Articles
TRANSFORMASI MPWAVELET 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
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DOI: 10.12962/j1829605X.v13i1.1779
Sekarang ini banyak dikembangkan metode penyelesaian masalah secara komputasi. Pada penelitian ini dikonstruksi suatu transformasi wavelet menggunakan operator dalam aljabar maxplus yang disebut sebagai MPWavelet. Hasil konstruksi ini secara komputasi membutuhkan waktu yang lebih cepat daripada transformasi wavelet pada umumnya. Pada konstruksi ini dihasilkan satu tipe MPWavelet yang disebut dengan MPWavelet tipe B. MPWavelet tipa ini merupakan pengembangan dari penelitian Fahim yang dipublikasikan pada âSeminar Nasional Pendidikan Sains Tahun 2014â dan âKonferensi Nasional Matemtika 17â. Tipe B ini digunakan untuk pemampatan citra. Untuk melihat hasil rekonstruksi pada proses pemampatan citra âLenaâ. Dari simulasi pemampatan ini didapatkan bahwa MPWavelet 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
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DOI: 10.5614/itbj.sci.2008.40.2.5
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 bMETRIK 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
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DOI: 10.12962/j1829605X.v13i2.1930
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 bmetrik pada ruang bmetrik cone dan dibuktikan beberapa teorema ekivalensi antara kedua ruang tersebut dengan disertai beberapa contoh terkait, khususnya ruang bmetrik cone bernilai
Syarat Perlu atau Cukup Fbounded di dalam Ruang Metrikα Fuzzy
Lukman Zicky;
Mahmud Yunus
Limits: Journal of Mathematics and Its Applications Vol 19, No 1 (2022)
Publisher : Institut Teknologi Sepuluh Nopember
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DOI: 10.12962/limits.v19i1.12327
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 Fbounded in the fuzzy metric space. The property of Fbounded 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 Fbounded.
Mathematical Modeling of Pressure on Cylindrical Ellipse using SidebySide Conﬁguration
Chairul Imron;
Mahmud Yunus
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 1, No 1 (2015)
Publisher : Institut Teknologi Sepuluh Nopember
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DOI: 10.12962/j24775401.v1i1.1474
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 sidebyside using the NavierStokes equations. NavierStokes equations–incompressible, viscous and unsteadyare solved using finite difference method staggered grid and SIMPLE (Semi Implicit Method for PressureLinked 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 2Normed 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
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DOI: 10.12962/j24775401.v1i1.1475
We introduce an idea of convergent sequence in a cone 2normed space. We show that the convergence in 2normed spaces using the definition of 2norm by considering its dual space. Then we construct the convergence in cone 2normed space, particularly for l2space.
Persistence Analysis on Precoalition Models of H1N1p 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
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DOI: 10.12962/j24775401.v2i2.1583
Influenza virus, H1N1p 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 precoalition between the two viruses. That phenomena is formulated in the form of a precoalition model of the virus. From the original precoalition model, a reduction process is done such that the models can be analyzed easily. Furthermore, the reduced precoalition model will be analyzed (i.e. existence and uniqueness of solutions), so that the system of equations is said to be wellposed. Persistence analysis result shows that in an unstable condition, H1N1p 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 H1N1Pp. This is indicated by the value of epsilon0 in H5N1 virus is smaller than in H1N1p 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
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DOI: 10.14710/jfma.v4i1.10653
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 EggShaped Surface Equations using Hugelschaffer’s EggShaped 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
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DOI: 10.5614/itb.ijp.2015.26.2.2
Hugelschaffer’s eggshaped curve is eggshaped curve that is constructed by two nonconcentric circles using Newton’s transformation known as hyperbolism. This study has goals to construct the eggshaped surface equations using Hugelschafer’s eggshaped curve that is rotated on xaxis, yaxis and zaxis; to get the volume formula of the eggshaped solid and the eggshaped surface area and also to visualize the eggshaped surface equations using GeoGebra. Hugelschaffer’s eggshaped curve is selected because its equation is simple. The procedures of the construction of the eggshaped surface equations are done by drawing the curve on xyplane and xzplane, then it is rotated on axes of the coordinate. Whereas, the volume formula of the eggshaped solid is gotten by using the disk method of the volume integral. The eggshaped surface area is attained by using the integral of surface area. Visualisation of the eggshaped 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
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DOI: 10.12962/j24775401.v9i1.15064
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.