https://myjms.mohe.gov.my/index.php/dismath/issue/feedMenemui Matematik (Discovering Mathematics)2023-11-22T19:46:59+08:00Adem Kilicmandismath13@gmail.comOpen Journal Systems<p><span class="style43">Menemui Matematik (Discovering Mathematics) </span><span class="style42">(ISSN 0126-9003) is open access journal and one of the flagship publications of the Malaysian Mathematical Science Society (PERSAMA) and is published twice a year (one volume per year). It is published jointly by the <a class="style10" href="http://www.persama.org.my/">Malaysian Mathematical Sciences Society</a> and <a class="style10" href="http://www.upm.edu.my/">Universiti Putra Malaysia</a>. It publishes original research papers and survey articles on all areas of pure mathematics, applied mathematics and mathematics education. </span>For the moment there is no publication fee for the article to publish in this journal. The articles of <span class="style1">Discovering Mathematics</span> are included in the following databases/resources:</p> <ul id="BltJournalIndexers"> <li class="style20 show">Zentralblatt MATH</li> <li class="style20 show"><a href="https://scholar.google.com/citations?hl=en&authuser=1&user=xy3-XYUAAAAJ">Google Scholar</a></li> <li class="style20 show"><a href="http://www.myjurnal.my/public/browse.php?page=18&status=1&sort=M&subject=&sub=">MyJurnal</a></li> </ul> <p class="style1"> </p>https://myjms.mohe.gov.my/index.php/dismath/article/view/24491 Predicting Value-at-Risk of Bitcoin and Ethereum Using Extreme Value Theory2023-11-21T16:24:32+08:00Wendy Shinyie Lingsy_ling@upm.edu.mySi Yin Tan202829@student.upm.edu.myFong Peng Limfongpeng@upm.edu.my<p>Extreme value theory (EVT) has been widely used in finance especially when extreme events such as crashes, brakes and peaks occur. EVT focuses on extreme events or situations, which are typically referred to as outliers, and is able to provide better estimation for risk models. Cryptocurrency is a popular but high-risk investment due to its high volatility and occurrence of extreme events. It is difficult and critical to predict the return of cryptocurrency, mainly because of its extreme nature. This research employs two different EVT approaches, namely, block maxima approach and peaks over threshold approach, are used to model the daily extreme returns of Bitcoin and Ethereum by encrypting the left tail of cryptocurrency return distributions. Apart from that, Value-at- Risk (VaR) plays an important role in estimating the investment risk in the financial sector. Therefore, before investing, it is very important to assess the risk of cryptocurrency. In this study, VaR is evaluated by using the age-weighted historical simulation method and normal distribution. This study finds that generalized extreme value distribution using the block maxima approach fits the cryptocurrencies returns data better and normal distribution outperformed other distributions in estimating VaR. In addition, the return levels of Bitcoin and Ethereum indicates that the biggest potential losses that Ethereum will face in the next 100 years is 105.02% higher than that of Bitcoin. The result of VaR estimation also shows that the risk of Ethereum is higher than that of Bitcoin, because its high risk values are 7.03% and 8.46% respectively. The findings in this study can assist investors in understanding the behaviour of the tails in the cryptocurrency market and in making financial decisions.</p>2023-11-19T21:11:11+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/24755 Uncover Weak Keys of RSADemo2 Software Using Batch Greatest Common Divisor Algorithm2023-11-21T16:24:33+08:00Luqman Hakeem Zainul Hisham1200581@student.upm.edu.myMuhammad Asyraf Asbullahma_asyraf@upm.edu.mySaidu Isah Abubakarsiabubakar82@gmail.com<p>RSA encryption is crucial for protecting our privacy and allowing us to transfer information over the internet without being concerned that unauthorised people will see it. RSA encryption can be deemed insecure in a variety of ways. This project focuses on factoring RSA moduli to detect weak RSA keys generated by an RSA simulator software called RSADemo2 (v2.1) (Darby, 2016). The approach used to factor RSA moduli is collecting samples from RSADemo2 and then using the batch-greatest common divisor (gcd) method. In addition, we will be using Maple software to simulate the batch-gcd algorithm on the collected samples.