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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Arjuna Subject : -
Articles 438 Documents
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GSTAR-X-SUR Model with Neural Network Approach on Residuals Rosyida, Diana; Iiriany, Atiek; Nurjannah, Nurjannah
CAUCHY Vol 5, No 4 (2019): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (665.562 KB) | DOI: 10.18860/ca.v5i4.5647

Abstract

One of the models that combine time and inter-location elements is Generalized Space Time Autoregressive (GSTAR) model. GSTAR model involving exogenous variables is GSTARX model. The exogenous variables which are used in GSTAR model can be both metrical and non-metrical data. Exogenous variable that can be applied into the forecasting of precipitation is non-metrical data which is in a form of precipitation intensity of a certain location. Currently, precipitation possesses patterns and characteristics difficult to identify, and thus can be interpreted as non-linear phenomenon. Non-linear model which is much developed now is neural network. Parameter estimation method employed is Seemingly Unrelated Regression (SUR) model approach, which can solve the correlation between residual models. This current research employed GSTARX-SUR modelling with neural network approach on residuals. The data used in this research were the records of 10-day precipitations in four regions in West Java, namely Cisondari, Lembang, Cianjur, and Gunung Mas, from 2005 to 2015. The GSTARX-SUR NN modelling resulted in precipitation deviation average of the forecast and the actual data at 4.1385 mm. This means that this model can be used as an alternative in forecasting precipitation.
Modification of the Curve and the Surface Polynomial Bezier Using de Casteljau Algorithm Juhari, Juhari
CAUCHY Vol 5, No 4 (2019): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (510.214 KB) | DOI: 10.18860/ca.v5i4.6346

Abstract

Research carried out to obtain a Bezier curve of degree six resulting curvature of the curve is more varied and multifaceted. Stages in formulating applications Bezier surfaces revolution in design, there are three marble objects. First, calculate the parametric representation revolution Bezier surface and shape modification in a number of different forms. Second, formulate Bezier parametric surfaces that are continuously incorporated. Lastly, apply the formula to the design objects using computer simulation. Results marble obtained are Bezier curves of degree six modified version of the Bezier curve of degree five and some form of revolution Bezier surfaces are varied and multifaceted.
On The Local Edge Antimagic Coloring of Corona Product of Path and Cycle Aisyah, Siti; Alfarisi, Ridho; Prihandini, Rafiantika M.; Kristiana, Arika Indah; Christyanti, Ratna Dwi
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (716.577 KB) | DOI: 10.18860/ca.v6i1.8054

Abstract

Let  be a nontrivial and connected graph of vertex set  and edge set  . A bijection  is called a local edge antimagic labeling if for any two adjacent edges  and , where for . Thus, the local edge antimagic labeling induces a proper edge coloring of G if each edge e assigned the color  . The color of each an edge e = uv is assigned bywhich is defined by the sum of label both and vertices  and  . The local edge antimagic chromatic number, denoted by  is the minimum number of colors taken over all colorings induced by local edge antimagic labeling of   . In our paper, we present the local edge antimagic coloring of corona product of path and cycle, namely path corona cycle, cycle corona path, path corona path, cycle corona cycle.Keywords: Local antimagic; edge coloring; corona product; path; cycle.
A Discrete Numerical Solution of The SIR Model with Horizontal and Vertical Transmission Fayeldi, Trija
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (883.748 KB) | DOI: 10.18860/ca.v6i1.6413

Abstract

The aim of this paper is to is to generalize the SIR model with horizontal and vertical transmission. In this paper, we develop the discrete version of the model. We use Euler method to approximate numerical solution of the model. We found two equilibrium points, that is disease free and endemic equilibrium points. The existence of these points depend on basic reproduction number R0. We found that if R0 1 then only disease free equilibrium points exists, while both points exists when R0 1. We also found that the stability of these equilibrium points depend on the value of step-size h. Some numerical experiments were presented as illustration.
On the Local Adjacency Metric Dimension of Generalized Petersen Graphs Marsidi, Marsidi; Dafik, Dafik; Agustin, Ika Hesti; Alfarisi, Ridho
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v6i1.6487

Abstract

The local adjacency metric dimension is one of graph topic. Suppose there are three neighboring vertex , ,  in path . Path  is called local if  where each has representation: a is not equals  and  may equals to . Let’s say, .  For an order set of vertices , the adjacency representation of  with respect to  is the ordered -tuple , where  represents the adjacency distance . The distance  defined by 0 if , 1 if  adjacent with , and 2 if  does not adjacent with . The set  is a local adjacency resolving set of  if for every two distinct vertices ,  and  adjacent with y then . A minimum local adjacency resolving set in  is called local adjacency metric basis. The cardinality of vertices in the basis is a local adjacency metric dimension of , denoted by . Next, we investigate the local adjacency metric dimension of generalized petersen graph.
A Finitely Generated Module over a Valuation Domain Mahanani, Dwi Mifta
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (527.899 KB) | DOI: 10.18860/ca.v6i1.6798

