cover
Contact Name
Sutrisno
Contact Email
tresno.math@live.undip.ac.id
Phone
-
Journal Mail Official
tresno.math@live.undip.ac.id
Editorial Address
-
Location
Kota semarang,
Jawa tengah
INDONESIA
Journal of Fundamental Mathematics and Applications (JFMA)
Published by Universitas Diponegoro
ISSN : 26216019     EISSN : 26216035     DOI : -
Journal of Fundamental Mathematics and Applications (JFMA), formerly known as Jurnal Matematika dan Komputer, is an indonesian journal published by Department of Mathematics, Diponegoro University, Semarang, Indonesia. In every year, JFMA has been published regularly in 2 scheduled times (on June and November). JFMA is established to highlight the newest update of mathematical researches in both theoretical and applied work. The scope in JFMA is pure mathematics and applied mathematics.
Arjuna Subject : -
Articles 42 Documents
MODUL NEUTROSOFIK KUAT Suryoto, Suryoto; Harjito, Harjito; Udjiani, Titi
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (3015.071 KB) | DOI: 10.14710/jfma.v1i2.15

Abstract

Abstract. Given any neutrosophic ring with unity and a commutatively additive neutrosophic group. Then we can formed a neutrosophic algebraic structure is called a strong neutrosphic module. From the concept of weak neutrosophic module we extend to the concept of strong neutrosophic module. In this paper, also elementary properties of strong neutrosophic module are given.Keywords: commutative neutrosophic group, neutrosophic ring with unity, weak neutrosophic module, strong neutrosophic module Abstrak. Diberikan sebarang ring neutrosofik dengan satuan dan sebuah grup neutrosofik aditif komutatif. Telah di bentuk suatu struktur aljabar neutrosofik yang disebut modul neutrosofik kuat. Dari konsep modul neutrosofik lemah, telah dikembangkan konsep modul neutrosofik kuat. Diberikan juga sifat-sifat dasar dari modul neutrosofik kuat dalam artikel ini.Keywords: Grup neutrosofik komutatif,, ring neutrosofik dengan satuan, modul neutrosofik lemah, modul neutrosofik kuat
PELABELAN TOTAL SUPER TRIMAGIC SISI PADA BEBERAPA GRAF Utomo, R. Heri Soelistyo; Tjahjana, Heru; Irawanto, Bambang; Ratnasari, Lucia
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (981.812 KB) | DOI: 10.14710/jfma.v1i1.4

Abstract

Abstract. This paper is addressed to discuss the edge super trimagic total labeling on some graphs which are corona, double ladder, quadrilateral snake and alternate triangular snake. The main results are the edge super trimagic total label for these graphs. Furthermore, it was prove that corona is a graph with edge super trimagic total labeling, a double ladder with odd ladder is graph with edge super trimagic total labeling, quadrilateral snake is a graph with edge super trimagic total labeling and finally an alternate triangular snake with odd ladder is graph with edge super trimagic total labeling. Abstrak. Dalam artikel ini, dibahas pelabelan total trimagic sisi untuk beberapa graf yaitu graf korona, graf double ladder, graf quadrilateral snake dan graf alternate triangular snake. Hasil utama dalam artikel ini adalah hasil-hasil pelabelan total trimagic sisi untuk graf-graf tersebut. Lebih lanjut, telah dibuktikan bahwa graf korona merupakan graf dengan pelabelan total trimagic sisi, graf double ladder dengan banyak ladder genap merupakan graf dengan pelabelan total trimagic sisi, graf quadrilateral snake merupakan graf dengan pelabelan total trimagic sisi, dan terakhir, graf alternate triangular snake merupakan graf pelabelan total trimagic sisi untuk banyak triangular genap.
MODEL REGRESI LINIER BAYESIAN DENGAN APLIKASI PADA DATA PENUNDAAN PENERBANGAN Lestari, Vemmie Nastiti; Subanar, Subanar
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (3912.594 KB) | DOI: 10.14710/jfma.v1i2.21

