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INDONESIA
MATEMATIKA
Published by Universitas Diponegoro
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Articles 300 Documents
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KEBERADAAN SOLUSI PERSAMAAN DIOPHANTIN MATRIKS POLINOMIAL DAN PENYELESAIANNYA MENGGUNAKAN TITIK-TITIK INTERPOLASI Istiani, Laila; Utomo, Robertus Heri
MATEMATIKA Vol 11, No 2 (2008): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Diophantine equation is a matrix polynomial equation of the form . Here, we investigate the existence of the solutions . It can be investigated by using the grestest common right divisors of the matrix . Then, the solutions can be solved by transforming to the form of the polynomial matrix equation . By taking the interpolation points will be obtained the solutions  of degree r.  
BARISAN SIMBOL DAN UKURAN INVARIAN FUNGSI MONOTON SEPOTONG-SEPOTONG KONTINU Kristina Ningrum, Rinurwati
MATEMATIKA Vol 14, No 1 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

. Let  is piecewise continuous monotone function. In this paper we going to construct g-invariant measure from piecewise continuous monotone function g using minus symbol sequences and plus symbol sequences. This space is generalization from invariant measure piecewise linear transformation
KELAS-KELAS BCI-ALJABAR DAN HUBUNGANNYA SATU DENGAN YANG LAIN ., Winarsih; ., Suryoto
MATEMATIKA Vol 17, No 2 (2014): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Several classes of BCI-algebras as the class of weakly implicative BCI-algebras, BCK-algebras, medial BCI-algebras, branchwise implicative BCI-algebras and branchwise commutative BCI-algebras have relation one another. A branchwise implicative BCI-algebras is a class of BCI-algebras which to fulfill condition of branchwise implicative. By using characters of the class of BCK-algebras and element of the class of medial BCI-algebras, we investigate relations between branchwise implicative BCI-algebras exist with others classes of the class of BCI-algebras as the class of weakly implicative BCI-algebras and branchwise commutative BCI-algebras.
SUBRUANG MARKED suryoto, Suryoto
MATEMATIKA Vol 4, No 1 (2001): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Misalkan V suatu ruang vektor berdimensi hingga atas lapangan kompleks C, T operator linier nilpoten pada V dan  W subruang T-invariant dari V. W dikatakan marked jika terdapat basis Jordan untuk W yang dapat diperluas menjadi basis Jordan untuk V. Dalam tulisan ini ditunjukkan bahwa suatu basis Jordan untuk W dapat diperluas menjadi basis Jordan untuk V jika dan hanya jika basis tersebut mempunyai sifat ketetapan dan sifat kedalaman. Syarat perlu dan cukup suatu subruang T-invariant adalah marked juga diberikan secara geometri dengan memanfaatkan Inti dan Peta dari T.  
PERAMALAN VOLATILITAS INDEKS HARGA SAHAM MENGGUNAKAN MODEL ASIMETRIK GARCH (GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY) DENGAN DISTRIBUSI SKEWED STUDENT-t Wahyuni, Susi Tri; Iriawan, Nur; AW, Dwi Atmono
MATEMATIKA Vol 8, No 1 (2005): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

The condition of Indonesian economic in the last fiew years fluctuatics following  konjungtur cycle. Besides in economic problem, non economic problem such as social and politic are also influence that fluctuation. It means, the instability had influenced of stock exchange practition in analyzing and predicting return. Financial data, such as stock exchange price indices often has heteroscedasticity. One of modeling technique to analyze the condition is using GARCH models. Unfortunately, GARCH models often do not fully capture the thick  tails property of high frequency financial time series. To cope this weakness, we’ll an Asymmetric GARCH model will be used. Using Box-Jenkins methods, the Composite Price Indices have mean model ARIMA (10 17 69,1,0). With the same data we can having  GARCH (2,1) model.  The Asymmetric GARCH (AGARCH) model in this research was not properly  proper to model the Composite Price Indices Volatility.
PENGEFEKTIFAN USAHA MEDIS DALAM MEMBATASI EPIDEMI DENGAN KONTROL BANG-BANG cahyadi, heru; ponidi, ponidi
MATEMATIKA Vol 5, No 2 (2002): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Dalam makalah ini akan dibahas mengenai aplikasi kontrol optimal dengan kontrol bang-bang pada efektifitas usaha medis dalam membatasi epidemi. Mula-mula dimodelkan tingkat perubahan jumlah penduduk yang terinfeksi penyakit dengan adanya usaha medis yang dilakukan yang menjadi kendala pada kontrol optimal ini, kemudian dimodelkan fungsi objektif yaitu akan diminimumkannya cost usaha medis dalam membatasi epidemi dengan batas akhir yang ditentukan. Kemudian dengan teori kontrol optimal yang menggunakan kontrol bang-bang akan dihasilkan sistem yang optimal. Dan hasilnya akan disimulasikan dengan kompute menggunakan software Mathlab.
HUBUNGAN ANTARA LOGIKA PROPOSISI DENGAN LOGIKA PREDIKAT (SUATU KAJIAN EPISTEMOLOGIS) Suyitno, Hardi
MATEMATIKA Vol 9, No 2 (2006): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

