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Journal : MATEMATIKA

ANALISIS KEKONTINUAN, KETERDIFERENSIALAN DAN KETERINTEGRALAN FUNGSI BLANCMANGE Soelistyo, Robertus Heri; Sumanto, YD
MATEMATIKA Vol 14, No 2 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

. This article presents differentiable characteristics of the Blancmange function on ℝ. The function has singularities of each point on ℝ. The first, it will be proven  that function is continuous at each point on ℝ, and then by constructing of an infinite series of the saw tooth function, will be proven that the Blancmange function is differentiable nowhere at each point on ℝ. At the end of this article, also discussed integrable analysis of Blancmange function.  
ANALISIS KESTABILAN MODEL PENYEBARAN VIRUS EBOLA Muntoyimah, Nok; Widowati, Widowati; Sumanto, YD
MATEMATIKA Vol 20, No 2 (2017): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

The Ebola virus disease is caused by the Ebola Virus Deceased (EVD), it belongs to the Fioviridae virus family. Ebola virus can be transmitted through direct contact with infected bodily fluids, organ secretions, blood, and surfaces or objects contaminated by the virus. The spread of the Ebola virus is examined in the form  of mathematical models of SEIR-D (Suspectible, Exposed, Infected, Recovery, Death). The value of the basic reproduction number ( ) was calculated to determine the spread of the Ebola virus. Then, look for disease-free equilibrium and endemic equilibrium and stability analysis of equilibrium points. Numerical simulations performed by entering the initial values and parameter values. From the numerical analysis it is known that the basic reproduction number  so that the stability point of disease-free equilibrium model of the Ebola virus is not stable, whereas the stability of endemic equilibirum point of the model ebola virus is locally asymptotically stable, which means it has spread ebola virus.
SOLUSI PERSAMAAN DIOPHANTINE DENGAN IDENTITAS BILANGAN FIBONACCI DAN BILANGAN LUCAS puspitasari, Ayu; Sumanto, YD; Widowati, Widowati
MATEMATIKA Vol 20, No 1 (2017): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

In this paper we propose diophantine equations with the form  and . These equations has integer solutions which can form Fibonacci numbers and Lucas numbers. Integer solutions of the Diophantine equations in the form of Fibonacci number and Lucas number are determined by using recursive formula, Binet?s Formula, and the most important is identity of Fibonacci numbers and Lucas numbers.
RUANG MATRIX LINEAR TRANSLASI INVARIAN PADA RUANG FUNGSI INTEGRAL HENSTOCK-DUNFORD PADA [a,b] Solikhin, Solikhin; Sumanto, YD; Hariyanto, Susilo; Aziz, Abdul
MATEMATIKA Vol 20, No 2 (2017): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

In this paper we study Henstock-Dunford integral on [a,b]. We discuss some properties of the integrable. We will construct norm and matrix on Dunford-Henstock integrable function space, $HD[a,b]$. We obtain that $HD[a,b]$ is linear space. A function $\left\| \,.\, \right\|:HD[a,b]\to R$ defined by $\left\| f \right\|=\underset{\begin{smallmatrix} {{x}^{*}}\in {{X}^{*}} \\ \left\| {{x}^{*}} \right\| \le 1 \end{smallmatrix}}{\mathop{\sup}}\, \\ left( \underset{A\subset[a,b]}{\mathop{\sup}}\,\,\left| \left( H \right) \int \limits_{A}{{{x}^{*}}f} \right| \right)$ for every $f \in HD[a,b]$ is norm on linear space $HD[a,b]$. A function $d:HD[a,b]\times HD[a,b]\to R$ defined by $d\left( f,g \right)=\left\| f-g \right\|$ for every $f,g\in HD[a,b]$ is a matrix on linear space $HD[a,b]$. Further more, linear space $HD[a,b]$ is linear matrix translation invarian space.
KONSTRUKSI INTEGRAL MENGGUNAKAN FUNGSI SEDERHANA – PADA [A,B] Aziz, Abdul; Sumanto, YD
MATEMATIKA Vol 19, No 3 (2016): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

In this paper, weconstruct the ? ?  simple functionusing the ?- fine Perron partition. By this function, we defineintegral, which is called Ho integral.