• 대한수학회보
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• 제34권4호
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• pp.603-615
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• 1997

In this paper, we introduce and study a new class of random completely generalized nonlinear variational inclusions with non-compact valued random mappings and construct some new iterative algorithms. We prove the existence of random solutions for this class of random variational inclusions and the convergence of random iterative sequences generated by the algorithms.

• 대한수학회지
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• 제57권3호
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• pp.617-640
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• 2020

In this paper, we introduce a parallel iterative method for finding a common fixed point of a finite family of Bregman strongly nonexpansive mappings in a real reflexive Banach space. Moreover, we give some applications of the main theorem for solving some related problems. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.

• East Asian mathematical journal
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• 제19권1호
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• pp.81-89
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• 2003

There are many algorithms for factoring integers. The trial division algorithm is one of the most efficient algorithms for factoring small integers(say less than 10,000,000,000). For a number n to be factored, the runtime of the trial division algorithm depends mainly on the size of a nontrivial factor of n. In this paper, we create a function named factors that can implement the trial division algorithm in ActionScript and using the factors function we construct an interactive Prime Factorization Movie and an interactive GCD Movie.

• East Asian mathematical journal
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• 제18권1호
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• pp.95-109
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• 2002

In this paper, we study a class of variational inequalities, which is called the generalized set-valued mixed variational inequality. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert spaces, we have established an existence theorem of solutions for generalized set-valued mixed variational inequalities, suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized set-valued mixed variational inequalities.

• 대한수학회논문집
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• 제31권4호
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• pp.879-893
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• 2016

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.161-197
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• 2020

Total variation minimization is standard in mathematical imaging and there have been numerous researches over the last decades. In order to process large-scale images in real-time, it is essential to design parallel algorithms that utilize distributed memory computers efficiently. The aim of this paper is to illustrate recent advances of domain decomposition methods for total variation minimization as parallel algorithms. Domain decomposition methods are suitable for parallel computation since they solve a large-scale problem by dividing it into smaller problems and treating them in parallel, and they already have been widely used in structural mechanics. Differently from problems arising in structural mechanics, energy functionals of total variation minimization problems are in general nonlinear, nonsmooth, and nonseparable. Hence, designing efficient domain decomposition methods for total variation minimization is a quite challenging issue. We describe various existing approaches on domain decomposition methods for total variation minimization in a unified view. We address how the direction of research on the subject has changed over the past few years, and suggest several interesting topics for further research.

• 대한수학회논문집
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• 제4권1호
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• pp.5-15
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• 1989

• 대한수학회논문집
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• 제10권2호
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• pp.301-304
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• 1995

Our main purpose in this paper is to discuss a new result on convergence of nonlinear contractive algorithms acting on different Banach spaces.

• International Journal of Computer Science & Network Security
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• 제23권1호
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• pp.46-52
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• 2023

With billions of IoT (Internet of Things) devices populating various emerging applications across the world, detecting anomalies on these devices has become incredibly important. Advanced Intrusion Detection Systems (IDS) are trained to detect abnormal network traffic, and Machine Learning (ML) algorithms are used to create detection models. In this paper, the NSL-KDD dataset was adopted to comparatively study the performance and efficiency of IoT anomaly detection models. The dataset was developed for various research purposes and is especially useful for anomaly detection. This data was used with typical machine learning algorithms including eXtreme Gradient Boosting (XGBoost), Support Vector Machines (SVM), and Deep Convolutional Neural Networks (DCNN) to identify and classify any anomalies present within the IoT applications. Our research results show that the XGBoost algorithm outperformed both the SVM and DCNN algorithms achieving the highest accuracy. In our research, each algorithm was assessed based on accuracy, precision, recall, and F1 score. Furthermore, we obtained interesting results on the execution time taken for each algorithm when running the anomaly detection. Precisely, the XGBoost algorithm was 425.53% faster when compared to the SVM algorithm and 2,075.49% faster than the DCNN algorithm. According to our experimental testing, XGBoost is the most accurate and efficient method.

• 대한수학회보
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• 제40권3호
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• pp.385-397
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• 2003

In this paper, we introduce and study a system of nonlinear implicit variational inclusions (SNIVI) in real Banach spaces: determine elements $x^{*},\;y^{*},\;z^{*}\;\in\;E$ such that ${\theta}\;{\in}\;{\alpha}T(y^{*})\;+\;g(x^{*})\;-\;g(y^{*})\;+\;A(g(x^{*}))\;\;\;for\;{\alpha}\;>\;0,\;{\theta}\;{\in}\;{\beta}T(z^{*})\;+\;g(y^{*})\;-\;g(z^{*})\;+\;A(g(y^{*}))\;\;\;for\;{\beta}\;>\;0,\;{\theta}\;{\in}\;{\gamma}T(x^{*})\;+\;g(z^{*})\;-\;g(x^{*})\;+\;A(g(z^{*}))\;\;\;for\;{\gamma}\;>\;0,$ where T, g : $E\;{\rightarrow}\;E,\;{\theta}$ is zero element in Banach space E, and A : $E\;{\rightarrow}\;{2^E}$ be m-accretive mapping. By using resolvent operator technique for n-secretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this system of nonlinear implicit variational inclusions. The convergence of iterative algorithms be proved in q-uniformly smooth Banach spaces and in real Banach spaces, respectively.