This paper presents  epistemological studies  of  propositional  logic and  predicate logic. The topic is a part of the dissertation proposal under title “Ëpistemology of Mathematical Logic According to Ludwig Wittgenstein”.   Author is a student of the Doctor Program  of Gajah Mada University,  the majorstudy  is  philosophy. There are some  difference, equality, and relation between propositional  logic and  predicate logic.  Both of them use the same ope-rator, method, and rule of  inference. There are five  operator of logic, that  are  disjunction, conjunction, negation, implication,  and biimplication. The truth value of proposition deter-minated by definition.  There are eighteen rules of  inference, four rules for removing quan-tifiers,  and four rules for  introducing quantifiers. There are two methods of validity test, that are direct proof and indirect proof; and  there is one common method for invalidity test , that is Counter Exampel Method. The basic component of  propositional logic is  simple statement. The basic component of predicate logic is predicate. In the predicate logic beside Counter Exampel Method for invalidity test,  there is another method for invalidity test that is Finite Universe Method.  The conclusion  of this research is  propositional logic  which a part of  predicate logic. If  a form is valid in propositional  logic, then  the form  is valid in predicate logics. Thus scope of predicate logic is wider than propositional logic.  
ANALISA KESTABILAN MODEL SIRC UNTUK INFLUENZA TIPE A sari, Eminugroho Ratna Sari Ratna
MATEMATIKA Vol 12, No 3 (2009): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Influenza is a disease caused by virus that always changes genetically. This paper will explain the spread of influenza type A. We introduce cross-immune (C) class i.e., those that recovered after being infected by different strains of the same viral subtype in the past years. Generally, the mathematical model for the spread of influenza A has two kinds of equilibrium point: free disease equilibrium and endemic equilibrium. Furthermore, the equilibrium point of system is investigated its stability. There is no influenza in the nature if contact rate less than sum of death rate and recovery rate. Then, there is influenza in the nature if contact rate more than sum of death rate and recovery rate    
PENENTUAN TRAJEKTORI KERETA DUBIN MELALUI KONTROL OPTIMUM Tjahjana, Redemtus Heru
MATEMATIKA Vol 15, No 1 (2012): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

This paper addressed the control of a Dubin’s vehicle. The Dubin’s vehicle control design, using the Pontryagin Maximum Principle. The application of this principle, bring the matter to the Hamiltonian system with some partial equations excess conditions, while others do not have any conditions. The difference approach, which used  in this paper to design of the control. This paper solve the problem by transforming the problem into the initial values problem, by finding the best approach to obtain the initial condition equations for some equations that do not have any conditions.
PENGARUH PEMILIHAN ARAH KETETANGGAAN PIKSEL DALAM PROSES WATERMARKING PADA METODE TRANSFORMASI INTEGER Wibawa, Helmie Arif Wibawa
MATEMATIKA Vol 13, No 2 (2010): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

.  Integer transformation as one of the reversible watermarking method can be used to embed the information into the image and be able to recover the original image. This method works on a single color layer by using properties of inter-pixel neighborhood. This paper discusses the influence of the direction selection of the neighborhood when assigning a pair of pixels to the number of saved bits, the maximum payload of quantity and quality of the watermarked image. The tested image is RGB color images. In the observations, the watermarking process performed on the two possible directions then analyze PSNR values of the watermarked image and quantity of data space to embed the information.  

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