Abstract

Abstract. Bayesian linear regression is an approach to linear regression where statistical analysis depend of Bayesian inference. The Bayesian model on big data uses a summary of data statistics as input; Statistical summary can be calculated from each subset, then a statistical summary of the full dataset is obtained from the sum of the summary statistics for each subset. Recent developments in data science and research, produce large datasets that are too large to be analyzed as a whole due to the limitations of computer memory or storage capacity. To overcome this, a program package was introduced from R namely BayesSummaryStatLM for the Bayesian linear regression model with the Markov Chain Monte Carlo implementation that overcomes this limitation. Then the program package from R, ff is used to read data in large datasets while calculating statistics summary. In this study Bayesian linear regression model used with several choices of prior distribution for unknown model parameters, and illustrates in simulation data and real datasets for flight delay data in US 2008. The application of simulation data and flight delay data produces a plot of density functions for the β parameters has a shape resembling a plot of Normal distribution density function, whereas for plot 2 parameters the density function has a shape resembling the plot of Inverse Gamma distribution density function. In the simulation data, the estimator for each parameter produced has a value that approach to the value of the specified parameter (True Value). This is also indicated by the narrow credible interval for each parameters.Keywords: Big Data, Bayesian Method, Markov Chain Monte Carlo, Bayesian Linear Regression, BayesSummaryStatLM.Abstrak. Model Regresi linier Bayesian merupakan pendekatan untuk regresi linier dimana analisis statistik yang dilakukan dalam konteks inferensi Bayesian. Perkembangan terbaru dalam ilmu data dan penelitian, menghasilkan dataset besar yang terlalu besar untuk dianalisis secara keseluruhan karena keterbatasan memori komputer atau kapasitas penyimpanan. Untuk mengatasi hal tersebut diperkenalkan paket program dari R yaitu BayesSummaryStatLM untuk model regresi linier Bayesian dengan implementasi Markov Chain Monte Carlo yang mengatasi keterbatasan ini. Selanjutnya paket program dari R yaitu ff digunakan untuk membaca data pada dataset besar sekaligus menghitung ringkasan statistik. Dalam penelitian ini digunakan model regresi linier Bayesian dengan beberapa pilihan distribusi prior untuk parameter model yang tidak diketahui, dan mengilustrasikannya pada data simulasi dan dataset real yaitu data penundaan penerbangan di US tahun 2008. Penerapan pada data simulasi maupun data penundaan penerbangan menghasilkan plot fungsi densitas untuk parameter ???? memiliki bentuk menyerupai plot fungsi densitas distribusi Normal, sedangkan untuk parameter plot fungsi densitasnya memiliki bentuk menyerupai plot fungsi densitas distribusi Inverse Gamma. Pada data simulasi, penduga untuk masing-masing parameter yang dihasilkan mempunyai nilai yang mendekati nilai parameter yang ditentukan (True Value). Hal ini juga ditunjukkan oleh sempitnya interval kredibel untuk masing-masing parameter. Kata Kunci : Big Data, Metode Bayesian, Markov Chain Monte Carlo, Regresi Linear Bayesian, BayesSummaryStatLM.
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (19.571 KB) | DOI: 10.14710/jfma.v1i1.10

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.
SOLUSI LEMAH MASALAH DIRICHLET PERSAMAAN DIFERENSIAL PARSIAL LINEAR ELIPTIK ORDER DUA Nugraheni, Sekar; Indrati, Christiana Rini
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1024.002 KB) | DOI: 10.14710/jfma.v1i1.2

Abstract

Abstract. The weak solution is one of solutions of the partial differential equations, that is generated from derivative of the distribution. In particular, the definition of a weak solution of the Dirichlet problem for second order linear elliptic partial differential equations is constructed by the definition and the characteristics of Sobolev spaces on Lipschitz domain in . By using the Lax Milgram Theorem, Alternative Fredholm Theorem and Maximum Principle Theorem, we derived the sufficient conditions to ensure the uniqueness of the weak solution of Dirichlet problem for second order linear elliptic partial differential equations. Furthermore, we discussed the eigenvalue of Dirichlet problem for second order linear elliptic partial differential equations with  respect to the weak solution. Abstrak. Solusi lemah merupakan salah satu jenis penyelesaian persamaan diferensial parsial yang didasarkan pada derivatif distribusi. Pada paper ini pendefinisian solusi lemah dibangun berdasarkan definisi dan karakteristik ruang Sobolev.  Untuk penentuan syarat batas ditentukan berdasarkan salah satu sifat anggota ruang Sobolev pada domain Lipschitz di R^n. Selanjutnya, dengan memanfaatkan Teorema Lax-Milgram, Teorema Alternatif Fredholm dan Teorema Asas Maksimum, diberikan syarat cukup untuk menjamin ketunggalan solusi lemah masalah Dirichlet persamaan diferensial parsial eliptik order dua. Lebih lanjut, dibahas mengenai nilai eigen masalah Dirichlet persamaan diferensial parsial linear eliptik order dua dalam kaitannya dengan solusi lemahnya.
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (3923.711 KB) | DOI: 10.14710/jfma.v1i2.17