</p>2023-11-19T00:00:00+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/24383 Nanofluid flow between disks in the presence of thermal radiation and heat source: Stability analysis2023-11-21T16:24:33+08:00Rusya Iryanti Yahayarusyairyanti@gmail.comAniza Abd Ghanianiza@upm.edu.myNorihan Md Arifinnorihana@upm.edu.myFadzilah Md Alifadzilahma@upm.edu.mySiti Suzilliana Putri Mohamed Isactsuzilliana@upm.edu.my<p>The internal flow between disks is used in various applications, including rotating machinery, air-cleaning machines, food processing technology, and gas turbine rotors. The present study analyses the nanofluid flow between a non-permeable, stationary disk and a permeable, rotating, shrinking disk. Radiation and heat generation effects are included in the proposed governing partial differential equations and boundary conditions. Then, non-linear ordinary differential equations and boundary conditions are derived through the similarity transformations for numerical computation in MATLAB. Dual solutions from the computation prompted a stability analysis; only the first solution is stable. Enhancing thermal radiation and heat generation parameters reduces and increases the temperature profile throughout the internal flow. Meanwhile, increasing the shrinking parameter and Reynolds number reduces the radial and tangential velocities in some regions close to the stationary, non-permeable disk.</p>2023-11-19T21:45:06+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/24754 On the solution of one-dimensional heat equation with higher-order non-central finite difference method of lines2023-11-21T16:24:34+08:00Gour Chandra Paulpcgour2001@yahoo.comMd. Emran Aliemran.ru.math.bd@gmail.com<p>In this paper, a one-dimensional heat equation with Dirichlet boundary condition is solved using the method of lines where the discretization is made with the help of higher-order noncentral finite difference approximation method. During imposing higher-order approximation method, the specification of the values of the field variable at some exterior points outside the domain are required which are made using proper assumption. It is found that the attained results agree well with the exact solution on the basis of the root mean square errors.</p>2023-11-19T21:58:00+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/23137 Diagonally Multistep Block Method for Solving Volterra Integro-differential Equation with Delay2023-11-21T16:24:34+08:00Nur Auni Baharumaunibaharum@gmail.comZanariah Abdul Majidam_zana@upm.edu.myNorazak Senunorazak@upm.edu.myHaliza Rosaliliza_r@upm.edu.my<p>Volterra integro-differential equation with delay (VIDED) is solved using a diagonally multistep block method (DMB). This study provides the derivation of the DMB utilizing Taylor series with a constant step size strategy for treating the first order VIDED. In predictor-corrector mode, the DMB method combines the predictor and corrector formulae. It approximates two numerical solutions simultaneously within a block. The algorithm for the approximation solution is developed and the Newton-Cotes formulae are adapted in the DMB method to estimate the solution for an integral component. Theoretically, the consistency and zero stability that led to convergence properties are examined. The stability region also has been plotted. The numerical results indicate that the developed method is superior in terms of the number of steps, accuracy and computation time taken.</p>2023-11-19T22:00:55+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/24687 Improved Stochastic Gradient Descent Algorithm with Mean-Gradient Adaptive Stepsize for Solving Large-Scale Optimization Problems2023-11-21T16:24:34+08:00Wah June Leongleongwj@upm.edu.myMunierah Zulkiflimunierahhhh@gmail.comNor Aliza Abd Rahminaliza@upm.edu.my<p>Stochastic gradient descent (SGD) is one of the most common algorithms used in solving large unconstrained optimization problems. It utilizes the concept of classical gradient descent method with modification on the gradient selection. SGD uses random or batch data sets to compute gradient in solving optimization problems. It is an iterative algorithm with descent properties that reduces computational cost by using derivatives of random data points. This paper proposes a new SGD algorithm with modified stepsize that employs function scaling strategy. Particularly, the stepsize parameter is coupled with function scaling by storing the mean of gradients in the denominator. The performance of the method is evaluated based on the ability to reduce function value after each iteration, ability to attain the lowest function value when applied to solve the well-known zebra-strip problem. Our results indicate that the proposed method performed favourable to the existing method.