Abstract

This article discusses about some properties which are equivalent between a finitely generated module over PID and a finitely generated module over a valuation domain. This can be done by considering a finitely generated module over a DVR. Although in general a PID is not a valuation domain or vice versa, these equivalence of some properties will be valid. It is because a DVR is a PID and a valuation domain at the same time. Those the equivalent properties in a finitely generated module over DVR are related with the decomposition of the module and the height of an element in that module.
Modification of Chaos Game with Rotation Variation on a Square Purnomo, Kosala Dwidja; Larasati, Indry; Agustin, Ika Hesti; Ubaidillah, Firdaus
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v6i1.6936

Abstract

Chaos game is a game of drawing a number of points in a geometric shape using certain rules that are repeated iteratively. Using those rules, a number of points generated and form some pattern. The original chaos game that apply to three vertices yields Sierpinski triangle pattern. Chaos game can be modified by varying a number of rules, such as compression ratio, vertices location, rotation, and many others. In previous studies, modification of chaos games rules have been made on triangles, pentagons, and -facets. Modifications also made in the rule of random or non-random, vertex choosing, and so forth. In this paper we will discuss the chaos game of quadrilateral that are rotated by using an affine transformation with a predetermined compression ratio. Affine transformation is a transformation that uses a matrix to calculate the position of a new object. The compression ratio r used here is 2. It means that the distance of the formation point is  of the fulcrum, that is  = 1/2. Variations of rotation on a square or a quadrilateral in chaos game are done by using several modifications to random and non-random rules with positive and negative angle variations. Finally, results of the formation points in chaos game will be analyzed whether they form a fractal object or not.
The Study Geometry Fractals Designed on Batik Motives Juhari, Juhari
CAUCHY Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (774.811 KB) | DOI: 10.18860/ca.v6i1.8081

Abstract

This research was conducted to gain some patterns of fractals Julia set and Seirpinski that applied on Batik then creating Batik that has many varied motives and multifaceted. There are three steps in formulating the patterns of fractals of Julia set and Seirpinski. First, build the fractals by analyzing the function of fractals Julia set and determine the plane’s coordinate which you want to use. In this case, we use square and rectangle which will be created by using fractals patterns Seirpinski. Second, create a batik motives from fractals pattern Julia set and Seirpinski by using geometry transformation. The geometry transformation which will be used are translation, dilatation, reflection, and rotation. The last, combine some batik motives which were created by using image processing. It was summation of two images processing. The result is batik motives that has many variated and multifaceted.
Mathematical Model Quartic Curve Bezier of Modification Cubic Curve Bezier Juhari, Juhari
CAUCHY Vol 6, No 2 (2020): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (924.278 KB) | DOI: 10.18860/ca.v6i2.9054

Abstract

The creative industries have become the government's attention for contributing to economic accretion. But due to the lack of artistic creativity and appeal, the evolution of the creative industries' craft section is not optimal. So that it was needed a variation of relief items to increase attractiveness. In general, an industrial object's design is still limited to the space geometry objects or a Bezier curve of degree two. Therefore, Bezier curves of degree are selected and modified it into a quartic Bezier forms and then applied to the design of industrial objects (glassware). The purpose of this research is to determine the formula of the quartic Bezier form of cubic Bezier modifications and to determine the rotary surface shape of quartic Bezier from cubic Bezier modifications. Then, from some form of the revolving surface of modified cubic Bezier, the glassware designs are generated. The results of this research are, first, the formula of the quartic Bezier result of Bezier cubic modifications. Second, the form of the revolving surface of modified cubic Bezier which is influenced by five control points P0, NP31, NP32, NP33, P3, and parameter lambda. For further research, it is expected to develop a modification of cubic Bezier into Bezier of degree-n
On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra Kurniadi, Edi
CAUCHY Vol 6, No 2 (2020): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (606.026 KB) | DOI: 10.18860/ca.v6i2.9094

Abstract

In this paper, we study irreducible unitary representations of a real standard filiform Lie group with dimension equals 4 with respect to its basis. To find this representations we apply the orbit method introduced by Kirillov. The corresponding orbit of this representation is genereric orbits of dimension 2. Furthermore, we show that obtained representation of this group is square-integrable. Moreover, in such case , we shall consider its Duflo-Moore operator as multiple of scalar  identity operator. In our case  that scalar is equal to one.

Page 16 of 44 | Total Record : 438

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