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Majalah Ilmiah Matematika dan Statistika (MIMS)
Published by Universitas Jember
ISSN : 14116669     EISSN : 27229866     DOI : https://doi.org/10.19184
Core Subject : Education,
Mathematics
The aim of this publication is to disseminate the conceptual thoughts or ideas and research results that have been achieved in the area of mathematics and statistics. MIMS, focuses on the development areas sciences of mathematics and statistics as follows: 1. Algebra and Geometry; 2. Analysis and Modelling; 3. Graph Theory and Combinatorics; 4. Computer Science and Big Data; 5. Application of Mathematics and Statistics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 120 Documents
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Determination of Fractal Area of the Koch Snowflake Kamil, Abdul; Hidayat, Rusli; Purnomo, Kosala Dwidja
Majalah Ilmiah Matematika dan Statistika Vol 17 No 1 (2017): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v17i1.23750

Abstract

The Koch Snowflake Island (Koch Snowflake) is composed of three Koch curves rotated by suitable angles and fitted together. The Koch curve is constructed using an iterative procedure beginning with the initiator of the set as the unit line segment. The unit line segment is divided into thirds and the middle third removed, then replaced with equilateral triangle without base. In this article to get formulation of the area fractals Koch Snowflake and its variations, generated by generator equilateral triangle, isosceles triangle and square to the sides of the regular polygon which has n sides.
VARIASI POHON FRAKTAL MENGGUNAKAN L-SYSTEMS Ramdhan, Pradifta Gilang; Purnomo, Kosala D.; Ubaidillah, Firdaus
Majalah Ilmiah Matematika dan Statistika Vol 21 No 2 (2021): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v21i2.25697

Abstract

Fractal tree is simply a trunk and a number of branches, each of which looks like the tree itself. The fractal tree can be generated using the IFS and L-Systems methods. In this article, the author develops fractal tree generation using L-Systems with additional variations. The variations given are in thickness, length, and branch angle. This development is expected to produce more diverse fractal tree patterns. In generating a fractal tree using L-Systems, it begins by determining the letters and symbols to be used. Then determine which axioms should be used. Then the production rules are made together with the determination of the parametric L-Systems. And the last is to determine the probability value for the stochastic L-Systems. In the deterministic L-Systems, thickness variations, length variations, and branch angle variations are carried out. In the variation of branch thickness, if the ratio of the thickness of the left branch is greater than that of the right branch, the fractal tree is skewed to the left. Then in the variation of branch length if the ratio of the length of the left branch is smaller than the ratio of the length of the right branch, the length of the left branch is longer than the length of the right branch. Then at the angle of the branching the smaller the ???? that is included causes the branches to be closer together. The use of stochastic L-Systems can produce more diverse fractal tree patterns, even though they use the same production rules and parameter values
KOMBINASI CAESAR CIPHER DAN REVERSE CIPHER BERDASARKAN CIPHER BLOCK CHAINING Najah, Maulidyah Lailatun; Santoso, Kiswara Agung
Majalah Ilmiah Matematika dan Statistika Vol 21 No 2 (2021): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v21i2.26978

Abstract

Communication in the current era of globalization is very developed. Many applications that can be used to facilitate communication. However, because of this convenience, the security of the information contained in it will be more easily hacked by irresponsible people. Cryptography is the science or art for security message. In cryptography there are two important processes, namely encryption and decryption. The sender's job is to encrypt the message and the receiver's job is to decrypt the message. The key used for this cryptographic process is the Cipher Block Chaining (CBC) operation mode. CBC mode is a very simple operation mode, so additional techniques are needed to make it more secure. The plaintext will be replaced with new plaintext resulting from a combination of Caesar Cipher and Reverse Cipher techniques. The results obtained indicate that the application of plaintext modifications to CBC can improve message security because the keys used are increasingly complex.
DESAIN MOZAIK PADA BINGKAI JAJARAN GENJANG DENGAN MOTIF GEOMETRIS Sakinah, Zulfatus; Juliyanto, Bagus; Ubaidillah, Firdaus
Majalah Ilmiah Matematika dan Statistika Vol 21 No 2 (2021): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v21i2.25337

