YD Sumanto
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Published : 17 Documents
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ANALISIS KESTABILAN MODEL PENYEBARAN VIRUS EBOLA Muntoyimah, Nok; Widowati, Widowati; Sumanto, YD
MATEMATIKA Vol 20, No 2 (2017): JURNAL MATEMATIKA
Publisher : MATEMATIKA

#### 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.
PERLUASAN DARI RING REGULAR Shinta, Devi Anastasia; Sumanto, YD
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

#### Abstract

Regular ring R is a nonempty set with two binary operations that satisfied ring axioms and qualifies for any x in R there is y in R such that x=xyx. Regular ring R ? is a ring of the set of endomorphism R^+ with identity. For any regular ring R and R' can be defined a bijective mapping from R to R' that satisfies ring homomorphism axioms or in the otherwords that mapping is an isomorphism from R to R'. By using the concept of regular ring and ring isomorphism can be determined extension of regular ring. Regular ring R is said to be embedded in regular ring R^R ?  if there exists a subring R^0 of R^R ?  such that R is isomorphic to R^0. Furthermore, regular ring R^R ?  can be said as an extension of regular ring R.
SEMIGRUP- INTRA-REGULAR DAN KETERKAITANNYA DENGAN BI-IDEAL,QUASI-IDEAL, SERTA IDEAL KANAN DAN KIRI Purwandani, Meiliana; Sumanto, YD
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

#### Abstract

. A -semigroup is generalization from semigroup, which concepts in -semigroup analogue with concepts in semigroup. is called a -semigroup if there is a mapping between two nonempty sets  and , written as , such that , for all  and . A -semigroup is said to be intra-regular if contains for all elements of intra regular, is if , for all  and . In this paper, discussed about intra-regular -semigroup and the relation based on bi-ideals, quasi-ideals, and ideals right and left.
SEMINORM PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin, Solikhin; Sumanto, YD; Aziz, Abdul
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 1 (2019): Journal of Fundamental Mathematics and Applications
Publisher : Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University

#### Abstract

Abstract. This article discussed the seminorm on Dunford integrable functional space. We show that the set of all Dunford integrable functions is linear space. The results were shown that ... is a seminorm space with function defined by .... Furthermore, ... is a pseudomatrix space with function defined by .... Abstrak. Pada artikel ini dibahas seminorm pada ruang fungsi terintegral Dunford. Ditunjukkan bahwa koleksi semua fungsi yang terintegral Dunford merupakan ruang linear. Selanjutnya ... merupakan ruang seminorma terhadap seminorma ... dan ... merupakan ruang pseudometrik terhadap pseudometrik ....
OPERATOR ACCRETIVE KUAT PADA RUANG HILBERT Saputro, Razis Aji; Hariyanto, Susilo; Sumanto, YD
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 1 (2018): Journal of Fundamental Mathematics and Applications
Publisher : Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University

#### Abstract

Abstract. Pre-Hilbert space is a vector space equipped with an inner-product. Furthermore, if each Cauchy sequence in a pre-Hilbert space is convergent then it can be said complete and it called as Hilbert space. The accretive operator is a linear operator in a Hilbert space. Accretive operator is occurred if the real part of the corresponding inner product will be equal to zero or positive. Accretive operators are also associated with non-negative self-adjoint operators. Thus, an accretive operator is said to be strict if there is a positive number such that the real part of the inner product will be greater than or equal to that number times to the squared norm value of any vector in the corresponding Hilbert Space. In this paper, we prove that a strict accretive operator is an accretive operator.Abstrak. Ruang Pre-Hilbert merupakan ruang vektor yang dilengkapi dengan perkalian dalam. Lebih lanjut, apabila setiap barisan Cauchy dalam suatu ruang Pre-Hilbert bersifat konvergen maka ia dapat disebut komplit dan ia disebut ruang Hilbert. Operator accretive merupakan operator linier dalam suatu ruang Hilbert. Operator accretive muncul jika bagian real dari perkalian dalam bernilai nol atau positif. Operator Accretive juga berasosiasi dengan operator non-negative self-adjoint. Kemudian, suatu operator accretive dikatakan kuat jika terdapat bilangan positif sedemikian sehingga bagian real dari perkalian dalam bernilai lebih besar atau sama dengan bilangan tersebut dikalikan nilai norma dikuadratkan dari sebarang vektor dalam ruang Hilbert yang bersangkutan. Dalam artikel ini, dibuktikan bahwa suatu operator accretive kuat juga merupakan operator accretive.
OPERATOR PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin, Solikhin; Sumanto, YD; Hariyanto, Susilo; Aziz, Abdul
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018): Journal of Fundamental Mathematics and Applications
Publisher : Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University

