bluuebunny/crossref_metadata_2025_split huggingface dataset:
Unique reconstruction of simple magnetizations from their magnetic potential
Authors: Baratchart L , Gerhards C , Kegeles A , Menzel P 
Published: August 2021

Abstract
Inverse problems arising in (geo)magnetism are typically ill-posed, in particular they exhibit non-uniqueness. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such spaces that accommodate constraints suited for applications. In this paper we treat the inverse magnetization problem on a Lipschitz domain with fairly general topology. We characterize the subspace of L
2-vector fields that causes non-uniqueness, and identify a subspace of harmonic gradients on which the inversion becomes unique. This classification has consequences for applications and we present some of them in the context of geo-sciences. In the second part of the paper, we discuss the space of piecewise constant vector fields. This vector space is too large to make the inversion unique. But as we show, it contains a dense subspace in L
2 on which the problem becomes uniquely solvable, i.e. magnetizations from this subspace are uniquely determined by their magnetic potential.
Correlations and structure of interfaces in the Ising model: theory and numerics
Authors: Squarcini Alessio , Tinti Antonio 
Published: August 2021

Abstract
We consider phase separation on the strip for the two-dimensional Ising model in the near-critical region. Within the framework of field theory, we find exact analytic results for certain two- and three-point correlation functions of the order parameter field. The analytic results for order parameter correlations, energy density profile, subleading corrections and passage probability density of the interface are confirmed by accurate Monte Carlo simulations we performed.
Comparative study of Stochastic Taylor Methods and Derivative-Free Methods for Stochastic Differential Equations
Authors: Fahmi Muhammad , Rosli Norhayati 
Published: August 2021

Abstract
Ordinary differential equations (ODEs) have been widely used to model the dynamical behaviour of biological and physical systems. However, modelling these systems using deterministic model such as ODEs is inadequate as the system is subjected to the uncontrolled factors of environmental noise. Stochastic differential equations (SDEs) which are originating from the irregular Brownian motion can be applied to model such systems that subjected to the uncontrolled factors of noisy behaviour. Numerical methods are required to approximate the solution of the model due to the complexity of the equation. Theoretically, methods with a higher order of convergence lead to a better approximation of the solutions. Though, the implementation of the methods might not reflect the theoretical finding as generating a lot of random numbers might contribute to the instability of the methods. This research is aimed to investigate the performance of stochastic Taylor methods of Euler-Maruyama, Milstein scheme, and derivative-free methods of second and fourth-order stochastic Runge-Kutta in approximating the solution of SDEs. Four types of mathematical models which include the Black-Scholes model, logistic model, stochastic Gompertz model, and prey-predator model are simulated using the aforementioned numerical methods. Numerical solutions of the Black-Scholes model are compared with the analytical solution meanwhile, the numerical solutions of the logistic model and stochastic Gompertz models are compared with the experimental data of the fermentation process and cancer cell growth, respectively. The simulated results of the prey-predator model are compared with the experimental data of the interaction between cancer cells (prey) and anticancer Chrondoitin Sulfate (predator). The prediction performance of the methods is measured using global error and root mean square errors (RMSE).
Implementing the reliability of data information in multi-criteria decision making process based on fuzzy TOPSIS and fuzzy entropy
Authors: Mohd Jamal N.J. , Ku Khalif K.M.N. , Mohamad M.S. 
Published: August 2021

AbstractA multi-criteria decision-making process utilizes real-time data information, which is inherently uncertain and imprecise. To be relevant in the decision-making process, real-time data information must be reliable. Because fuzziness alone is insufficient to solve decision-making problems, measuring the information’s reliability is critical. Z-number, which incorporates both restrictions and reliability in its definition is considered as a powerful tool to depict the imperfect information. In this paper, a new methodology is developed based on fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method and fuzzy entropy for solving the multi-criteria decision-making problems where the weight information for decision makers and criteria is incomplete. The evaluation of the information is represented in the form of linguistic terms and the following calculation is performed using Z-numbers. Fuzzy entropy is applied to determine the weights of the criteria and fuzzy TOPSIS is used to rank the alternatives. An empirical study of subjective well-being of working women is used to demonstrate the proposed methodology.
Stochastic modelling of the oral cancer proliferation and death in the presence of Thymoquinone as anticancer therapeutics
Authors: Tabassum Shabana , Rosli Norhayati , Suriyah Wastuti Hidayati , Ichwan Solachuddin Jauhari Arief 
Published: August 2021