Abstract

This research is intended to obtain the steps of a parallelogram frame mosaic design with a Pinwheel tile pattern with geometric motifs. The design of the basic shape of the mosaic on the interior of a parallelogram which is then filled with several geometric motifs in the basic shape of the mosaic is the method used in this study. The results obtained from this study are the basic modeling procedure for the mosaic with a parallelogram frame. the first step, setting the second repetition (iteration) pinwheel tile. the second step, dividing the field on the frame into several basic shapes of mosaics. then for the procedure for filling the basic shape of the geometric patterned mosaic with the following steps. First, determine the geometric motifs that match the selected mosaic shapes. Secondly, fill the motif into each basic form. Thirdly, fill colour on the background.
MODELISASI KURSI DENGAN PENGGABUNGAN HASIL DEFORMASI BENDA-BENDA RUANG MENGGUNAKAN KURVA BEZIER Nadzira, Annisa Ayu; Juliyanto, Bagus; Kamsyakawuni, Ahmad
Majalah Ilmiah Matematika dan Statistika Vol 21 No 2 (2021): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v21i2.20733

Abstract

Chairs are needed by humans to do some work, especially students and office workers. The parts contained in the chair are the chair legs, chair legs eats and chair backs. The purpose of this study is to obtain variations in the shape of office chairs using Bezier curves and incorporate the results of deformation of space geometric objects. In modeling this chair, it is divided into several stages, namely first, building the chair leg components. This chair leg component consists of chair wheels, connecting two wheels with tube deformation, modeling the chair leg branch components and modeling chair leg supports. Second, namely the model of the chair leg seat. Chair leg seat consists of regular hexagon prism deformation and regular quadrangle prism deformation. The third is the modelization of the back of the chair by using a rectangular prism model. The result of combining several components of the chair using one modeling axis produces 36 chair models, with special provisions, namely that the seat support parts can only be joined using a tube.
MODELISASI KOTAK TISU DENGAN PENGGABUNGAN KURVA BEZIER, KURVA HERMIT DAN HASIL DEFORMASI BENDA GEOMETRI Safitri, Dian; Juliyanto, Bagus; Ubaidillah, Firdaus
Majalah Ilmiah Matematika dan Statistika Vol 21 No 2 (2021): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v21i2.22818

Abstract

The tissue box is a place to store tissues to make them look neat and protect the tissues from dirt and dust. Tissue boxes are often used in households, restaurants and also as room decorations. Therefore, the shapes of tissue boxes that are being developed are increasingly varied according to consumer interests. The tissue box consists of three main parts, namely the cover, body and base of the box. This research was carried out by developing variations in the shape of the tissue box components using the Bezier curve, the Hermit curve and the results of the deformation of geometric objects. The deformation techniques used are rotation, dilation, and curve interpolation. Tissue box modeling processes are divided into four stages. The first, modeling the tissue box by dividing into three models, namely model A, model B and model C. The second, determining the size of the tissue box components based on the model. The third, modeling tissue box components. Finally, visualizing the results of the tissue box model by combining the components so that a variety of tissue box models are produced.
ANALISIS SURVIVAL DENGAN COX PROPORTIONAL HAZARD PADA KASUS DEMAM TIFOID Baisaku, Nurul Azizah; Jajang, Jajang; Nurhayati, Nunung
Majalah Ilmiah Matematika dan Statistika Vol 22 No 1 (2022): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v22i1.29325

