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Jurnal Matematika
Published by Universitas Diponegoro
ISSN : -     EISSN : -     DOI : -
Core Subject : Education,
Mathematics
Arjuna Subject : -
Articles 97 Documents
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PERLUASAN DARI RING REGULAR Devi Anastasia Shinta; YD Sumanto
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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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.
BILANGAN KROMATIK-b DAN KONTINU-b PADA GRAF VERTEX SWITCHING DAN GRAF SPLIT Rahmatika Fajar Safitri
Jurnal Matematika Vol 4, No 4 (2015): (OKTOBER2015)
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

 . Diberikan graf  dengan himpunan titik  dan himpunan sisi . Pewarnaan-b dengan  warna adalah pewarnaan pada titik-titik dari suatu graf sedemikian sehingga untuk setiap kelas warna terdapat sebuah titik yang mempunyai ketetanggaan dengan  kelas warna lainya. Jika titik  dengan suatu kelas warna c mempunyai tetangga dengan semua kelas warna lainya maka titik  disebut color dominating vertex dan dinotasikan dengan . Bilangan bulat terbesar  sedemikian sehingga  memenuhi pewarnaan-b disebut dengan bilangan . Sebuah graf  disebut kontinu-b jika pewarnaan-b ada untuk setiap bilangan bulat  yang nilainya antara bilangan kromatik dan bilangan kromatik-b. Dalam tugas akhir ini akan dikaji mengenai bilangan kromatik-b dan kontinu-b pada graf vertex switching, graf split, dan graf split sisi .Kata Kunci :        .
Pelabelan Product Cordial Graf Gabungan pada Beberapa Graf Sikel dan Shadow Graph Sikel Ana Mawati; Robertus Heri Sulistyo Utomo
Jurnal Matematika Vol 1, No 2 (2012): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

Abtrak Misalkan graf G=V, E , Pelabelan product cordial adalah pelabelan titik biner f:EG→0, 1 yang menginduksi pelabelan sisi f*:EG→0, 1 dengan f*u,v=fu.fv, ∀u, v∈E(G) sehingga memenuhi syarat vf0-vf1≤1 dan ef0-ef1≤1 , dengan vf0,vf1,ef0,ef1 berturut – turut menyatakan banyaknya titik yang berlabel 0, banyaknya titik yang berlabel 1, banyaknya sisi yang berlabel 0 dan banyaknya sisi yang berlabel 1. Path gabungan dari graf G adalah graf yang diperoleh dengan menambahkan sisi antara Gi dan Gi+1 untuk i=1, 2, …, n-1 , dimana G1, G2, …, Gn,  n≥2 dengan n salinan graf G. Shadow graph dari graf sikel dinotasikan dengan D2(Cn) adalah graf yang diperoleh dari dua graf sikel Cn' dan Cn" dengan menghubungkan setiap titik uij'∈Cn' dengan sebuah sisi ke titik yang adjacent dengan uij"∈Cn" (titik uij"∈Cn" adalah bayangan atau shadow dari uij'∈Cn' ). Dalam Tugas Akhir ini dibahas tentang pelabelan product cordial pada beberapa graf sikel serta shadow graph sikel
MODEL DINAMIK PADA SISTEM PROSES PENGOLAHAN AIR LIMBAH KOLAM STABILISASI FAKULTATIF Dian Huliyun Rahmania
Jurnal Matematika Vol 4, No 2 (2015): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

