Dear colleagues and researchers,
The Journal of the Korean Society for Industrial and Applied Mathematics (J-KSIAM) Volume 26 Number 4 (December 2022 issue) has been posed on KSIAM Journal Archive or other information on the journal is available on the KSIAM website http://www.ksiam.org or https://ksiam.org/journal/journal01.asp.
The journal is one of Korea Citation Indexed (KCI) journals since 2007 and is indexed in Emerging Sources Citation Index (ESCI) since 2017.
Readers interested in the following articles may download each of articles free of charge from our website and authors are encouraged to submit a paper via the online submission site.
Jae-Hun Jung, Editor-in-Chief
Minseok Choi, Gunjin Yun, Managing Editors
ANALYTICAL AND NUMERICAL SOLUTIONS OF A CLASS OF GENERALISED LANE-EMDEN EQUATIONSRICHARD OLU AWONUSIKA AND PETER OLUWAFEMI OLATUNJI
The classical equation of Jonathan Homer Lane and Robert Emden, a nonlinear second-order ordinary differential equation, models the isothermal spherical clouded gases under the influence of the mutual attractive interaction between the gases’ molecules. In this paper, the Adomian decomposition method (ADM) is presented to obtain highly accurate and reliable analytical solutions of a class of generalised Lane-Emden equations with strong nonlinearities. The nonlinear term f(y(x)) of the proposed problem is given by the integer powers of a continuous real-valued function h(y(x)), that is, f(y(x)) = hm(y(x)), for integer m ≥ 0, real x > 0. In the end, numerical comparisons are presented between the analytical results obtained using the ADM and numerical solutions using the eighth-order nested second derivative two-step Runge-Kutta method (NSDTSRKM) to illustrate the reliability, accuracy, effectiveness and convenience of the proposed methods. The special cases h(y) = sin y(x), cos y(x); h(y) = sinh y(x), cosh y(x) are considered explicitly using both methods. Interestingly, in each of these methods, a unified result is presented for an integer power of any continuous real-valued function - compared with the case by case computations for the nonlinear functions f(y). The results presented in this paper are a generalisation of several published results. Several examples are given to illustrate the proposed methods. Tables of expansion coefficients of the series solutions of some special Lane-Emden type equations are presented. Comparisons of the two results indicate that both methods are reliably and accurately efficient in solving a class of singular strongly nonlinear ordinary differential equations.
LARGE TIME BEHAVIOR TO THE 2D MICROPOLAR BOUSSINESQ FLUIDS
UEWEN WANG, KEKE LEI, AND PIGONG HAN
In this paper, we prove the global existence of classical solutions to the 2D incompressible Boussinesq equations for the micropolar fluid. Furthermore, applying the Fourier splitting methods, we obtain the lager time decay properties.
HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR ELLIPTIC EQUATIONS WITH NONLINEAR COEFFICIENTS
In this paper, we analyze the hybridizable discontinuous Galerkin (HDG) method for second-order elliptic equations with nonlinear coefficients, which are used in many fields. We present the HDG method that uses a mixed formulation based on numerical trace and flux. Under assumptions on the nonlinear coefficient and H2-regularity for a dual problem, we prove that the discrete systems are well-posed and the numerical solutions have the optimal order of convergence as a mesh parameter. Also, we provide a matrix formulation that can be calculated using an iterative technique for numerical experiments. Finally, we present representative numerical examples in 2D to verify the validity of the proof of Theorem 3.10.
DEFECT INSPECTION IN SEMICONDUCTOR IMAGES USING HISTOGRAM FITTING AND NEURAL NETWORKS
JINKYU YU, SONGHEE HAN, AND CHANG-OCK LEE
This paper presents an automatic inspection of defects in semiconductor images. We devise a statistical method to find defects on homogeneous background from the observation that it has a log-normal distribution. If computer aided design (CAD) data is available, we use it to construct a signed distance function (SDF) and change the pixel values so that the average of pixel values along the level curve of the SDF is zero, so that the image has a homogeneous background. In the absence of CAD data, we devise a hybrid method consisting of a model-based algorithm and two neural networks. The model-based algorithm uses the first right singular vector to determine whether the image has a linear or complex structure. For an image with a linear structure, we remove the structure using the rank 1 approximation so that it has a homogeneous background. An image with a complex structure is inspected by two neural networks. We provide results of numerical experiments for the proposed methods.
IMPROVING GLOBAL SUPPLY CHAIN RISK IDENTIFICATION USING RCF
MYUNGHYUN JUNG, SEYEON LEE, MINJUNG GIM, HYUNGJO KIM, AND JAEHO LEE
This paper contains an introduction to industrial problems, solutions, and results conducted with the Korea Association of Machinery Industry. The client company commissioned the problem of upgrading the method of identifying global supply risky items. Accordingly, the factors affecting the supply and demand of imported items in the global supply chain were identified and the method of selecting risky items was studied and delivered. Through research and discussions with the client companies, it is confirmed that the most suitable factors for identifying global supply risky items are ’import size’, ’import dependence’, and ’trend abnormality’. The meaning of each indicator is introduced, and risky items are selected using export/import data until October 2022. Through this paper, it is expected that countries and companies will be able to identify global supply risky items in advance and prepare for risks in the new normal situation: the economic situation caused by infectious diseases such as the COVID-19 pandemic; and the export/import regulation due to geopolitical problems. The client company will include in his report, the method presented in this paper and the risky items selected by the method.
