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TRANSFORMASI MP-WAVELET TIPE B DAN APLIKASINYA PADA PEMAMPATAN CITRA Fahim, Kistosil; Yunus, Mahmud; Suharmadi, S
Limits: Journal of Mathematics and Its Applications Vol 13, No 1 (2016)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (890.079 KB) | DOI: 10.12962/j1829605X.v13i1.1779

Abstract

Sekarang ini banyak dikembangkan metode penyelesaian masalah secara komputasi. Pada penelitian ini dikonstruksi suatu transformasi wavelet menggunakan operator dalam aljabar max-plus yang disebut sebagai MP-Wavelet. Hasil konstruksi ini secara komputasi membutuhkan waktu yang lebih cepat daripada transformasi wavelet pada umumnya. Pada konstruksi ini dihasilkan satu tipe MP-Wavelet yang disebut dengan MP-Wavelet tipe B. MP-Wavelet tipa ini merupakan pengembangan dari penelitian Fahim yang dipublikasikan pada “Seminar Nasional Pendidikan Sains Tahun 2014” dan “Konferensi Nasional Matemtika 17”. Tipe B ini digunakan untuk pemampatan citra. Untuk melihat hasil rekonstruksi pada proses pemampatan citra “Lena”. Dari simulasi pemampatan ini didapatkan bahwa MP-Wavelet tipe B ini menghasilkan rekonstruksi citra yang lebih baik daripada tipe I yang dikonstruksi oleh Nobuhara (2010); dan tipe I serta tipe A Fahim (2014).
Tight Wavelet Frame Decomposition and Its Application in Image Processing Mahmud Yunus; Hendra Gunawan
Journal of Mathematical and Fundamental Sciences Vol. 40 No. 2 (2008)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/itbj.sci.2008.40.2.5

Abstract

This paper is devoted to the formulation of a decomposition algorithm using tight wavelet frames, in a multivariate setting. We provide an alternative method for decomposing multivariate functions without accomplishing any tensor product. Furthermore, we give explicit examples of its application in image processing, particularly in edge detection and image denoising. Based on our numerical experiment, we show that the edge detection and the image denoising methods exploiting tight wavelet frame decomposition give better results compare with the other methods provided by MATLAB Image Processing Toolbox and classical wavelet methods.
PEMETAAN KONTRAKTIF PADA RUANG b-METRIK CONE R BERNILAI R^2 Sunarsini Sunarsini; Mahmud Yunus; S Sadjidon; Auda Nuril Zazilah
Limits: Journal of Mathematics and Its Applications Vol 13, No 2 (2016)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (858.146 KB) | DOI: 10.12962/j1829605X.v13i2.1930

Abstract

Ruang b–metrik cone merupakan perluasan dari ruang b–metrik dan ruang metrik cone. Pada paper ini, diselidiki eksistensi dan sifat ketunggalan titik tetap pemetaan kontraktif pada ruang b–metrik cone yang lengkap. Selanjutnya, dikaji fungsi b-metrik pada ruang b-metrik cone dan dibuktikan beberapa teorema ekivalensi antara kedua ruang tersebut dengan disertai beberapa contoh terkait, khususnya ruang b-metrik cone bernilai 
Syarat Perlu atau Cukup F-bounded di dalam Ruang Metrik-α Fuzzy Lukman Zicky; Mahmud Yunus
Limits: Journal of Mathematics and Its Applications Vol 19, No 1 (2022)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v19i1.12327

Abstract

Metrics have an important role in mathematics, both in analysis as well as applications. One of the new concepts of metric space is fuzzy -metric space. This metric space is an expansion of the fuzzy metric space by adding  generator. In this paper, we discuss characterization of F-bounded in the fuzzy -metric space. The property of F-bounded is obtained from the compact subset of a given universe set. This characteristic has been discussed by Changqing and Kedian in Hausdorff fuzzy metric spaces. In this paper, the necessary and sufficient conditions are obtained so that the fuzzy  -metric space satisfies the properties of F-bounded.
Mathematical Modeling of Pressure on Cylindrical Ellipse using Side-by-Side Configuration Chairul Imron; Mahmud Yunus
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 1, No 1 (2015)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (84.451 KB) | DOI: 10.12962/j24775401.v1i1.1474

Abstract

The application of the concept of fluid is often used to solve problems in the daily life. One of them is the problem of fluid around an elliptical cylinder. This study aims to solve the problems of the fluid around two elliptical cylinder configuration with side-by-side using the Navier-Stokes equations. Navier-Stokes equations–incompressible, viscous and unsteady-are solved using finite difference method staggered grid and SIMPLE (Semi Implicit Method for Pressure-Linked Equation) algorithms. Finite difference method is used to complete the grid arrangement, whereas the SIMPLE algorithm is used to obtain components of velocity and pressure value. Results of this study are the pressure value based on fluid flow profile and a mathematical model which received an elliptical cylinder pressure. Profile of fluid flow is simulated by varying the Reynolds number of 100, 1000, 7000, and 10000 as well as variations in the distance between the cylinder with a ratio of 2 <= S/a <= 6 where L is the distance between the cylinder and a is the minor axis of the cylinder ellipse. Then the pressure is calculated based on the value of the received cylinder pressure components. After obtaining the pressure value, then we create a mathematical model of the stresses imposed on the elliptical cylinder.
Construction of Convergent Sequence in Cone 2-Normed Spaces Sadjidon Sadjidon; Mahmud Yunus; Sunarsini Sunarsini
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 1, No 1 (2015)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (46.168 KB) | DOI: 10.12962/j24775401.v1i1.1475

