• 대한수학회논문집
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• 제22권2호
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• pp.247-258
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• 2007

In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed co coercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.

• Management Science and Financial Engineering
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• 제16권1호
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• pp.59-79
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• 2010

This paper considers bandwidth allocation and scheduling problems on Ethernet Passive Optical Networks (EPON). EPON is one of the good candidates for the optical access network. This paper formulates the bandwidth allocation problem as a nonlinear mathematical one and characterizes the optimal bandwidth allocation which maximizes weighted sum of throughput and fairness. Based upon the characterization, two heuristic algorithms are suggested with various numerical tests. The test results show that our algorithms can be used for efficient bandwidth allocation on the EPON. This paper also shows that the WSPT (Weighted Shortest Processing Time) rule is optimal for minimization the total delay time in transmitting the traffic of the given allocated bandwidth.

• 대한수학회지
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• 제58권3호
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• pp.525-552
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• 2021

In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권1호
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• pp.23-37
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• 2020

The quadratic error metric (QEM) algorithm has been frequently used for simplification of triangular surface models that utilize the vertex-pair algorithm. Simplified models obtained using such algorithms present the advantage of smaller storage capacity requirement compared to the original models. However, a number of cases exist where significant features are lost geometrically, and these features can generally be preserved by utilizing the advantages of the curvature-weighted algorithm. Based on the vertex-based geometric features, a method capable of preserving the geometric features better than the previous algorithms is proposed in this work. To validate the effectiveness of the proposed method, a simplification experiment is conducted using several models. The results of the experiment indicate that the geometrically important features are preserved well when a local feature is present and that the error is similar to those of the previous algorithms when no local features are present.

• 설비공학논문집
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• 제22권2호
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• pp.70-77
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• 2010

In order to improve the efficiency of a main transformer in a train, the optimal operation of a cooling system is necessary. For the development of optimal control algorithms of a cooling system, mathematical models of a main transformer cooling system were developed. These include static and dynamic models of a main transformer, an oil pump, an oil cooler, and a blower. Static models were used to find optimal oil temperatures of the inlet and the outlet of a transformer. Dynamic models were used to predict transient performances of control algorithms of a blower and an oil pump. Simulation results showed good predictions of the static and the dynamic behavior of a main transformer cooling system. Therefore, mathematical models developed in this study may be effectively used for the development of control algorithms of a main transformer cooling system.

• Tuberculosis and Respiratory Diseases
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• 제86권4호
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• pp.251-263
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• 2023

The stethoscope has long been used for the examination of patients, but the importance of auscultation has declined due to its several limitations and the development of other diagnostic tools. However, auscultation is still recognized as a primary diagnostic device because it is non-invasive and provides valuable information in real-time. To supplement the limitations of existing stethoscopes, digital stethoscopes with machine learning (ML) algorithms have been developed. Thus, now we can record and share respiratory sounds and artificial intelligence (AI)-assisted auscultation using ML algorithms distinguishes the type of sounds. Recently, the demands for remote care and non-face-to-face treatment diseases requiring isolation such as coronavirus disease 2019 (COVID-19) infection increased. To address these problems, wireless and wearable stethoscopes are being developed with the advances in battery technology and integrated sensors. This review provides the history of the stethoscope and classification of respiratory sounds, describes ML algorithms, and introduces new auscultation methods based on AI-assisted analysis and wireless or wearable stethoscopes.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제2권1호
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• pp.5-12
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• 1998

The COM curriculum provides first a core of mathematics for all students, and then offers opportunities for students to enter different streams of mathematics studies. The flexible curriculum (COM) is certainly welcome as it focuses on a transition from concrete to conceptual mathematics and on sequentially learning the power of mathematical language and symbols from simple to complex. This approach emphasizes the use of computers in mathematics education in the upper secondary grades. In Mathematics A, one unit is developed to computer operation, flow charts and programming, and computation using the computer. In mathematics B, a chapter addresses algorithms and the computer where students learn the functions of computers, as well as programs of various algorithms. Mathematics C allots a chapter for numerical computation in which approximating solutions for equations, numerical integration, mensuration by parts, and approximation of integrals. But, unfortunately, they do not have any plan for the cooperation study.

• Journal of Information Processing Systems
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• 제17권1호
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• pp.1-13
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• 2021

In this research, we study the problem of font image skeletonization using an end-to-end deep adversarial network, in contrast with the state-of-the-art methods that use mathematical algorithms. Several studies have been concerned with skeletonization, but a few have utilized deep learning. Further, no study has considered generative models based on deep neural networks for font character skeletonization, which are more delicate than natural objects. In this work, we take a step closer to producing realistic synthesized skeletons of font characters. We consider using an end-to-end deep adversarial network, SkelGAN, for font-image skeletonization, in contrast with the state-of-the-art methods that use mathematical algorithms. The proposed skeleton generator is proved superior to all well-known mathematical skeletonization methods in terms of character structure, including delicate strokes, serifs, and even special styles. Experimental results also demonstrate the dominance of our method against the state-of-the-art supervised image-to-image translation method in font character skeletonization task.

• Korean Journal of Mathematics
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• 제14권1호
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• pp.125-136
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• 2006

Using the Bumping algorithm for the shifted rim hook tableaux described in [5], we construct Schensted insertion and deletion algorithms for shifted rim hook tableaux. This may give us the combinatorial proof for the orthogonality of the second kind of the spin characters of $S_n$.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.1-12
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• 2009

Iterative algorithms are proposed for the least-squares symmetric solution of AXB = E with a submatrix constraint. We characterize the linear mappings from their independent element space to the constrained solution sets, study their properties and use these properties to propose two matrix iterative algorithms that can find the minimum and quasi-minimum norm solution based on the classical LSQR algorithm for solving the unconstrained LS problem. Numerical results are provided that show the efficiency of the proposed methods.