THE VALUATION OF TIMER POWER OPTIONS WITH STOCHASTIC VOLATILITY
MIJIN HA, DONGHYUN KIM, SERYOONG AHN, AND JI-HUN YOON
Timer options are one of the contingent claims that, for given the variance budget, its payoff depends on a random maturity in terms of the realized variance unlike the standard European vanilla option with a fixed time maturity. Since it was first launched by Société Générale Corporate and Investment Banking in 2007, the valuation of the timer options under several stochastic environment for the volatility has been conducted by many researches. In this study, we propose the pricing of timer power options combined with standard timer options and the index of the power to the underlying asset for the investors to actualize lower risks and higher returns at the same time under the uncertain markets. By using the asymptotic analysis, we obtain the first-order approximation of timer power options. Moreover, we demonstrate that our solution has been derived accurately by comparing it with the solution from the Monte-Carlo method. Finally, we analyze the impact of the stochastic volatility with regards to various parameters on the timer power options numerically.
ANOMALY DETECTION FOR AN ORAL HEALTH CARE APPLICATION USING ONE CLASS YOLOV3
JAEHUN BAEK, SEUNGWON KIM, AND DONGWOOK SHIN
In this report, we apply an anomaly detection algorithm to a mobile oral health care application. In particular, we have investigated one class YOLOv3 as an anomaly detection model to classify pictures of mouths which will be used as inputs in the following machine learning model. We have achieved outstanding performances by proposing appropriate annotation strategies for our data sets and modifying the loss function. Moreover, the model can classify not only oral and non-oral pictures but also output preprocessed pictures that only contain the area around the lips by using the predicted bounding box. Thus, the model performs prediction and preprocessing simultaneously.
SMOOTHERS BASED ON NONOVERLAPPING DOMAIN DECOMPOSITION METHODS FOR H(curl) PROBLEMS: A NUMERICAL STUDY
This paper presents a numerical study on multigrid algorithms of V –cycle type for problems posed in the Hilbert space H(curl) in three dimensions. The multigrid methods are designed for discrete problems originated from the discretization using the hexahedral Nédélec edge element of the lowest-order. Our suggested methods are associated with smoothers constructed by substructuring based on domain decomposition methods of nonoverlapping type. Numerical experiments to demonstrate the robustness and the effectiveness of the suggested algorithms are also provided.
DIRECT COMPARISON STUDY OF THE CAHN–HILLIARD EQUATION WITH REAL EXPERIMENTAL DATA
DARAE JEONG, SEOKJUN HAM, AND JUNSEOK KIM
In this paper, we perform a direct comparison study of real experimental data for domain rearrangement and the Cahn–Hilliard (CH) equation on the dynamics of morphological evolution. To validate a mathematical model for physical phenomena, we take initial conditions from experimental images by using an image segmentation technique. The image segmentation algorithm is based on the Mumford–Shah functional and the Allen–Cahn (AC) equation. The segmented phase-field profile is similar to the solution of the CH equation, that is, it has hyperbolic tangent profile across interfacial transition region. We use unconditionally stable schemes to solve the governing equations. As a test problem, we take domain rearrangement of lipid bilayers. Numerical results demonstrate that comparison of the evolutions with experimental data is a good benchmark test for validating a mathematical model.
MOBILE APP FOR COMPUTING OPTION PRICE OF THE FOUR-UNDERLYING ASSET STEP-DOWN ELS
JUNSEOK KIM, DAEUN JEONG, HANBYEOL JANG AND HYUNDONG KIM
We present the user-friendly graphical user interface design and implementation of Monte Carlo simulation (MCS) for computing option price of the four-underlying asset stepdown equity linked securities (ELS) using the Android platform. The ELS has been one of the most important and influential financial products in South Korea. Most ELS products are based on one-, two-, and three-underlying assets. However, currently there is a demand for higher coupon payment from ELS products because of the increased interest rate in financial market. In order to allow the investors to have higher coupon payment, it is necessary to design a multiasset ELS such as four-asset step-down ELS. We conduct the computational experiments to demonstrate the performance of the Android platform for pricing four-asset step-down ELS. Furthermore, we perform a comparison test with a three-asset step-down ELS.
A WEIGHTED EULER METHOD FOR SOLVING STIFF INITIAL VALUE PROBLEMS
BEONG IN YUN
For an initial value problem, using a weighted average between two adjacent approximates, we propose a simple one-step method based on the Euler method. This method is useful for solving stiff initial value problem, even when the step size is not very small. Moreover, it can be seen that the proposed method with some selected weights results in improved approximation errors.