</p>2023-11-19T22:03:25+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/24688 Heat Transfer Characteristics of Boundary Layer Flow on a Non-Linear Porous Shrinking Sheet With Radiation Effect2023-11-22T19:46:59+08:00Fadzilah Md Alifadzilahma@upm.edu.myAhmad Zaim Zuhdi Amranahmadzaimzuhdi@gmail.com<p>This present study investigates the problem of magnetohydrodynamics (MHD) boundary layer flow over a non-linear porous shrinking sheet. This study is also considered the effect of radiation. Firstly, the governing partial differential equations are reduced to ordinary differential equations by similarity transformations. Then, the transformed equations are been solved by using bvp4c method in Matlab solver in order to obtain numerical solutions for various parameters. Parameters involved in this problem are magnetic parameter, non-dimensional controlling parameter, suction parameter, radiation parameter and Prandtl number. The present results earned are being compared with previous published results and it gives a significant agreement between them. It is found that there exist dual solutions. It is also found that the magnetic parameter delays the thermal boundary layer separation, while the non-dimensional controlling parameter enhances the thermal boundary layer separation. It is also observed that the turning point for various values of radiation parameter occurs at the same value. The impact of radiation on the heat transfer rate at the surface becomes lesser when the radiation parameter increases.</p>2023-11-19T22:06:02+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/24686 Survival Analysis of Initial Public Offerings in Malaysia2023-11-21T16:24:35+08:00Fong Peng Limfongpeng@upm.edu.myLee Kwee Siangkweesiangks@gmail.comWendy Ling Shin Yiesy_ling@upm.edu.myYap Hong Keatyaphk@utar.edu.myKek Sie Longslkek@uthm.edu.my<p>This study presents a survival analysis on both existing public listed companies in Bursa Malaysia and future initial public offering (IPO) companies in Malaysia. The analyses includes both types of explanatory variable: financial information and non-financial information within the prospectuses of IPOs. Initially, we validate the proportional hazards assumptions through the Schoenfeld residual test and Kaplan-Meier survival curves. It then is followed by the univariate analyses wherein we use Wald test for continuous explanatory variables, and both Chi-square test and Fisherâ€™s exact test for categorical explanatory variables. We then conduct the multivariate analysis by applying the Cox proportional hazards model for investigating the influence of potential factors on the survival of IPOs in the context of Malaysia. The best-fitted Cox proportional hazards model is obtained via stepwise model selection. The results indicate that the ratio of working capital to gross proceeds, ratio of listing expenses to gross proceeds, return on equity, debt ratio and debt to equity ratio are significantly influence the survival of IPOs in Malaysia.</p>2023-11-19T22:08:21+08:00##submission.copyrightStatement##https://myjms.mohe.gov.my/index.php/dismath/article/view/24695 Modified Multivariate Cumulative Sum Control Chart Based On Robust Estimators2023-11-21T16:24:35+08:00Nazihah Mohd Alinazihanma@upm.edu.myA.S. Razaleedismath13@gmail.comN. Alidismath13@gmail.comN. A. A. Rahmindismath13@gmail.com<p>Multivariate cumulative sum (MCUSUM) control charts are one of the popular tools for monitoring multivariate statistical process control aside from the Hotelling and the multivariate exponentially weighted moving average (MEWMA) control chart. However, these charts are easily affected by outliers or shifts in the dataset. To overcome the problem, this study will integrate several robust approaches to the classical MCUSUM control chart. These approaches used robust location and scale estimator to substitute the usual mean and covariance matrix, respectively into the classical MCUSUM. The two robust location estimators used are the modified one-step M estimator (MOM) and Hodges Lehmann estimator (HL). Then, a scale estimator named Mad<sub>n</sub> was introduced and functioned accordingly to the robust location estimators. Altogether, two robust MCUSUM control charts were proposed. The performance of each control chart was monitored based on their probability in detecting mean shifts. Various conditions were created to investigate the performance of proposed and classical control chart, namely the subgroup size number of quality characteristics and the level mean shifts The simulation results show that all the proposed charts are able to outperform the classical chart in term of their probability of detecting mean shift. This shows that the proposed robust MCUSUM charts can be used as an alternative if outliers or shifts happen to present in the dataset.</p>2023-11-19T22:11:07+08:00##submission.copyrightStatement##