MODEL DINAMIK PADA SISTEM PROSES PENGOLAHAN AIR LIMBAH KOLAM STABILISASI FAKULTATIF                                                           Dian Huliyun Rahmania1, Sunarsih2, Nikken Prima Puspita31,2,3Program Studi Matematika FSM Universitas DiponegoroJl. Prof. H. Soedarto, S.H. Tembalang Semarang dianhuliyun@gmail.comsunarsihmat@gmail.com ABSTRACT. Domestic wastewater is wastewater generated from a household activities that can pollute the environment. If this wastewater pollution did not dealt seriously can cause several problems. To overcome these problems, the wastewater needs to undergo treatment processing in advance. One of the treatment processing system is using units Wastewater Treatment Plant (WWTP). The purpose of this thesis is to contruct dynamic model of wastewater treatment on facultative stabilization ponds in simulating these model and then validate it. The result of model simulation shows that there is an error rate of <10% by comparing model and observation data toward algae, bacteria, dissolved oxygen, and substrate. Model is done numerically using euler method. Keywords: Domestic Wastewater, Facultative Stabilization Ponds, Dynamic Modeling, Euler Method. 
PENYELESAIAN PROGRAM LINIER VARIABEL FUZZY TRIANGULAR MENGGUNAKAN METODE DEKOMPOSISI DAN METODE SIMPLEKS Nanda Puspitasari
Jurnal Matematika JURNAL MATEMATIKA NO 2 2016
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

 ABSTRACT. Fuzzy Variable Linear Programming (FVLP) with triangular fuzzy variable is part of not fully fuzzy linear programming with decision variables and the right side is a fuzzy number. Solving  FVLP with triangular fuzzy variables used Decomposition Methods and Simplex Methods or Big-M Methods by using Robust Ranking to obtain crisp values. Decomposition  Methods of resolving cases maximization and minimization FVLP by dividing the problems into three parts CLP. Solving FVLP with Simplex method for maximizing case and Big-M Methods to directly solve the minimization case FVLP do without confirmation first. The optimal solution fuzzy, crisp optimal solution, optimal objective function fuzzy and crisp optimal objective function  generated from Decomposition Methods and Simplex Methods for maximizing case has same solution. So as Decomposition Methods and Big-M Methods for minimizing case has same solution. Decomposition Methods has a longer process because it divides the problem into three parts CLP and Simplex Methods or Big-M Methods has a fewer processes but more complicated because the process without divide the problems into three parts.Keywords : 
HUBUNGAN BENTUK-BENTUK KHUSUS K-ALJABAR HIPER IMPLIKATIF Ratna Kusuma Ayu; Djuwandi Djuwandi
Jurnal Matematika Vol 2, No 1 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

ABSTRAK.Setiap K-aljabar hiper dapat dipandang sebagai BCK-aljabar dimana peran operasi biner pada BCK-aljabar diambil alih oleh operasi hiper yang berlaku pada K-aljabar hiper. Operasi hiper merupakan pemetaaan dari himpunan ke keluarga himpunan sehingga operasi hiper yang berlaku pada K-aljabar merupakan generalisasi dari operasi biner yang berlaku pada BCK-aljabar. Dalam Tugas Akhir ini, akan dijelaskan Definition-Definition dan teorema-teorema dalam K-aljabar hiper, K-aljabar hiper implikatif, K-aljabar hiper implikatif kuat dan K-aljabar hiper implikatif lemah serta hubungan antara ketiganya.Kata kunci : K-aljabar hiper, K-ideal hiper, K-aljabar hiper implikatif lemah, K-aljabar hiper implikatif kuat.
ANALISIS KEPADATAN LALU LINTAS DI PERLIMAAN JALAN (STUDI KASUS DI JALAN SOEKARNO HATTA-TLOGOSARI-SUPRIYADI-MEDOHO) Ignatia Yolanda Yolanda; Kartono Kartono
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

Pengaturan traffic light di persimpangan jalan diperlukan untuk mengatur kelancaran arus lalu lintas, namun faktanya sering terjadi penumpukan pengguna jalan pada suatu ruas jalan tertentu. Sebagai contoh kondisi arus di persimpangan Jalan Soekarno Hatta-Tlogosari-Supriyadi-Medoho, Kota Semarang sering terjadi penumpukan. Hal ini disebabkan oleh masalah pengaturan waktu tunggu di persimpangan itu, sehingga skripsi ini mengkaji pengaturan waktu tunggu di persimpangan tersebut. Menurut pengamatan salah satu penyebab terjadinya penumpukan tersebut dimungkinkan oleh pengaturan waktu nyala trafficlight. Oleh karena itu, skripsi ini mengkaji perhitungan waktu tunggu dengan mengaplikasikan konsep graf kompatibel. Penerapan konsep graf kompatibel ini untuk melakukan simulasi perekayasaan arus lalu lintas dan hasilnya diperoleh waktu tunggu minimal.
ANALISA KESTABILAN MODEL MATEMATIKA UNTUK PENYEMBUHAN KANKER MENGGUNAKAN ONCOLYTIC VIROTHERAPY Via Novellina Via Novellina
Jurnal Matematika JURNAL MATEMATIKA NO 3 2016
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