Abstract
Oral cancer is one of the most commonly known cancer worldwide. Thymoquinone (TQ) an extract from Nigella sativa, has clinically been proven as an anticancer therapeutic agent for oral cancer due to its intrinsic pharmacological characteristics. Understanding the mechanisms of oral cancer proliferation and death in the presence of TQ is crucial so that the insight of the interaction of cancer cells and TQ can be discovered. Cancer cells in the presence of TQ is subjected to the uncontrolled factors of the environmental noise. Deterministic model is inadequate to explain this behaviour. Herein, a stochastic model is proposed to illustrate the dynamics of HSC-3 oral cancer cell lines in the presence of TQ. The deterministic model is perturbed with the noisy behaviour which then leads to the stochastic model. The model is simulated by using a four-stage stochastic Runge-Kutta (SRK4) method and the kinetic parameters are estimated by using the maximum likelihood estimation (MLE) method. The prediction quality of the model is measured by using root mean square error (RMSE). The low values of RMSE show the best-fit of the stochastic model.
Performance of 5-stage, 4-stage and specific stochastic Runge-Kutta methods in approximating the solution of stochastic biological model
Authors: Ariffin Noor Amalina Nisa , Rosli Norhayati , Kasim Abdul Rahman Mohd , Mazlan Mazma Syahidatul Ayuni 
Published: August 2021

Abstract
In recent years, the transition on modelling physical systems via stochastic differential equations (SDEs) has attracted great interest among researchers. This is due to the limitations of ordinary differential equations in presenting the real phenomenon. To the fact that the stochastic models incorporate the random effects that may influence the behaviour of physical systems, SDEs seems to be the best model that can be used i n assessing those systems. The growing interest among researchers in modelling the systems via SDEs comes with the rise in the need of numerical methods to approximate the solutions for SDEs. This is because by taking into account the random fluctuations in SDEs resulting to the complexity of finding the exact solution of SDEs. Therefore, it contribute to the increasing number of research to decide on the best numerical approach to solve the systems of SDEs. This paper is devoted to investigate the performance of 5-stage stochastic Runge-Kutta ( SRK5) with order 2.0, 4-stage stochastic Runge-Kutta ( SRK4), specific stochastic Runge-Kutta with order 1.5 ( SRKS1.5) and commutative specific stochastic Runge-Kutta with order 1.5 (SRKST2) in approximating the solution of stochastic model in biological system. A comparative study of SRK5, SRK4, SRKS1.5 and SRKST2 methods will be presented in this paper. The linear SDE model and the stochastic model of C. Acetobutylicum cell growth will be used to examine the performance of those methods and the numerical experiment will be conducted. The numerical solutions obtained will be discussed.
Vector Soliton in Coupled Nonlinear Schrödinger Equation
Authors: Aklan N A B , Ishak N A S , Umarov B A 
Published: August 2021

Abstract
Researchers are currently interested in studying the dynamics of the wave field in a nonlinear and dispersive medium. The Nonlinear Schrödinger Equation (NLSE), which is the fundamental equation that explains the phenomenon, has paved the way for research in a variety of fields, including soliton scattering. However, if the fields have a large number of components, the Coupled NLSE should be considered. We used orthogonally polarised and equal-amplitude vector solitons with two polarization directions to model the interactions. The effect of vector soliton scattering by external Delta potential in Coupled NLSE was studied in this paper. The scattering process is primarily determined by the initial velocity, amplitude of the soliton and potential strength. The variational approximation and direct numerical methods of Coupled NLSE were used to investigate the scattering process. The variational approximation (VA) method was used to analyse the dynamics of soliton’s width and center of mass position. The soliton may thus be reflected, transmitted or trapped within the potential. Uncoupled solitons may initially create a coupled state if their kinetic energy is less than the attractive interaction potential between solitons, but once their velocity surpasses the critical velocity, the soliton will easily pass through each other. To validate the approximation, a direct numerical simulation of CNLSE was performed. The results of the VA method and direct numerical simulation of Coupled NLSE are in good agreement when the parameters for both solutions are set to the same value. The initial velocity, potential strength and soliton amplitude play a role in the scattering of the vector soliton with Delta potential.
Analysis on sustainable manufacturing criteria of automotive industry
Authors: Jalaludin Siti Aisyah , Bakar Sumarni Abu 
Published: August 2021

Abstract
In this paper, criteria within the most significant domain of manufacturing in automotive industry in Malaysia is analysed and prioritized. This paper aims to propose a multi criteria decision making (MCDM) procedure using concept of fuzzy theory, graph theory and Laplacian matrix approach which is embedded into Graph Theory and Matrix approach (GTMA). The manufacturing domains are ranked using Laplacian energy while the criteria within the most significant domain is prioritized using method of graph drawing whereby the criteria’s is ranked based on the average distance among other criteria in Cartesian coordinate system. The result indicates that cost, quality and service in economic domain are among significant criteria’s that practitioners should give an attention in developing a quality sustainable manufacturing framework so that the industry could sustain for a longer period of time.
Directed network of Shariah-compliant stock in Bursa Malaysia
Authors: Musa Muhammad Hasannudin , Razak Fatimah Abdul 
Published: August 2021

