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Journal of Fundamental Mathematics and Applications
Published by Universitas Diponegoro
ISSN : 26216019     EISSN : 26216035     DOI : https://doi.org/10.14710
Core Subject : Science,
Decision Sciences, Operations Research & Management
Journal of Fundamental Mathematics and Applications (JFMA) is an Indonesian journal published by the Department of Mathematics, Diponegoro University, Semarang, Indonesia. JFMA has been published regularly in 2 scheduled times (June and November) every year. JFMA is established to highlight the latest update of mathematical researches in both theoretical and applied works. The scope in JFMA is pure mathematics and applied mathematics. All accepted papers will be published both in print and online versions. The online version can be accessed via the DOI link of each article. The print version can be ordered to the journal administrator. JFMA welcomes both theoretical and applied research work to be published in the journal. The topics include but are not limited to: (1) Mathematical analysis and geometry (2) Algebra and combinatorics (3) Discrete Mathematics (4) Mathematical physics (5) Statistics (6) Numerical method and computation (7) Operation research and optimization (8) Mathematical modeling (9) Mathematical Logic in Computer Science, Informatics, etc.
Arjuna Subject : Matematika - Matematika Terapan
Articles 87 Documents
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TOPOLOGI DI RUANG METRIK PSEUDO-b_s Zahra Aulia Emeralda; Christiana Rini Indrati
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 1 (2021)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1709.561 KB) | DOI: 10.14710/jfma.v4i1.10386

Abstract

Dalam tulisan ini dibahas mengenai beberapa sifat metrik pseudo-$b_s$ dan topologi dalam ruang metrik pseudo-$b_s$ di antaranya kekonvergenan-$b_s$ barisan, barisan Cauchy-$b_s$, ruang metrik pseudo-$b_s$ lengkap, serta himpunan tertutup-$b_s$.
A SECRET SHARING SCHEME BASED ON MULTIVARIATE POLYNOMIALS Ari Dwi Hartanto; Sutjijana Sutjijana
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 2 (2019)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (525.376 KB) | DOI: 10.14710/jfma.v2i2.41

Abstract

A Secret sharing scheme is a method for dividing a secret into several partialinformation. The secret can be reconstructed if a certain number of partial information is collected. One of the known secret sharing schemes is the Shamir’s secret sharing scheme. It uses Lagrange interpolation (with one indeterminate) for reconstructing the secret. In this paper, we present a secret sharing scheme using multivariate polynomials with the secret reconstruction process using the multivariate interpolation formula derived by Saniee (2007). The resulted scheme can be considered as a generalization of the Shamir’s secret sharing scheme.
IMPLEMENTASI KRIPTOGRAFI KURVA ELIPTIK ELGAMAL DI LAPANGAN GALOIS PRIMA PADA PROSES ENKRIPSI DAN DEKRIPSI BERBANTUAN SOFTWARE PYTHON Ummu Wachidatul Latifah; Puguh Wahyu Prasetyo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 1 (2021)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2057.193 KB) | DOI: 10.14710/jfma.v4i1.9278

Abstract

Perkembangan teknologi memberikan dampak terhadap kemajuan di segala bidang kehidupan manusia terutama dalam bidang informasi. Hal ini memberikan dampak positif dan negatif. Salah satu dampak positifnya adalah mudahnya bertukar informasi dari yang bersifat umum atau rahasia melalui internet. Dampak negatifnya adalah data yang bersifat rahasia menjadi kurang aman dan dapat disalahgunakan oleh pihak yang tidak berwenang. Kriptografi kurva eliptik El-Gamal (ECC: Eliptic Curve Cryptosystem) memberikan solusi untuk keamanan suatu informasi. ECC merupakan salah satu metode kriptografi kunci publik yang mempunyai tingkat keamanan tinggi dibandingkan dengan algoritma kunci publik lainnya. Tujuan dari penelitian ini adalah memahami konsep kriptografi kurva eliptik El-Gamal yang akan didefinisikan di Galois field prima. Hasil dari penelitian ini, yaitu penggunaan kurva eliptik El-Gamal di Galois field prima untuk proses pembentukan kunci, proses enkripsi dan proses dekripsi pada suatu data dengan menggunakan Python.
BEBERAPA KELAS RUANG BARISAN SELISIH DIPERUMUM TIPE CESARO Mizan Ahmad
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 1 (2022)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1024.615 KB) | DOI: 10.14710/jfma.v5i1.13285

Abstract

In this paper, we discuss about some classes of Cesaro Generalized differencesequence spaces. We observe their completeness and the relationships betweenthem. At the end of this paper, we construct the Kothe-Toeplitz dual of some class of Cesaro difference sequence spaces.
MODEL REGRESI LINIER BAYESIAN DENGAN APLIKASI PADA DATA PENUNDAAN PENERBANGAN Vemmie Nastiti Lestari; Subanar Subanar
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018)
Publisher : Diponegoro University

