• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1365-1388
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• 2019

In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.8
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• pp.156-167
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• 1995

In this paper, we propose a 3-D range finding method for situation that stereo camera has small translational motion. Binocular stereo generally tends to produce stereo correspondence errors and needs huge amount of computation. The former drawback is because the additional constraints to regularize the correspondence problem are not always true for every scene. The latter drawback is because they use either correlation or optimization to find correct disparity. We present a method which overcomes these drawbacks by moving the stereo camera actively. The method utilized a motion parallax acquired by monocular motion stereo to restrict the search range of binocular disparity. Using only the uniqueness of disparity makes it possible to find reliable binocular disparity. Experimental results with real scene are presented to demonstrate the effectiveness of this method.

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

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.501-515
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• 2024

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.3
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• pp.60-67
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• 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 Communications and Networks
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• v.16 no.2
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• pp.121-129
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• 2014

The trend of an increasing demand for a high-quality user experience, coupled with a shortage of radio resources, has necessitated more advanced wireless techniques to cooperatively achieve the required quality-of-experience enhancement. In this study, we investigate the critical problem of rate splitting in heterogeneous cellular networks, where concurrent transmission, for instance, the coordinated multipoint transmission and reception of LTE-A systems, shows promise for improvement of network-wide capacity and the user experience. Unlike most current studies, which only deal with spectral efficiency enhancement, we implement an optimal rate splitting strategy to improve both spectral efficiency and energy efficiency by exploring and exploiting cooperation diversity. First, we introduce the motivation for our proposed algorithm, and then employ the typical cooperative bargaining game to formulate the problem. Next, we derive the best response function by analyzing the dual problem of the defined primal problem. The existence and uniqueness of the proposed cooperative bargaining equilibrium are proved, and more importantly, a distributed algorithm is designed to approach the optimal unique solution under mild conditions. Finally, numerical results show a performance improvement for our proposed distributed cooperative rate splitting algorithm.

• Research in Mathematical Education
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• v.7 no.3
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• pp.163-189
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• 2003

The purpose of this study is to develop a test, which can be used in creative problem solving ability in mathematics of the mathematically gifted and the regular students. This test tool is composed of three categories; fluency (number of responses), flexibility (number of different kinds of responses), and originality (degree of uniqueness of responses) which are the factors of the creativity. After applying to 462 middle school students, this test was analyzed into item analysis. As a results of item analysis, it turned out to be meaningful (reliability: 0.80, validity: item 1(1.05), item 2(1.10), item 3(0.85), item 4(0.90), item 5(1.08), item difficulty: item 1(-0.22), item 2(-0.41), item 3(0.23), item 4(0.40), item 5(-0.01), item discriminating power: item 1(0.73), item 2(0.73), item 3(0.67), item 4(0.51), item 5(0.56), over the level of a standard basis. This means that the test tool was useful in the test process of creative problem solving ability in mathematics

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

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

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