Abstract
Stock network is a type of financial network based on stock price data used for analysing stock market dynamics. In this paper, a directed stock network is developed. This model was built using 480 shariah-compliant stocks traded in Bursa Malaysia from the year 2016 until 2018. Transfer Entropy was used as a measuring tool to build the stock network. Different networks are built and evaluated using network analysis methods. To determine the important stocks in the networks, centrality measures are applied such as degree centrality. The findings showed that Borneo Oil Berhad (BRNL) is the most influential and important stock among the 480 shariah-compliant stock in the Bursa Malaysia.
Level set method for free boundary of invasive cancer cell using different functions of matrix metalloproteinases
Authors: Yaacob Noorehan , Shafie Sharidan , Suzuki Takashi , Admon Mohd Ariff 
Published: August 2021

Abstract
The secondary tumor is stated to be more dangerous among cancer patients and this tumor is created through metastasis. Metastasis is the process of spreading a tumor from the primary location to the second part of the human body. This is an unpleasant problem among cancer patients because metastasis can contribute to high mortality cases among them. The presence of finger-like protrusions on the plasma membrane of cancer cells is known as the invadopodia. This structure can contribute to cancer cell invasion through the metastasis process. The formation of invadopodia involves several molecular interactions between extracellular matrix (ECM), ligand, actin, and matrix metalloproteinases (MMPs). The degradation of the ECM by the MMPs is mentioned as the starting point for the occurrence of cancer cell invasion. In this paper, the concentration of MMPs is taken in several functions of g to observe the formation of invadopodia on the plasma membrane. Two-dimensional mathematical model of ligand and signal is solved numerically using the method of level set, ghost fluid with linear extrapolation, and finite-difference. Credit is given to the level set method which successfully detected the movement of the free boundary interface (plasma membrane) by setting the interface as a zero-level set function. Also, the neighboring meshes can be identified using this method. Results showed that the above-mentioned integrated methods effectively describe the movement of the free boundary interface and this directly points out the formation of protrusions on the plasma membrane.
Generalized fuzzy number and graph theory matrix approach in fuzzy decision making of smartphone selection
Authors: Bakar Sumarni Abu , Fauzi Noor Syahida , Rahman Kahartini Abd 
Published: August 2021

Abstract
A number of studies have proposed a method of ranking a smartphone due to the fact that newly smartphones in the market are offering more features which could give more benefit to the user and thus become increasingly important as a tool in helping them to make everyday decisions. But most of the studies have exhibited shortcoming associated to level of confidence of decision makers’ in giving a judgement, which significantly influences final ranking result. This study proposes Graph Theory and Matrix Approach (GTMA) on ranking smartphone alternatives that ensures consideration of uncertainty and confidence level upon their judgement towards smartphone selection. A Generalized Triangular Fuzzy Number (GTFN) is used in the calculation of interrelation matrix which leads to give more meaningful value of importance weights of the attributes. Selection index is then calculated to rank the smartphone through fuzzy determinant. A numerical example is provided to illustrate the proposed approach whereby five well-known smartphones brand are considered which are apple, Samsung, Huawei, OPPO and Asus. The result shows that Huawei is the most preferred brand followed by OPPO and Apple in selecting the best smartphone.
Numerical construction of deformation field in converging channel
Authors: Damanhuri N A , Ayob S , Sabri I S 
Published: August 2021

Abstract
This work proposes the computational method for the construction of the stress field in the deformation region in a converging channel. The stress components are assumed to satisfy Mohr-Coulomb yield criteria under plane strain condition. The governing equation for the model is the first-order partial differential equation, which is the stress equilibrium equations. The deformation region is made up of the union of adjacent elementary boundary value problem and solved numerically. The region is constructed by using Matlab, and it shows the formation of the two symmetrical deformation region at both upper and lower part of the converging channel. From the computation, we obtained the stress variables and the velocity distribution in the deformation region. The work rate for the corresponding velocity was calculated, then it is shown that the solutions are physically significant since the condition of the work rate is everywhere positive. This method is of great interest as it will bring about an increase in efficiency and hence improvement in industrial productivity, especially in designing granular flow device. The technique is also an alternative for the solution of the deformation problems as it is simple and more reliable.
Mathematical modeling on application of wireless networks for industrial automation-factory automation
Authors: Ming W H , Hawari M Z K , Apandi N I 
Published: August 2021