Abstract

A common problem found in survival data is the presence of censored data. The length of hospitalization of Typhoid fever patients until declared cured is one of example of this data. Here, we use Cox regression model to analysis this data. Partial likelihood is one of the methods of estimating parameters for Cox regression model. In many cases of censored data, two objects (patients) have the same length of hospitalization (ties). Therefore, to estimate the parameters of the model must use the right method. Here we used partial likelihood Breslow, Efron, and Exact methods. The study was motivated by how the three methods performed for Cox regression model. The data used for the implementation of these methods is length of hospitalization of Typhoid fever patients at Mekar Sari Hospital-Bekasi in 2020. Based on AIC criteria, we found that exact method is the best model (minimum AIC) for parameter estimation of Cox regression model. Referring to the Cox regression model by using a significance level of 10%, there are five predictor variables that affects the length of patient hospitalization. The five variables are age, vomiting, dirty tongue, hemoglobin, and leukocyte.Keywords: Typhoid fever, Cox regression, Breslow method, Efron method, exact method.MSC2020: 62N02, 62N03
ANALISIS KESTABILAN LOKAL TITIK EKUILIBRIUM MODEL EPIDEMI SEIV DENGAN PERTUMBUHAN LOGISTIK Harianto, Joko; Sari, Inda Puspita
Majalah Ilmiah Matematika dan Statistika Vol 22 No 1 (2022): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v22i1.30174

Abstract

The SEIV model uses population growth which is assumed to follow logistical growth. The model is studied then analyzed. The analysis shows that the non-endemic (disease-free) equilibrium point is locally asymptotically stable when the basic reproduction number less than one, while the endemic equilibrium point is locally asymptotically stable when the basic reproduction number greater than one. Then a numerical simulation was carried out using Maple software to support the results of the local stability analysis of the equilibrium point. Based on numerical simulations, it shows that a disease will disappear from the population when the basic reproduction number less than one and for a long time a disease will remain in the population (still an epidemic) when the basic reproduction number greater than one.Keywords: SEIV model, logistical growth, equilibrium point, basic reproduction numberMSC2020: 92C60
MODEL MATEMATIKA TIPE SEIQR PADA PENYEBARAN PENYAKIT DIFTERI Saltina, Saltina; Achmad, Novianita; Resmawan, Resmawan; Nuha, Agusyarif Rezka
Majalah Ilmiah Matematika dan Statistika Vol 22 No 1 (2022): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v22i1.29337

Abstract

The present work discusses a mathematical model of diphtheria transmission. Diphtheria is an infection of the throat and upper respiratory tract that is caused by bacteria called corynebacterium. The model was developed by adding latent population and death parameter resulted from this infection. The purpose of this study was to construct a mathematical model, analyze the stability of the equilibrium point, and interpret the simulation of the SEIQR mathematical model in the trasnsmission of diphteria. From the constructed model, there were bacis reproduction number () and two equilibrium points, namely disease-free and endemic equilibrium point would be stable if and , respectively. Moreover, a nunerical simulation was carried out to determine the dynamics of the diphteria transmission. The simulation results showed that if the rates of vaccinated propotion and individual are increased, the infaction woud grandually go away from the population. In short, diphteria transmission be prevented by increasing the rate of vaccnation.Keywords: Basic reproduction number, Diphtheria, Equilibrium point, Mathematical model, Numerical simulationMSC2020: 37A99, 37A10, 37C10
DIMENSI METRIK GRAF HASIL OPERASI JEMBATAN DARI CATERPILLAR HOMOGEN DAN POT BUNGA DIPERUMUM Hidayanti, Gusma; Amrullah, Amrullah; Kurniati, Nani; Hayati, Laila
Majalah Ilmiah Matematika dan Statistika Vol 22 No 1 (2022): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v22i1.30350

Abstract

The metric dimension is a concept that has many applications, such as robotic navigation. This concept will distinguish each vertex of a graph based on some vertices. The distinguishing vertices are called the basis of the graph. Let G be a connected graph, the metric dimension, dim(G), is the smallest cardinality of the basis of graph G. On this paper, we present the metric dimensions of the bridge graph of a homogeneous caterpillar graph Cm,n and a generalized flower pot graph $C_p-K_{(q_1, q_2,\cdos,q_p}$. This research was conducted by the approach of structure analysis by location of the bridge vertices, the edge of the bridge, and the order of the graph. The results show that the metric dimensions of the bridge graph are at least can be reduced at most 2, and the maximum values are the same as the value of $m(n-1)+ \sum_{i=1}^p q_i- 2p$.Keywords: Metric dimension, caterpillar, unicyclic, bridgeMSC2020: 05C12

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