#### Abstract

Artikel ini membahas tentang integral Dunford dan operator pada ruang fungsi terintegral Dunford. Diperoleh hasil bahwa ruang fungsi yang terintegral Dunford merupakan ruang linear. Untuk setiap fungsi   yang terintegral Dunford pada $[a,b]$, maka operator $T$  dengan formula $T\left( {{x}^{*}} \right)={{x}^{*}}\left( f \right)$ merupakan operator linear terbatas dan operator kompak lemah. Sedangkan operator adjoint , dengan rumus ${{T}^{*}}\left( g \right)\left( {{x}^{*}} \right)=\int\limits_{a}^{b}{g{{x}^{*}}\left( f \right)}$ juga merupakan operator linear terbatas dan kompak lemah. Operator  kompak lemah jika dan hanya jika operator adjoint ${{T}^{*}}$ kompak lemah. Lebih lanjut $\left\| {{T}^{*}} \right\|=\left\| T \right\|$.
BEBERAPA KARAKTERISTIK BARU PADA FUNGSI TERDEKATI Aziz, Abdul; Sumanto, YD; Solikhin, Solikhin; Utomo, R. Heri Soelistyo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 1 (2019): Journal of Fundamental Mathematics and Applications
Publisher : Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University

#### Abstract

Abstract. In this paper, discuss the relationship between approachable function with bounded variations, measurement, and absolute continuity. Futhermore, If f is approachable function of interval [a, b] then f is a bounded variation function and f is a measurable function of interval [a, b]. In relation with absolute continuity, if f is an absolute continuous of interval [a, b] then f is approachable function of [a, b]. Abstrak. Pada artikel ini, digali keterkaitan antara fungsi terdekati dengan variasi terbatas, keterukuran, dan kekontinuan absolut. Selanjutnya diperoleh bahwa jika f adalah fungsi terdekati pada [a,b] maka f bervariasi terbatas dan terukur pada [a, b]. Dalam kaitannya dengan kekontinuan absolut diperoleh bahwa jika f adalah fungsi yang kontinu absolute pada [a,b] maka f adalah fungsi terdekati pada [a,b].
OPERATOR PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin, Solikhin; Sumanto, YD; Hariyanto, Susilo; Aziz, Abdul
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018): Journal of Fundamental Mathematics and Applications
Publisher : Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University

#### Abstract

Artikel ini membahas tentang integral Dunford dan operator pada ruang fungsi terintegral Dunford. Diperoleh hasil bahwa ruang fungsi yang terintegral Dunford merupakan ruang linear. Untuk setiap fungsi   yang terintegral Dunford pada $[a,b]$, maka operator $T$  dengan formula $T\left( {{x}^{*}} \right)={{x}^{*}}\left( f \right)$ merupakan operator linear terbatas dan operator kompak lemah. Sedangkan operator adjoint , dengan rumus ${{T}^{*}}\left( g \right)\left( {{x}^{*}} \right)=\int\limits_{a}^{b}{g{{x}^{*}}\left( f \right)}$ juga merupakan operator linear terbatas dan kompak lemah. Operator  kompak lemah jika dan hanya jika operator adjoint ${{T}^{*}}$ kompak lemah. Lebih lanjut $\left\| {{T}^{*}} \right\|=\left\| T \right\|$.
FUNGSI TERDEKATI DAN SIFAT-SIFATNYA Aziz, Abdul; Sumanto, YD; Hariyanto, Susilo; Solikhin, Solikhin
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018): Journal of Fundamental Mathematics and Applications
Publisher : Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University

#### Abstract

Abstract. In this paper, we have defined an approachable function using a simple function on a compact sets. Furthermore the simple properties of the function was examined and it was obtained that measurable function, continuous function, and bounded function are approachable function along the function space is a linier space.Keywords: Simple function, Measurable function, Tag partition  Abstrak. Pada artikel ini, didefinisikan fungsi terdekati menggunakan suatu fungsi sederhana pada himpunan kompak. Selanjutnya dikaji sifat – sifat sederhana dari fungsi tersebut dan diperoleh bahwa fungsi terukur, fungsi kontinu, dan fungsi terbatas semuanya merupakan fungsi terdekati serta ruang fungsi tersebut merupakan ruang linier.Kata kunci: Fungsi sederhana, fungsi terukur, partisi tanda
PERLUASAN DARI RING REGULAR Shinta, Devi Anastasia; Sumanto, YD
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

#### Abstract

Regular ring R is a nonempty set with two binary operations that satisfied ring axioms and qualifies for any x in R there is y in R such that x=xyx. Regular ring R ? is a ring of the set of endomorphism R^+ with identity. For any regular ring R and R' can be defined a bijective mapping from R to R' that satisfies ring homomorphism axioms or in the otherwords that mapping is an isomorphism from R to R'. By using the concept of regular ring and ring isomorphism can be determined extension of regular ring. Regular ring R is said to be embedded in regular ring R^R ?  if there exists a subring R^0 of R^R ?  such that R is isomorphic to R^0. Furthermore, regular ring R^R ?  can be said as an extension of regular ring R.