• Kyungpook Mathematical Journal
• /
• v.61 no.4
• /
• pp.859-888
• /
• 2021

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annulus associated with Robin-Dirichlet conditions. At first, by applying the Faedo-Galerkin method, we prove existence and uniqueness results. Then, by constructing a Lyapunov functional, we prove a blow up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.

• Korean Journal of Mathematics
• /
• v.30 no.4
• /
• pp.603-614
• /
• 2022

The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in b-metric-like spaces, which remains an extended version of corresponding results in b-metric spaces and metriclike spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in b-metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in b-metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.

• Journal of applied mathematics & informatics
• /
• v.41 no.3
• /
• pp.487-510
• /
• 2023

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.

• Kyungpook Mathematical Journal
• /
• v.63 no.3
• /
• pp.437-450
• /
• 2023

In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a 𝓩^*_λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.28 no.1
• /
• pp.33-58
• /
• 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.

• Journal of the Korean School Mathematics Society
• /
• v.14 no.1
• /
• pp.101-122
• /
• 2011

In this paper, we investigated teachers' awareness for the gifted education using technology. We chose teachers who were taking a course(60 hours) in the gifted education at Educational Training Institute in Chonnam National University, and analyzed their awareness for gifted education using technology. We found teachers' awareness as followings. First, teachers think that their ability using technology is contained ability developing and performing program for the gifted education. Second, using technology in the gifted education have an effect on ability of inventively solving problem and extension of thinking power of the gifted. Third, the gifted education using technology is helpful to developing abilities of the gifted, which are intuitional discernment, organizing information, space perception and visualization. Also, that is helpful to developing fluency, flexibility and uniqueness of the gifted in terms of sub-factors of creativity (fluency, flexibility, uniqueness, sophistication).

• Communications of Mathematical Education
• /
• v.33 no.3
• /
• pp.255-273
• /
• 2019

In order to help students to understand the essence of prime concepts, this study looked at the history of prime concept development and analyzed how to introduce the concept of textbooks. In ancient Greece, primes were multiplicative atoms. At that time, the unit was not a number, but the development of decimal representations led to the integration of the unit into the number, which raised the issue of primality of 1. Based on the uniqueness of factorization into prime factor, 1 was excluded from the prime, and after that, the concept of prime of the atomic context and the irreducible concept of the divisor context are established. The history of the development of prime concepts clearly reveals that the fact that prime is the multiplicative atom is the essence of the concept. As a result of analyzing the textbooks, the textbook has problems of not introducing the concept essence by introducing the concept of prime into a shaped perspectives or using game, and the problem that the transition to analytic concept definition is radical after the introduction of the concept. Based on the results of the analysis, we have provided several pedagogical implications for helping to focus on a conceptual aspect of prime number.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.46 no.3
• /
• pp.60-67
• /
• 2009

The phase retrieval problem is a problem of reconstructing a signal or the phase of Fourier transform of the signal from the magnitude of its Fourier transform. In this paper we address the problem of reconstructing an unknown signal from the magnitude of its Fourier transform and the magnitude of Fourier transform of another signal that is given by the addition of the desired signal. After we briefly mention the uniqueness conditions under which a signal can be uniquely specified from the given information and key equations of the iterative algorithm, we present mathematical background that the iterative algorithm converges to the desired signal, present an example that illustrates the performance of the reconstruction algorithm, and show its convergence property.

• Journal of Biosystems Engineering
• /
• v.38 no.2
• /
• pp.129-137
• /
• 2013

Purpose: Modeling has been used for elucidating the mechanism of complex biosystems. In spite of importance and uniqueness of adolescent calcium (Ca) metabolism characterized by a threshold Ca intake, its regulatory mechanism has not been covered and even not proposed. Hence, this study aims at model-based proposing potential mechanisms regulating adolescent Ca metabolism. Methods: Two different hypothetic mechanisms were proposed. The main mechanism is conceived based on Ca-protein binding which induces renal Ca filtration, while additional mechanism assumed that active renal Ca re-absorption regulated Ca metabolism in adolescents. Mathematical models were developed to represent the proposed mechanism and simulated them whether they could produce adolescent Ca profiles in serum and urine. Results: Simulation showed that both mechanisms resulted in the unique behavior of Ca metabolism in adolescents. Based on the simulation insulin-like growth factor-1 (IGF-1) is suggested as a potential regulator because it is related to both growth, a remarkable characteristic of adolescence, and Ca metabolism including absorption and bone accretion. Then, descriptive modeling is employed to conceptualize the hypothesized mechanisms governing adolescent Ca metabolism. Conclusions: This study demonstrated that modeling is a powerful tool for elucidating an unknown mechanism by simulating potential regulatory mechanisms in adolescent Ca metabolism. It is expected that various analytic applications would be plausible in the study of biosystems, particularly with combination of experimental and modeling approaches.

• Journal of Communications and Networks
• /
• v.18 no.4
• /
• pp.589-599
• /
• 2016

Most existing resource management problem models arise from the original desire of allocating resources in either a user-centric or network-centric manner. The difference between their objectives is obvious: user-centric methods attempt to optimize the utility of individual users, whereas network-centric models intend to optimize the collective utilities of the entire network. In this paper, from the above two aspects, we analyze the robust power control problem in device-to-device (D2D) communication underlaying cellular networks, where two types of channel uncertainty set (e.g., ellipsoidal and column-wise) are considered. In the user-centric method, we formulate the problem into the form of a Stackelberg game, where the energy efficiency (EE) of each user is the ingredient of utility function. In order to protect the cellular user equipment's (CUE) uplink transmission, we introduce a price based cost function into the objectives of D2D user equipment (DUE). The existence and uniqueness of the game with the influence of channel uncertainty and price are discussed. In the network-centric method, we aim to maximize the collective EE of CUEs and DUEs. We show that by the appropriate mathematical transformation, the network-centric D2D power control problem has the identical local solution to that of a special case of the user-centric problem, where price plays a key role. Numerical results show the performance of the robust power control algorithms in the user-centric and network-centric models.