Abstract

We introduce an idea of convergent sequence in a cone 2-normed space. We show that the convergence in 2-normed spaces using the definition of 2-norm by considering its dual space. Then we construct the convergence in cone 2-normed space, particularly for l2-space.
Persistence Analysis on Pre-coalition Models of H1N1-p with H5N1 virus in L 2 Space Hariyanto Hariyanto; Mahmud Yunus; Gusti Yuni Shinta Lestari
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 2, No 2 (2016)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (471.706 KB) | DOI: 10.12962/j24775401.v2i2.1583

Abstract

Influenza virus, H1N1-p and H5N1, are dangerous viruses. Medium of virus transmissions is the interaction or contact between individuals. The virus transmission to other individuals is easy. This happens due to a new strain that occurs as a result of pre-coalition between the two viruses. That phenomena is formulated in the form of a pre-coalition model of the virus. From the original pre-coalition model, a reduction process is done such that the models can be analyzed easily. Furthermore, the reduced pre-coalition model will be analyzed (i.e. existence and uniqueness of solutions), so that the system of equations is said to be well-posed. Persistence analysis result shows that in an unstable condition, H1N1-p influenza virus is “strongly uniformly persistence” over the system under the assumption that the H5N1 influenza virus is in a steady state. A similar result is also true for the H5N1 influenza virus. The H5N1 virus is more pathogenic than the H1N1-P-p. This is indicated by the value of epsilon0 in H5N1 virus is smaller than in H1N1-p virus, where epsilon0 shows the distance of interactions between individuals.
CONDITIONS ON UNIQUENESS OF LIMIT POINT AND COMPLETENESS IN CONE POLYGONAL METRIC SPACES Sie, Evan Setiawan; Mahmud Yunus
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 (1627.506 KB) | DOI: 10.14710/jfma.v4i1.10653

Abstract

This paper discusses cone polygonal metric spaces. We analyze some characteristics derived from convergence and Cauchyness of sequences. Our result consists of some conditions on uniqueness of limit point and completeness in cone polygonal metric spaces.
The Constructions of Egg-Shaped Surface Equations using Hugelschaffer’s Egg-Shaped Curve Ahmat Rif’an Maulana; Mahmud Yunus; Dwi Ratna Sulistyaningrum
Indonesian Journal of Physics Vol 26 No 2 (2015): Vol. 26 No. 2, December 2015
Publisher : Institut Teknologi Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1408.681 KB) | DOI: 10.5614/itb.ijp.2015.26.2.2

Abstract

Hugelschaffer’s egg-shaped curve is egg-shaped curve that is constructed by two non-concentric circles using Newton’s transformation known as hyperbolism. This study has goals to construct the egg-shaped surface equations using Hugelschafer’s egg-shaped curve that is rotated on x-axis, y-axis and z-axis; to get the volume formula of the egg-shaped solid and the egg-shaped surface area and also to visualize the egg-shaped surface equations using GeoGebra. Hugelschaffer’s egg-shaped curve is selected because its equation is simple. The procedures of the construction of the egg-shaped surface equations are done by drawing the curve on xy-plane and xz-plane, then it is rotated on axes of the coordinate. Whereas, the volume formula of the egg-shaped solid is gotten by using the disk method of the volume integral. The egg-shaped surface area is attained by using the integral of surface area. Visualisation of the egg-shaped surface equations are done by choosing vary of parameter values of the equations that aims to know the effect of the parameter values with the shaped surface.
Convergence and Completeness in L_2 (P) with respect to a Partial Metric Annisa Rahmita Soemarsono; Mahmud Yunus; Erna Apriliani; Adam Adam
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 9, No 1 (2023)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.v9i1.15064

Abstract

Metric spaces can be generalized to be partial metric spaces. Partial metric spaces have a unique concept related to a distance. In usual case, there is no distance from two same points. But, we can obtain the distance from two same points in partial metric spaces. It means that the distance is not absolutely zero. Using the basic concept of partial metric spaces, we find analogy between metric spaces and partial metric spaces. We define a metric d^p formed by a partial metric p, with applying characteristics of metric and partial metric. At the beginning, we implement the metric d^p to determine sequences in L_2 (P). We then ensure the convergence and completeness in L_2 [a,b] can be established in L_2 (P). In this study, we conclude that the convergence and completeness in L_2 [a,b]  can be established in L_2 (P) by constructing a partial metric p_2 induced by a metric d^p.