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 $\left\| {{T}^{*}} \right\|=\left\| T \right\|$.
HASIL PERBANDINGAN METODE IMPROVED NEWTON-RAPHSON BERBASIS DEKOMPOSISI ADOMIAN DAN BEBERAPA METODE KLASIK PADA MASALAH PERSAMAAN NON-LINIER Jumawanti, Indah; Sutrisno, Sutrisno; Surarso, Bayu
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (202.819 KB) | DOI: 10.14710/jfma.v1i1.8

Abstract

Abstract. In this paper, we work with ten nonlinear equations to compare a new method in nonlinear equation solving, Improved Newton-Raphson based on Adomian Decomposition method (INR-ADM) that consisting of two types called INR-ADM 1 and INR-ADM 2. The difference between INR-ADM 1 and INR-ADM 2 is on the iteration formula form. From our results, it was showed that INR-ADM 1 and INR-ADM 2 are not always better than classic Newton-Raphson method in term of the iteration number. However, if INR-ADM 1 and INR-ADM 2 are compared to Regula False method and Secant method, they are always better i.e. they had fewer number of iteration. The INR-ADM 1 and INR-ADM 2 had shorter computational time than Regula False method. Furthermore, the computational time of INR-ADM 1 and INR-ADM 2 cannot be claimed that they had shorter or longer if they are compared to Newton-Raphson method and Secant method.Abstrak. Pada artikel ini, kami bekerja dengan sepuluh buah persamaan nonlinier untuk membandingkan hasil dalam penyelesaian persamaan nonlinier dari suatu metode baru bernama Improved Newton-Raphson berbasis dekomposisi Adomian (INR-ADM) yang memuat dua tipe yang disebut INR-ADM 1 dan INR-ADM 2. Perbedaan antara INR-ADM 1 dan INR-ADM 2 terdapat pada bentuk rumus iterasi yang digunakan. Berdasarkan hasil-hasil yang didapatkan, diperoleh bahwa INR-ADM 1 dan INR-ADM 2 adalah tidak selalu lebih baik dibanding Newton-Raphson klasik jika dipandang dari banyak iterasi. Akan tetapi, jika INR-ADM 1 dan INR-ADM 2 dibandingkan dengan metode Regula Falsi dan metode Secant, mereka selalu lebih baik, yaitu banyak iterasinya selalu lebih sedikit. INR-ADM 1 dan INR-ADM 2 memiliki waktu komputasi lebih singkat dibanding Regula Falsi. Lebih lanjut, waktu komputasi INR-ADM 1 dan INR-ADM 2 tidak dapat diklaim apakah mereka selalu lebih singkat atau lebih lama jika dibandingkan dengan Newton Raphson dan Secant.
IMPLEMENTASI LOGIKA FUZZY MAMDANI UNTUK MENENTUKAN KOMPOSISI OPTIMAL PUPUK ORGANIK DAN ANORGANIK NPK PADA TANAMAN MENTIMUN Analistyawan, Fajar Ridwan; Sutrisno, Sutrisno; Zaki, Solichin
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2794.798 KB) | DOI: 10.14710/jfma.v1i2.20

