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MATEMATIKA
Published by Universitas Diponegoro
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Articles 300 Documents
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MODEL PREDATOR DAN PREY DENGAN MODEL SUSCEPTIBLE - INFECTED – SUSCEPTIBLE HIDAYATI, FIRSTY Nur; SUNARSIH, SUNARSIH
MATEMATIKA Vol 13, No 1 (2010): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

 A predator-prey model with infected prey is an interaction between a predator and a prey population with infected prey. This model is a result of the predator-prey model with logistic growth in the prey population which is combined with Susceptible-Infected-Susceptible (SIS) model in the prey. The equations in this model are non linear differential equation with three dependent variables. In this system, is size of prey population at time , is the fraction of the prey that are infectious at time and is size of predator population at time . It is assumed that infected prey are vulnerable than by a factor . Stability analysis system is done to all five equilibriain this linearized. Each of stability in those equilibria points is based on theeigen values.  
ENDOMORFISMA L0 DARI BCH-ALJABAR Citra, Restia Sarasworo; ., Suryoto
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

BCH-algebras is an algebraic structure which built on a commutative group. In BCH-algebra there is a mapping from this structure to itself which called  a BCH-endomorphism. In BCH-algebra context, we denote L as a set of all left mapping and it contains L0 which the only non-identity BCH-endomorphism in L with some properties : the left map L0 is a center of BCH-endomorphism, L0 both be a periodic mapping dan an epimorphism on BCH-algebra. Such as a group with the fundamental group homomorphism theorem, in a BCH-algebra we have a fundamental BCH-algebra homomorphism theorem.
PERKALIAN BINER BILANGAN N DIGIT DENGAN 3, 4, 5 DAN 6 Sriwasito, Putut
MATEMATIKA Vol 11, No 1 (2008): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

In this paper we discuss about binary multiplication of n digits number with numbers 3, 4, 5 and 6. To dispose of carry in and carry out in union result table of summation and table of multiplication, those operation are related to  half of k.  
APLIKASI SISTEM MULTI AGEN PADA PENGENDALIAN TIGA KAPAL SEKALIGUS Tjahjana, R. Heru
MATEMATIKA Vol 14, No 2 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

This paper presented a problem controlling the three ships as the application of multi-agent system. The multi-agent system model which used in this exposition is linear multi-agent system  and the ship model  which used in this paper is linear ship model from Hocking. The Control design completion for each ship used the optimal control design strategy by utilizing Pontryagin Maximum Principle. This principle leads to the classical problem of optimum control  that treatment using the steepest descent method.  
PROGRAM FRAKSIONAL LINIER DENGAN KOEFISIEN INTERVAL Sari, Annisa Ratna; ., Sunarsih; ., Suryoto
MATEMATIKA Vol 17, No 3 (2014): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Linear fractional programming is a special case of nonlinear programming which the objective function is a ratio of two linear function with linear constraints. Linear fractional programming is used to optimize the efficiency of the activities  of the other activities. In some case, coefficients of the objective function is uncertain. Therefore, It can be selected the interval numbers as coefficients. First step in solving linear fractional programming with interval coefficients in the objective function is transforming it into linear programming using the Charnes - Cooper method. The result of the transformation is linear programming with interval coefficients (LPIC). To solve the LPIC is used method proposed by K Ramadan. In this method, LPIC converted into two linear programming that obtains the best optimum solution and the worst optimum solution, respectively. This optimum solution is the optimum solution for linear fractional programming problem with interval coefficients in the objective function.
SYARAT PERLU LAPANGAN PEMISAH Irawanto, bambang
MATEMATIKA Vol 4, No 2 (2001): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Field is integral domain and is a such that every non-zero elemen in it has multiplicative inverse. Extension field F of field K is splitting field of collections polinomial { fi(x) | i Î I } of K if F is the smallest  subfield  containing K and all the zeros in  of the polinomial fi(x). Elemen a Î F is algebra over K if f (a) = 0 for some 0 ¹ f (x) Î K[x]. Splitting field is extension algebra.
MATRIKS INVERS MOORE PENROSE ATAS DAERAH INTEGRAL SRRM, Titi udjiani
MATEMATIKA Vol 2, No 8 (2005): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

The Inverse Moore Penrose matrix has been applied in various areas, for example in statistic and optimization. In this paper we study Inverse Moore Penrose matrix which is applied to Integral Domain. We will first discuss the characterization of all matrices over Integral Domain which admits Moore Penrose Inverse. With this characterization we will derive  necessary and sufficient conditions for a matrix to have a Moore Penrose Inverse. We also show the relations between Moore Penrose Inverse matrix and Compound matrix. The aim of this paper is to obtain an explicit formula for the Moore Penrose Inverse when it exist and gives a necessary and sufficient condition for a matrix to have a Moore Penrose Inverse under the assumption that a matrix has a rank factorization.  
SIFAT-SIFAT DAN STRUKTUR ALJABAR MATRIKS PENYAJIAN DARI PERSEGI AJAIB Suryoto, Suryoto; Harjito, Harjito; Udjiani, Titi; Puspita, Nikken Prima
MATEMATIKA Vol 20, No 2 (2017): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Penelitian ini membahas sifat-sifat dasar dari persegi ajaib dan struktur aljabar dari himpunan semua matriks penyajian dari persegi ajaib berordo . Struktur aljabar yang dapat dibentuk dari himpunan matriks persegi ini antara lain berupa grup komutatif terhadap operasi penjumlahan matriks, modul atas daerah bilangan bulat , dan juga merupakan ruang vektor (atas lapangan rasional ℚ, lapangan real ℝ maupun lapangan kompleks ℂ). Diberikan pula nilai karakteristik dari matriks persegi ajaib salah satunya adalah konstanta ajaib dari matriks persegi ajaib yang bersangkutan.
OPTIMASI PORTOFOLIO INVESTASI DENGAN MENGGUNAKAN MODEL MARKOWITZ Priyatna, Yayat; Sukono, F
MATEMATIKA Vol 6, No 1 (2003): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Permasalahan pokok dalam paper ini adalah memilih dua saham unggulan dan proporsi dana yang akan diinvestasikan dalam pembentukan suatu portofolio. Optimasi portofolio investasi di sini dilakukan dengan menggunakan model Markowitz. Dari empat saham unggulan versi LQ 45 yang dianalisis menunjukkan bahwa saham HM Sampurna dan Telkom memberikan hasil yang optimum dalam pembentukan portofolio investasi dengan proporsi dana berturut-turut sebesar 51% dan 49%.  
SISTEM PERSAMAAN LINEAR ATAS RING KOMUTATIF SRRM, Titi udjiani
MATEMATIKA Vol 9, No 3 (2006): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Linear systems  equations over commutatif ring are linear systems  equations with the coeffici-ents of these equations are elements from commutatif ring. This paper discusses about basic theorems on solution of linear systems equations over commutatif ring. The basic theorems will be found by using characteristic of ideal ,annihilator and rank of coefficient matrices of linear systems equations over commutatif ring. The ideal  is generated by minors of coefficient matrices of linear systems equations over commutatif ring. Computing the annihilator of ideal we get the rank of coefficient matrices of linear systems equations over commutatif ring

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