• Journal of the Korean Mathematical Society
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• 제50권4호
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• pp.715-725
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• 2013

In this paper, a finite difference scheme for a two-point boundary value problem of 2nth-order ordinary differential equations is presented. The convergence and uniqueness of the solution for the scheme are proved by means of theories on matrix eigenvalues and norm. Numerical examples show that our method is very simple and effective, and that this method can be used effectively for other types of boundary value problems.

• Journal of the Korean Mathematical Society
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• 제40권2호
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• pp.195-205
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• 2003

In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with setvalued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized setvalued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma ［16］, ［17］ as special cases.

• Journal of Biosystems Engineering
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• 제22권2호
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• pp.163-176
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• 1997

Sesame was one of the economical crops in Korea. However, cultivation area of sesame has been decreasing rapidly due to the lack of mechanization for this crop and the opening of agricultural product market. Sesame seed is so small that ordinary seeder can not seed properly. In rural practice, farmers seed sesame with hand and do thinning after shoot emerges. Seeding and thinning in sesame cultivation take more than 40% of total labor To reduce labor in seeding and thinning, a pellet seed machine for sesame has been developed. The pellet seed machine is very simple in structure. It utilizes the chemical reaction between alginate solution and $CaCl_2$. Two material forms a membrane when they meet The uniqueness of the pellet seed machine for sesame were 1) a counter rotating roller for metering the mixture of activated carbon and alginate and 2) swinging plate for submerging seed into the mixture. The prototype machine can produce 30, 000 pellets per hour and costs ￦6, 891 per 1 km sesame.

• Journal of the Chungcheong Mathematical Society
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• 제31권1호
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• pp.13-27
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• 2018

By using of the Banach fixed point theorem, the theory of a strongly continuous semigroup of operators and resolvent operator, we investigate the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some differential (integrodifferential) equations with piecewise constant argument when specially ${\omega}$ is an integer.

• The Pure and Applied Mathematics
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• 제26권3호
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• pp.111-131
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• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• Information and Communications Magazine
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• 제32권6호
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• pp.39-49
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• 2015

In cryptographic applications, the key protection is either knowledge-based (passwords) or possession-based (tamper-proof device). Unfortunately, both approaches are easily forgotten or stolen, thus introducing various key management issues. By incorporating biometrics technologies which utilize the uniqueness of personal characteristics, the security of cryptosystems could be strengthened as authentication now requires the presence of the user. Biometric Cryptosystem (BC) encompasses the design of cryptographic keys protection methods by incorporating biometrics. BC involves either key-biometrics binding or direct key generation from biometrics. However, the wide acceptance and deployment of BC solutions are constrained by the fuzziness related with biometric data. Hence, error correction codes (ECCs) should be adopted to ensure that fuzziness of biometric data can be alleviated. In this overview paper, we present such ECC solutions used in various BCs. We also delineate on the important facts to be considered when choosing appropriate ECCs for a particular biometric based solution from accuracy performance and security perspectives.

• Journal of Integrative Natural Science
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• 제14권4호
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• pp.197-204
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• 2021

Under the two-phase warranty, the warranty period is divided into two intervals, one of which is for renewing replacement warranty, and the other is for minimal repair warranty. Jung^[13] discusses the two types of extended two-phase warranty models. In this paper, we suggest the replacement model after the extended two-phase warranty that has been proposed by Jung^[13]. To determine the optimal replacement policy, we adopt the expected cost rate per unit time. So, the expressions for the total expected cost, the expected length of the cycle and the expected cost rate per unit time from the user's point of view are derived. Also, we discuss the optimal replacement policy and the uniqueness of the solution for the optimization. Furthermore, the numerical examples are provided to illustrate the proposed the replacement model.

• Bulletin of the Korean Mathematical Society
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• 제39권4호
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• pp.589-606
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• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권1호
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• pp.33-58
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• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.989-1004
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• 2023

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.