 ABSTRACT. Oncolytic virotherapy is one type of cancer treatment using oncolytic virus. In this paper, we will present a mathematical model for treatment of cancer using  oncolytic virotherapy with the burst size of a virus (the number of new viruses released from lysis of an infected cell) and we considering the presence of syncytia which is a fusion between infected tumor cell and uninfected tumor cell. In this mathematical model we introduced the population of uninfected tumor cells which fusion in syncytia. So, in this model contains four population, which are, uninfected tumor cell population, infected tumor cell population, uninfected tumor cell population which fusion in syncytia, and free virus particles which are outside cells. Then, these models are analyzed to determine the stability of the equilibrium points. The stability of the equilibrium points criteria is based on basic reproduction number () and we show that there exist a disease free equilibrium point and a disease endemic equilibrium point. By the Routh-Hurwitz criterion of stability, we prove that the disease free equilibrium point is locally asymptotically stable if  and the disease endemic equilibrium point is locally asymptotically stable if . In this numerical simulations using software Maple we have, if  then the graphic of this mathematical model will reach the disease free equilibrium point, then virotherapy fails. While, if  then the graphic of this mathematical model will reach the disease endemic equilibrium point, then virotherapy success
PELABELAN CORDIAL UNTUK GRAF SPLIT DARI BEBERAPA GRAF Nisa Erma Fitriana; Lucia Ratnasari
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

Cordial labeling is a binary point labeling that have absolute value condition of the difference in the number of vertices having label 0 and the number of vertices having label 1 is less than or equal to 1 dan absolute value of the difference in  the number of edges having label 0 and the number of edges having label 1 is less than or equal to 1. Graph which qualified of cordial labeling is called cordial graph. Split graph S(G) is the graph obtained by taking a new vertex v’ for each vertex v of a graph G , a new vertex v’ is connected to all vertices of G which adjacent to v . In this final paper explored about cordial labeling for split graph of path graph, cycle graph, wheel graph, matching graph, fan graph, bipartite complete graph, and k copies star graph
PENGUJIAN FRACTAL MARKET HYPOTHESIS (FMH) PADA DINAMIKA RETURN HARIAN NILAI TUKAR DOLLAR AMERIKA SERIKAT (USD) TERHADAP YEN JEPANG (JPY) Florenta Florenta; Kartono kartono
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

The concept of Fractal Market Hypothesis (FMH) gives aneconomic and mathematical structure in analyzing the forex market. Fractal has characteristics that are not random, but has a pattern. Fractal experienced recurrence patterns or structures with different scales and sizes, therefore it can show a trend that will occur in the next period.Exchange rate fluctuations cause the trader will have a hard time taking a position of ‘sell’ or ‘buy’. Technical Analysis is the right choice for traders in determining the time to transact. It consists of candlestick analysis in determining the pattern, gradient analysis to determine the level of steepness of exchange rate fluctuations, Rescaled Range analysis (R / S) and the value of Hurst exponent (H) to see characteristics of the return movement, measuring the level of risk (α), measuring the degree of correlation (C) and the fractal dimension (D). In order to complete the final project, the authors do an internship at PT. Futures Monex Investindo Yogyakarta with the data of the exchange rate of United States Dollar (USD) to Japanese Yen (JPY) in the period of January 1, 2005 until December 31, 2013.Based on the results, it can be concluded that the movement of the daily price return of the United States Dollar exchange rate (USD) to Japanese Yen (JPY) result in a system series that is anti-persistent, which means that the series which was up in the previous period, is likely to fall in the next period.

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