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

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  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.
TEOREMA TITIK TETAP FUNGSI YANG KONTRAKSI TEGAS Michael Inuhan; Ch. Rini Indrati
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 2 (2019)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (236.441 KB) | DOI: 10.14710/jfma.v2i2.33

Abstract

In this paper, it will be discussed some fixed point theorems in ultrametric spaces. By using spherically complete properties, it can be shown that there exists a unique fixed point of strictly contractive function. At the end, it will be shown there exists fixed point of strictly contracting on orbits function.
SOLVING THE 106 YEARS OLD 3^k POINTS PROBLEM WITH THE CLOCKWISE-ALGORITHM Marco Ripà
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1907.297 KB) | DOI: 10.14710/jfma.v3i2.8551

Abstract

In this paper, we present the clockwise-algorithm that solves the extension in ????-dimensions of the infamous nine-dot problem, the well known two-dimensional thinking outside the box puzzle. We describe a general strategy that constructively produces minimum length covering trails, for any ???? ∈ N−{0}, solving the NP-complete (3×3×⋯×3)-points problem inside a 3×3×⋯×3 hypercube. In particular, using our algorithm, we explicitly draw different covering trails of minimal length h(????) = (3^???? − 1)/2, for ???? = 3, 4, 5. Furthermore, we conjecture that, for every ???? ≥ 1, it is possible to solve the 3^????-points problem with h(????) lines starting from any of the 3^???? nodes, except from the central one. Finally, we cover 3×3×3 points with a tree of size 12.
DETERMINAN MATRIKS CENTROSYMMETRIC BENTUK KHUSUS ORDO 4×4 BERPANGKAT BILANGAN BULAT POSITIF Ade Novia Rahma; Esty Erizona; Rahmawati Rahmawati
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 1 (2021)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1853.367 KB) | DOI: 10.14710/jfma.v4i1.8921

Abstract

Penelitan ini bertujuan untuk menentukan determinan dari suatu matriks centrosymmetric bentuk khusus ordo  berpangkat bilangan bulat positif. Dalam menentukan determinan matriks centrosymmetric bentuk khusus terdapat beberapa langkah yang perlu dikerjakan. Pertama perhatikan bentuk pola matriks centrosymmetric bentuk khusus  sampai  sehingga didapat bentuk umumnya kemudian dibuktikan dengan induksi matematika. Kedua perhatikan bentuk pola determinan matriks centrosymmetric bentuk khusus  sampai  sehingga didapat bentuk umumnya lalu dibuktikan dengan pembuktian langsung. Hasil akhir dalam penelitian ini diperoleh bentuk umum matriks, determinan dari matriks centrosymmetric berpangkat bilangan bulat positif dengan  ganjil dan  genap.
ANALISIS AKURASI DARI PERBEDAAN FUNGSI KERNEL DAN COST PADA SUPPORT VECTOR MACHINE STUDI KASUS KLASIFIKASI CURAH HUJAN DI JAKARTA Noviana Pratiwi; Yudi Setyawan
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 2 (2021)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1387.13 KB) | DOI: 10.14710/jfma.v4i2.11691

Abstract

Abstrak. Penelitian ini difokuskan pada perbandingan beberapa fungsi kernel, cost dan proporsi data training pada Support Vector Machine terhadap akurasi pengklasifikasian curah hujan di Jakarta. Fungsi-fungsi kernel linier, Gauss dan polynomial digunakan untuk memodifikasi metode Support Vector Machine guna menyelesaikan kasus nonlinier yang sering terjadi pada kondisi real.  Variabel yang digunakan dalam penelitian ini meliputi temperatur, kelembaban, penyinaran matahari dan kecepatan angin. Hasil analisis menunjukkan bahwa nilai support vector terkecil tidak memberikan akurasi yang tertinggi pada masing-masing fungsi kernel. Selain itu, proporsi dataset (training:testing) sebesar  90%:10% memberikan akurasi sedikit lebih tinggi dibandingkan dengan akurasi untuk proporsi 80%:20% untuk masing-masing fungsi kernel. Secara keseluruhan, akurasi tertinggi diperoleh pada proporsi 90%:10% oleh fungsi kernel linier dan polinom untuk cost 1 dan 1000 secara bersamaan yaitu 78,38%.Kata Kunci : Cost, Gauss, Kernel, linear, polynomial, Abstract. This research focuses on the comparison of several kernel functions, costs and proportions of data training on the Support Vector Machine to the accuracy of classifying rainfall in Jakarta. The linear, Gaussian and polynomial kernel functions were applied to modify the Support Vector Machine method to solve non-linear cases that often occur in actual conditions. The variables used in this study comprised of temperature, humidity, sunlight and wind speed. The analysis disclosed that the smallest support vector value did not provide the highest accuracy value for each kernel. In addition, the proportion of the dataset (training:testing) of 90%:10% provided a slightly higher accuracy compared to the accuracy for the proportion of 80%:20% for each kernel function. Overall, the highest accuracy attained at the proportion of 90%:10% by linear and polynomial kernel functions for cost 1 and 1000 simultaneously, which was 78.38%.
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)
Publisher : Diponegoro University

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

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.

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