Abstract

Abstract. In this article, we have determined the optimal composition of organic fertilizer and NPK inorganic fertilizer for cucumber plants. We have formulated two fuzzy systems which are fuzzy system 1 and fuzzy system 2. The inputs for fuzzy system 1 are plants’ height and the number of leaves where the output is the growth rate. Fuzzy system 2 had input of growth rate and NPK concentration and output of organic fertilizer concentration. By processing the data using fuzzy system, we have compared the cucumber plant with organic fertilizer and NPK to cucumber plant that was used only NPK fertilizer. The result had shown that the cucumber plant with organic fertilizer and NPK was produced the better outcome than the cucumber plants with NPK only.Keywords: Fuzzy Set, Mamdani Fuzzy Logic, Cucumber, NPK Fertilizer, Organic Fertilizer. Abstrak. Pada artikel ini, telah didapatkan komposisi optimal dari pupuk organik dan pupuk anorganik NPK untuk tumbuhan mentimum. Telah diformulasikan dua sistem fuzzy yang disebut sistem fuzzy 1 dan sistem fuzzy 2. Input untuk sistem fuzzy 1 adalah tinggi tanaman dan banyaknya daun sedangkan outputnya adalah tingkat pertumbuhan. Pada sistem fuzzy 2, inputnya meliputi tingkat pertumbuhan dan konsentrasi NPK sedangkan outputnya adalah konsentrasi pupuk organik. Dengan memproses data pengamatan menggunan sistem fuzzy tersebut, telah diperoleh hasil perbandingan tanaman mentimum dengan pupuk organik dan NPK yang dibandingkan dengan tanaman mentimun yang hanya dipupuk dengan NPK. Hasilnya menunjukkan bahwa tanaman mentimun dengan pupuk organik dan NPK memberikan luaran yang lebih baik daripada tanaman mentimun yang hanya dipupuk dengan NPK. Kata kunci: Himpunan Fuzzy, Logika Fuzzy Mamdani, Mentimun, Pupuk NPK, Pupuk Organik.
IMPLEMENTASI METODE MULTINOMIAL NAÏVE BAYES CLASSIFIER UNTUK ANALISIS SENTIMEN Woro Ningrum, Eva Liyan; Widodo, Aris Puji
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (3440.01 KB) | DOI: 10.14710/jfma.v1i2.18

Abstract

GO-JEK is an information technology-based service consisting of 3 main services, namely GO-JEK, GO-LIFE, and GO-PAY. As time goes by, customer complaints arise about the lack of satisfaction with GO-JEK services. One measure of GO-JEK customer service satisfaction can be acknowledged by way of analyzing sentiments on the data of public opinion twett submitted on the twitter official account, @gojekindonesia. In this research, sentiment analysis was carried out using the Naïve Bayes Classifier learning algorithm. The number of data twitts used is 9987. The twit data is labeled according to the class which includes positive, negative and neutral classes. Then the next process is data preprocessing consisting of cleansing, tokenization, filtering, stemming, and stopword removal. The evaluation method using 10-fold cross validation with the results obtained is precision value of 80%, recall of 80%, f1-score of 80%, maximum accuracy of 82% and average accuracy of 79%.
ANALISIS BEBERAPA TEOREMA KETUNGGALAN TITIK TETAP DI RUANG METRIK MULTIPLIKATIF (MULTIPLICATIVE METRIC SPACES) Malahayati, Malahayati
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1701.971 KB) | DOI: 10.14710/jfma.v1i1.5

Abstract

Abstract. This research was conducted to analyze several theorems about fixed point uniqueness on multiplicative metric space. Firstly, the proof of fixed point uniqueness theorem on complete multiplicative metric space is analyzed with involving multiplicative continuous functions. Then, several fixed point uniqueness theorems is analyzed without involving multiplicative continuous functions. The proof of fixed point uniqueness theorem on complete multiplicative metric space with involving multiplicative continuous functions can be done without requirement of contraction multiplicative mapping. If this mapping is satisfying a condition with involving multiplicative continuous functions then it was proven that it had the unique fixed point. Furthermore, the proof of fixed point uniqueness theorem on complete multiplicative metric space without involving multiplicative continuous functions can be done by requiring the mapping is contraction. Abstrak. Penelitian ini menganalisa beberapa teorema ketunggalan titik tetap di ruang metrik multiplikatif. Pembahasan diawali dengan menganalisa pembuktian teorema ketunggalan titik tetap di ruang metrik multiplikatif lengkap dengan melibatkan bantuan fungsi kontinu multiplikatif. Selanjutnya di analisa beberapa teorema ketunggalan titik tetap tanpa melibatkan fungsi kontinu multiplikatif. Pembuktian teorema ketunggalan titik tetap di ruang metrik multiplikatif lengkap dengan bantuan fungsi kontinu multiplikatif dapat dibuktikan tanpa mensyaratkan pemetaannya kontraksi multiplikatif. Apabila pemetaan tersebut memenuhi suatu kondisi dengan bantuan suatu fungsi kontinu multiplikatif maka terbukti mempunyai titik tetap tunggal. Sedangkan Pembuktian teorema ketunggalan titik tetap di ruang metrik multiplikatif lengkap tanpa bantuan fungsi kontinu multiplikatif dibuktikan dengan mensyaratkan pemetaannya kontraksi.