknologi Bandung
ISSN : 23375760     EISSN : 23385510     DOI : https://doi.org/10.5614/j.math.fund.sci.
Core Subject : Science, Education,
Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics
Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, Biology, Health, Medical, Pharmacy), Mathematics, Physics, and Statistics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 3 Documents
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Search results for , issue "Vol. 2 No. 4 (1963)" : 3 Documents clear
The Photoelectric Instrument at the Bosscha Observatory Santoso Nitisastro
Journal of Mathematical and Fundamental Sciences Vol. 2 No. 4 (1963)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Ichtisar. Sebuah uraian tentang pesawat ptotoelectris photometer di Observatorium Bosscha Lembang, dengan mempergunakan sebuh photomultiplier type 1P21 jang didinginkan dengan es kering atau sebuah multiplier type EMI pada pendinginan telah disadjikan dibawah ini. Photometer tersebut jang diperlengkapi dengan filter2 U, B, V dan R, dipasangkan pada teropong lensa 37 cm Bamberg-Schmidt dan baru dapat dipergunakan untuk menentukan ekstingsi atmosfir untuk Observatorium Bosscha di Lembang pada penghabisan musim terang dalam tahun 1962.Abstract. A description of the photoelectric photometer at the Bosscha Observatory Lembang, operated with a photomultiplier of type IP21 refrigerated with dry ice  or using an EMI-type of multiplier (non-refrigerated) is presented below. The photometer, provided with U, B, V, and R filters and attached to the 37 cm Bamberg-Schmidt refractor, has been used for determining the atmospheric extinction of the Observatory during the last part of the dr season in 1962.
Tindjauan atas Masalah Hubungan Kerdja Praktis dan Pendidikan Kesardjanaan pada Bagian Mesin Institut Teknologi Bandung M. Aroef
Journal of Mathematical and Fundamental Sciences Vol. 2 No. 4 (1963)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Abstract

Tulisan ini dibuat bersandarkan dasar fikiran jang dianut pada Bagian Mesin I.T.B. dalam mentugaskan para mahasiswanja mendjalankan kerdja praktis diberbagai perusahaan industry Indonesia. Kerdja praktis ini adalah dalam rangka pengisiskan para tjalon sardjana teknik mesin jang dinjatakan dalam rentjana peladjarannja. Bahan2 dikumpulkan berdasarkan pertjakapan2 dengan berbagai pihak dalam soal ini selama djangka waktu penulis mendjadi pengurus kerdja praktis pada Bagian Mesin tersebut. Bahan2 pembahasan akan dibagi kedalam golongan2 tindjauan berikut :* Hubungan kerdja praktis dengan pendidikan mahasiswa* Kerdja praktis sebagai penghubung I.T.B. dengan dunia perusahaan.* Kerdja praktis sebagai djalan bagi dunia industri untuk mengenal mahasiswa2 I.T.B. This article reviews the significance of the practical engineering work experience given by the various industries and workshops in Indonesia to the students of Bandung Institute of Technology, especially related to the mechanical engineering education. This review looks upon the problem utilizing the interest of the parties involved as the bases, namely:the interest of the education of the mechanical engineer to bethe interest of Bandung Institute of Technology as an institute of higher engineering learningthe interest of industrial enterprises.It is endeavored to express the viewpoints as clearly as possible  in agreement with the many statements and opinions conceived by the author during many discussion with various parties about this practical engineering  work experience of the mechanical engineering students of Bandung Institute of Technology. The parts of this article concerning these statements and opinions are presented based on memory, and therefore this article is far from being all inclusive. The author is of the opinion that the most important aspects are sufficiently covered in this short article.
Limiting Behavior of A Sequence of Density Ratios Sunardi Wirjosudirdjo
Journal of Mathematical and Fundamental Sciences Vol. 2 No. 4 (1963)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Abstract

Let X1, X2,"¦.. be a sequence of random variables and Ð = {Pθ,θ Є (-)} be a family of distributions of the sequence.  For each n, An is the σ-field generated by X1,"¦, Xn.If θ1,θ2 Ð„ (-), we define Rn (θ1,θ2) as the density ratio of Pθ1,Pθ2 on An.The main purpose of the paper is to investigate limiting behavior of the sequence Rn with respect to any Pθ. This has applications in sequential analysis, where it is desired to know whether a sequential probability ratio test terminates with probability one.  The same conclusion can be drawn in the case of generalized sequential probability ratio test, under some restriction as to how the stopping bounds vary with n.If the Xi are independent and identically distributed, then we can write in Rn  as  where the Yi are independent and identically distributed. We have then that  converges to ~ or to -~ a.e. according as Eθ {Yi}>0 or <0. For any θ, say θ0, for which Eθ0{Yi}=0 we have lim inf Rn="0" and lim sup Rn=~ a.e. Pθ0.A sequence of non-independent nor identically distributed random variables {Xi} may arise in tests of composite hypotheses in the presence of nuisance parameters. An example of the situation is the sequential t-test, by some authors called the WAGR test. In this example we have the same qualitative  result as if the  Xi are independent and identically distributed.The foregoing example suggested the more general problem with the assumption A  and B (see chapters 2 and 3). The result can be described as follows: If θ1 < θ2then Rn converges a.e. to 0 if θ≤θ1 and to ~ if 0 ≥ θ2. For θ between θ1and θ2, except perhaps for one θ0, then lim inf is 0 or lim sup is ~ a.e. So that a sequential probability ratio test terminates with probability one, except perhaps for one value of θ. There is no example known to show  that there may exist a θ0 for which  the sequence density ratios has a positive lim inf and a finite lim sup.

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