Abstract
Since traditional automation relies on wires, the machines’ versatility will be restricted. Thus maintenance is required to prevent cable wear and breakage, which would be costly and highlighted the importance of wireless connectivity in overcoming some of the limitations of conventional factory automation. Moreover, two of the most critical considerations, reliability and latency, need to be fulfilled so that a factory automation system can perform flawlessly. However, in factory automation, 0ms is the perfect condition since many machines share the same network. Furthermore, it can only reduce latency to a certain extent but not to zero. This study focuses on wireless networks for Industrial Automation Factor Automation’s system architecture, including network devices and topology, and then demonstrates one of the wireless networks’ main technologies, retransmission. This paper develops a mathematical analysis based on Negative Acknowledgement (NACK)-based retransmission mode as default retransmission for field devices to send data frames to the gateway device periodically. The results demonstrate an automatic on-demand retransmission (AODR) scheme able to provide higher efficiency of retransmission rate.
Mathematical foundations of modeling economic indicators
Authors: Abilkayeva Zh N , Gabbassov M B 
Published: August 2021

Abstract
This paper describes the mathematical foundations for modeling multidimensional economic indicators that form a linear space with mathematical operations defined therein, such as addition and multiplication. The concept of factors is introduced as an enumerated type of possible values, as well as the concept of indicators that can depend on factors and have a multidimensional structure. We determined the space of factors and the space of measurements in which the basic arithmetic operations are identified and their properties are proved. Examples of modeling real economic indicators are given on the example of calculating the cost of services for the transportation of goods by rail. An important advantage of using the described abstract mathematical space of meters is the ability to automatically track the integrality or differentiability of economic indicators in the corresponding economic information systems. The proposed mathematical apparatus can be used to solve various economic problems and to design the structure of an economic information systems’ database. References are given to the results of specific projects carried out in the Republic of Kazakhstan, in which the proposed mathematical apparatus is used.
Group decision making-based TODIM under Linguistic Aggregation Majority Additive operator
Authors: Rosli N N N C , Yusoff B , Wahab A F , Madi E N 
Published: August 2021

Abstract
This paper proposes an extension of TODIM (interactive multi-criteria decision making) under group decision making (GDM) using the Linguistic Aggregation Majority Additive (LAMA) operator. TODIM is an effective method in modelling experts’ psychological behaviour in the decision-making process. However, under the GDM, the method is based solely on the average of all experts’ judgments without any consideration to soft aggregation processes that include majority and/or minority concepts. In this work, the LAMA operator is used to be integrated with TODIM-GDM to aggregate the experts’ opinions with respect to the majority concept under the linguistic domain. This is to provide a greater flexibility in reaching a consensus instead of only considering equally average using the classical averaging operators. Two linguistic representations, namely, symbolic approach and 2-tuple linguistic approach for LAMA operator are proposed to be utilised in the method. A numerical example in investment selection problem is provided to illustrate the applicability of the proposed method. Finally, the comparison of these two linguistic approaches is presented. The results show that LAMA under the 2-tuple linguistic approach is preferable to the symbolic approach in case of there is a tie between alternatives in the final ranking.
Numerical solution of third-order Robin boundary value problems using diagonally multistep block method
Authors: Nasir N M , Majid Z A , Ismail F , Bachok N 
Published: August 2021

Abstract
This numerical study exclusively focused on developing a diagonally multistep block method of order five (2DDM5) to get the approximate solution of the third-order Robin boundary value problems directly. The mathematical derivation of the developed 2DDM5 method is by approximating the integrand function with Lagrange interpolation polynomial. The proposed direct integrator scheme was applied to compute numerical solution at two-point concurrently. Shooting technique adapted with the Newtons divided difference interpolation method was implemented throughout the proposed algorithm. The theoretical characteristics of the developed method including the order, consistency, zero-stable and convergence are discussed. The method are tested on four Robin boundary value problems. The numerical results signify that the computational performances of the proposed method is competitive in terms of accuracy and efficiency than the existing method.
Variable step block backward differentiation formula with independent parameter for solving stiff ordinary differential equations
Authors: Zawawi I S M , Ibrahim Z B , Othman K I 
Published: August 2021

Abstract
Over the last decade, the evolution of block backward differentiation formulas (BBDF) has involved the modifications of the formulation techniques in order to solve ordinary differential equations (ODEs). Better still, if the modified methods have the ability of computing solutions efficiently with any prescribed parameter. Therefore, this research focuses on the derivation of 2-point variable step block backward differentiation formulas (VSBBDF) that possesses independent parameter in the coefficients. In this formula, each block contains two points, which compute two approximate solutions simultaneously. Varying the value of parameter will lead to multiple choice of solutions with different level of accuracy. Since the method is derived using variable step size scheme, the strategy in controlling the step size ratio is also discussed. The capability of the derived method is demonstrated by solving initial value problem of stiff ODEs. A comparison of its performance with several existing methods is made to shed light on the superiority and shortcomings of VSBBDF with respect to independent parameter.